Bibliography

A. Aaboe, Episodes from the Early History of Mathematics (Random House, New York, 1964) A.D. Aczel, Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem (Four Walls Eight Windows, New York, 1996) D. Adamson, Blaise Pascal: Mathematician, Physicist, and Thinker About God (St. Martin’s Press, New York, 1995) R.P. Agarwal, H. Agarwal, S.K. Sen, Birth, Growth and Computation of Pi to ten trillion digits. Adv. Differ. Equat. 2013, 100 (2013) A.A. Al-Daffa’, The Muslim Contribution to Mathematics (Humanities Press, Atlantic Highlands, 1977) A.A. Al-Daffa’, J.J. Stroyls, Studies in the Exact Sciences in Medieval Islam (Wiley, New York, 1984) E.J. Aiton, Leibniz: A Biography (A. Hilger, Bristol, Boston, 1984) R.E. Allen, Greek Philosophy: Thales to Aristotle (The Free Press, New York, 1966) G.J. Allman, Greek Geometry from Thales to Euclid (Arno Press, New York, 1976) E.N. da C. Andrade, Sir Issac Newton, His Life and Work (Doubleday & Co., New York, 1954) W.S. Anglin, Mathematics: A Concise History and Philosophy (Springer, New York, 1994) W.S. Anglin, The Queen of Mathematics (Kluwer, Dordrecht, 1995) H.D. Anthony, Sir Isaac Newton (Abelard-Schuman, New York, 1960) H.G. Apostle, Aristotle’s Philosophy of Mathematics (The University of Chicago Press, Chicago, 1952) R.C. Archibald, Outline of the history of mathematics.Am. Math. Monthly 56 (1949) B. Artmann, Euclid: The Creation of Mathematics (Springer, New York, 1999) C.N. Srinivasa Ayyangar, The History of Ancient Indian Mathematics (World Press Private Ltd., Calcutta, 1967) A.K. Bag, Mathematics in Ancient and Medieval India (Chaukhambha Orientalia, Varanasi, 1979) W.W.R. Ball, A Short Account of the History of Mathematics (Dover, New York, 1960) S.F. Barker, Philosophy of Mathematics (Prentice-Hall, Englewood Cliffs, 1964) M.E. Baron, The Origin of Infinitesimal Calculus (Dover, New York, 1993) J.D. Barrow, Pi in the Sky: Counting, Thinking, and Being (The Clarendon Press, New York, 1992) C. Baumgardt, Johannes Kepler: Life and Letters (Victor Gollancz, London, 1952) P. Beckman, A History of  (St. Martin’s Griffin, New York, 1976) A. Beiler, Recreations in the Theory of Numbers (Dover, New York, 1964) B. Belhoste, Augustin–Louis Cauchy: A Biography, Translated by F. Ragland (Springer, New York, 1990) E.T. Bell, Men of Mathematics (Touchstone Books, New York, 1986)

© Springer International Publishing Switzerland 2014 453 R.P. Agarwal, S.K. Sen, Creators of Mathematical and Computational Sciences, DOI 10.1007/978-3-319-10870-4 454 Bibliography

E.T. Bell, The Development of Mathematics, 2nd edn. (Dover, New York, 1992) D.C. Benson, The Moment of Proof: Mathematical Epiphanies (Oxford University Press, New York, 1999) J.L. Berggren, Episodes in the Mathematics of Medieval Islam (Springer, New York, 1986) D. Berlinski, A Tour of Calculus (Vintage, New York, 1995) B.E. Berndt, Notebooks of S. Ramanujan (Springer, New York, 1985) B.C. Berndt, R.A. Rankin, Ramanujan Letters and Commentary (Affiliated East West Press, New Delhi, 1997) E.W. Beth, The Foundations of Mathematics (North-Holland, Amsterdam, 1959) E.W. Beth, Mathematical Thought: An Introduction to the Philosophy of Mathematics (D. Reidel, Dordrecht, 1965) T.G. Bhaskar, D. Kovach, V. Lakshmikantham, The hybrid set theory. Nonlinear Anal. Hybrid Syst. 1, 414–416 (2007) M.G. Bishop, Pascal, the Life of Genius (Reynal & Hitchcock, New York, 1936) M. Black, The Nature of Mathematics: A Critical Survey (Routledge & Kegan Paul, London, 1965) D. Blatner, The Joy of Pi (Walker Publishing Co., New York, 1997) D.M. Bose, S.N. Sen, B.V. Subbarayappa, A Concise History of Science in India (Indian National Science Academy, New Delhi, 1971) C. Boyer, The History of the Calculus and Its Conceptual Development (Dover, New York, 1959) C. Boyer, A History of Mathematics, 2nd edn. (Wiley, New York, 1991) J.W. Brewer, M. Smith, Emmy Noether, a Tribute to Her Life and Work (Marcel Dekker Inc., New York, 1981) D.E. Brody, A.R. Brody, The Science Class You Wish You Had: The Seven Greatest Scientific Dis- coveries in History and the People Who Made Them (Berkeley Publishing Group, New York, 1997) R.S. Brumbaugh, Plato’s Mathematical Imagination (Indiana University Press, Bloomington, 1954) L.N.H. Bunt, P.S. Jones, J.D. Bedient, The Historical Roots of Elementary Mathematics (Prentice- Hall, Englewood Cliffs, 1976) D.M. Burton, The History of Mathematics: An Introduction, 4th edn. (McGraw-Hill, New York, 1999) F. Cajori, The history of the notations of calculus. Ann. Math. 25, 1–46 (1923) F. Cajori, Leibniz, the master builder of notations. Isis 7, 412–429 (1925) F. Cajori, A History of Mathematics, 4th edn. (Chelsea Publishing, New York, 1985) R. Calinger, Gottfried Wilhelm Leibniz (Rensselaer Polytechnic Institute, Troy, 1976) R. Calinger (ed.), Classics of Mathematics (Prentice-Hall, Englewood Cliffs, 1995) R. Calinger, A Contextual History of Mathematics: To Euler (Prentice Hall, Upper Saddle River, 1999) G. Cantor, Contributions to the Founding of the Theory of Transfinite Numbers, Translated by P.E.B. Jourdain (Dover, New York, 1952) M. Cantor, Vorlesungen über Geschichte der Mathematik (Teubner, Leipzig, 1907) G. Cardano, The Book of My Life, Translated by J. Stoner (Dover, New York, 1962) G. Cardano, The Great Art, Translated by T.R. Witmer (MIT Press, Cambridge, 1968) S. Chandrasekhar, Newton’s Principia for the Common Reader (Oxford University Press, Oxford, 1995) M. Ranga Charya (ed.), Mahavira (author), Ganita Sara Sangraha (Madras Government Publica- tions, Madras, 1912) D. Chattopadhyaya, History of Science and Technology in Ancient India: The Beginnings (Firma KLM PVT, Calcutta, 1986) M. Clagett, Greek Science in Antiquity (Collier, New York, 1963) W.E. Clark (ed.), The Aryabhatia of Aryabhata (The University of Chicago Press, Chicago, 1930) C.C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers (Plenum Press, New York, 2000) M.P. Closs (ed.), Native American Mathematics (University of Texas Press, Austin, 1986) Bibliography 455

I.B. Cohen, Sir Issac Newton’s Papers and Letters on Natural Philosophy (Harvard University Press, Cambridge, 1958) J.R. Cole, Pascal: The Man and His Two Loves (New York University Press, New York, 1995) L. Conant, The Number Concept. Its Origin and Development (Macmillan, New York, 1923) R. Cooke, The Mathematics of Sonya Kovalevskaya (Springer, New York, 1984) J.L. Coolidge, The Mathematics of Great Amateurs (Dover, New York, 1963) N. Copernicus, On the Revolutions of Heavenly Spheres. Great Mind Series (Prometheus Books, New York, 1995) R. Courant, H. Robbin, I. Stewart, What Is Mathematics? (Oxford University Press, New York, 1996) J.G. Crowther, Six Great Scientists (Barnes & Noble, USA, 1995) C. Cullen, Astronomy and Mathematics in Ancient China: The Zhou Bi Suanjing (Cambridge University Press, Cambridge, 1996) P. Damerow, Mathematics in Ancient Iraq: A Social History (Princeton University Press, Princeton, 2008) B. Datta, The Bakhshali manuscript. Bull. Calcutta Math. Soc. 21, 1–60 (1929) B. Datta, The Science of the Sulbas: A Study in Early Hindu Geometry (Calcutta University Press, Calcutta, 1932) B. Datta, A.N. Singh, History of Hindu Mathematics, vol. 2 (Asia Publishing House, Bombay, 1962) B. Datta, Ancient Hindu Geometry: The Science of the Sulba (South Asia Books, Bombay, 1993) J.W. Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite (Harvard University Press, Cambridge, 1979) J.W. Dauben (ed.), The History of Mathematics from Antiquity to the Present. A Selective Bibliography (Garland, New York, London, 1985) M. Davis, The Universal Computer: The Road from Leibniz to Turing (W.W. Norton & Co., New York, 2000) P.J. Davis, R. Hersh, The Mathematical Experience (Birkhäuser, Boston, 1981) P. Dedron, J. Itard, Mathematics and Mathematicians, vol. 2 (The Open University Press, Milton Keynes, England, 1973) R. Descartes, The Geometry, Translated by D.E. Smith and M.L. Latham (Dover, New York, 1954) R. Descartes, Discourse on Method and the Meditations on First Philosophy, 4th edn. (Hackett Publishing Company, Indianapolis, 1998) A. Dick, Emmy Noether 1882–1935 (Birkhäuser, Basel, 1970) L.E. Dickson, History of the Theory of Numbers (Chelsea, New York, 1971) E.T. Drake, Restless Genius: Robert Hooke and His Earthly Thoughts (Oxford University Press, Oxford, 1996) J.L.E. Dreyer, A History of Astronomy from Thales to Kepler (Dover, New York, 1953) J.M. Dubbey, The Mathematical Work of Charles Babbage (Cambridge University Press, Cambridge, 1978) W. Dunham, Journey Through Genius: The Great Theorems of Mathematics (Penguin, New York, 1991) W. Dunham, The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities (Wiley, New York, 1994) W. Dunham, Euler: The Master of Us All (MAA, Washington, DC, 1999) G.W. Dunnington, Carl Friedrich Gauss, Titan of Science: A Study of His Life and Work (Hafner, New York, 1955) M. Dzielska, Hypatia of Alexandria, Revealing Antiquity (Harvard University Press, Cambridge, 1996) S. Edeen, J. Edeen, Women Mathematicians (Dale Seymour Publications, Parsippany, 1990) C.H. Edwards Jr., The Historical Development of the Calculus (Springer, New York, 1979) H.M. Edwards, Fermat’s Last Theorem. A Genetic Introduction to Algebraic Number Theory (Springer, New York, 1977) A. Einstein, Ideas and Opinions (Bonanza Books, New York, 1986) 456 Bibliography

A. Einstein, World As I See It (Citadel Press, New York, 1993) H.W. Eves, An Introduction to the History of Mathematics (Holt, Rinehart and Winston, New York, 1969) H.W. Eves, In Mathematical Circles: A Selection of Mathematical Stories and Anecdotes (Weber & Schmidt, Boston, 1969) H.W. Eves, In Mathematical Circles: A Second Collection of Mathematical Stories and Anecdotes (Weber & Schmidt, Boston, 1971) H.W. Eves, Great Moments in Mathematics: Before 1650 (The Mathematical Association of America, Washington, DC, 1981) H.H. Eves, Great Moments in Mathematics: After 1650 (The Mathematical Association of America, Washington, DC, 1982) H.W. Eves, Return to Mathematical Circles: A Fifth Collection of Mathematical Stories and Anecdotes (PWS-Kent Publishing, Boston, 1988) J.J. Fahie, Galileo, His Life and Work (John Murray, London, 1903) J. Fauvel, J.J. Gray, The History of Mathematics: A Reader (The Open University, London, 1987) L.P. Fibonacci, The Book of Squares, annotated and Translated by L.E. Sigler (Academic, Boston, 1987) J.V. Field, J.J. Gray, The Geometrical Work of Girard Desargues (Springer, New York, 1987) M. Fierz, Girolamo Cardano, 1501–1576 (Birkhäuser, Boston, 1983) D.H. Fowler, The Mathematics of Plato’s Academy: A New Reconstruction (Clarendon Press, Oxford, 1987) H.A. Freebury, A History of Mathematics (Macmillan, New York, 1961) W. Frucht, Imaginary Numbers (Wiley, New York, 2000) G. Galilei, Dialogue on the Great World Systems (The University of Chicago Press, Chicago, 1953) G. Galilei, Dialogues Concerning Two New Sciences. Great Mind Series (Prometheus Books, New York, 1995) M.J. Gazale, Number: From Ahmes to Cantor (Princeton University Press, Princeton, 2000) C. Gillespie, Pierre–Simon Laplace 1749–1827: A Life in Exact Science (Princeton University Press, Princeton, 1997) R.J. Gillings, Mathematics in the Time of the Pharaohs (Dover, New York, 1982) H.H. Goldstine, A History of Numerical Analysis from the 16th Through the 19th Century (Springer, New York, 1977) H.H. Goldstine, A History of the Calculus of Variations from the 17th Through the 19th Century (Springer, New York, 1977) J. Gow, A Short History of Greek Mathematics (Hafner, New York, 1923) R.P. Graves, Life of Sir William Rowan Hamilton, vol. 3 (Hodges, Figgis, Dublin, 1882) J.V. Grabiner, The Origins of Cauchy’s Rigorous Calculus (MIT Press, Cambridge, 1981) I. Grattan-Guinness, The Development of the Foundations of Mathematical Analysis from Euler to Riemann (MIT Press, Cambridge, 1971) I. Grattan-Guinness (ed.), From the Calculus to Set Theory, 1630–1910. An Introductory History (Duckworth, London, 1980) I. Grattan-Guinness, The Fontana History of the Mathematical Sciences (Fontana Press, Glasgow, 1997) R. Grimsley, Jean d’Alembert [1717–1783] (The Clarendon Press, Oxford, 1963) L.S. Gristien, P.J. Campbell, Women of Mathematics: A Biobibliographic Sourcebook (Greenwood Press, New York, 1987) M. Guillen, Five Equations that Changed the World (MJF Books, New York, 2000) J. Gullberg, P. Hilton, Mathematics: From the Birth of Numbers (W.W. Norton & Co., New York, 1997) R.C. Gupta, Madhava’s and other medieval Indian value of pi. Math. Educ. 9, B45–B48 (1975) J. Hadamard, An Essay on the Psychology of Invention in the Mathematical Field (Princeton University Press, Princeton, 1945) E. Hairer, G. Wanner, Analysis by Its History (Springer, New York, 1996) A.R. Hall, From Galileo to Newton 1630–1720 (Harper & Row, New York, 1963) Bibliography 457

A.R. Hall, Philosophers at War: The Quarrel Between Newton and Leibniz (Cambridge University Press, Cambridge, 1980) T. Hall, Gauss, a Biography (MIT Press, Cambridge, 1970) T.L. Hankins, Sir William Rowan Hamilton (Johns Hopkins University Press, Baltimore, 1980) G.H. Hardy, Mathematical proof. Mind 38, 1–25 (1928) G.H. Hardy, Ramanujan (Chelsea, New York, 1959) G.H. Hardy, A Mathematician’s Apology (Cambridge University Press, Cambridge, 1967) R. Harre (ed.), Early Seventeenth Century Scientists (Pergamon, Oxford, 1965) T.L. Heath, The Thirteen Books of Euclid’s Elements, vol. 3 (Dover, New York, 1956) T.L. Heath, The Works of Archimedes (Dover, New York, 1953) T.L. Heath, A Manual of Greek Mathematics (Dover, New York, 1963) T.L. Heath, A History of Greek Mathematics, vol. 2 (Dover, New York, 1981) J.L. Heilbron, Geometry Civilized: History, Culture and Technique (Clarendon Press, Oxford, 1998) R. Hersh, What Is Mathematics, Really? (Oxford University Press, New York, 1997) D. Hilbert, Foundations of Geometry, Translated by E.J. Townsend (Open Court, Chicago, 1902) P. Hoffman, Archimedes’ Revenge: The Joys and Perils of Mathematics (W.W. Norton, New York, London, 1988) A. Hooper, Makers of Mathematics (Random House, New York, 1948) D. Hutchings (ed.), Late Seventeenth Century Scientists (Pergamon, Oxford, 1969) G. Ifrah, From One to Zero: A Universal History of Numbers (Viking, New York, 1985) G. Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer (Wiley, New York, 1999) P. Jha, Aryabhata I and His Contributions to Mathematics (Bihar Research Society, Patna, 1988) G.G. Joseph, TheCrestofthePeacock(Princeton University Press, Princeton, 2000) V. Kagan, N. Lobachevski and His Contributions to Science (Foreign Languages Publishing House, Moscow, 1957) R. Kaplan, The Nothing that Is: A Natural History of Zero (Oxford Press, New York, 1999) L.C. Karpinski, The History of Arithmetic (Rand McNally, Chicago, 1925) D.S. Kasir (ed.), The Algebra of Omar Khayyam (AMS Press, New York, 1972) V.J. Katz, A History of Mathematics: An Introduction (Harper Collins, New York, 1993) V.J. Katz, Ideas of calculus in Islam and India. Math. Mag. 68, 163–174 (1995) G.R. Kaye, Indian Mathematics (Amd Simla, Calcutta, 1915) A. Keller, Expounding the Mathematical Seed. Vol. 2 (The Translation & the Supplements): A Translation of Bhaskara 1 on the Mathematical Chapter of the Aryabhatiya (Birkhäuser, Basel, 2006) B. Kemp, Ancient Egypt: Anatomy of a Civilization (Routledge, London, 1991) H. Kennedy, Peano: Life and Work of Giuseppe Peano (D. Reidel, Dordrecht, Holland, 1980) J. Kepler, Epitome of Copernican Astronomy & Harmonies of the World. Great Mind Series (Prometheus Books, New York, 1995) F. Klein, Development of Mathematics in the Nineteenth Century, Translated by M. Ackerman (Math Science Press, Brookline, 1979) M. Kline, Mathematics in Western Culture (Oxford University Press, New York, 1953) M. Kline, Mathematics: A Cultural Approach (Addison-Wesley, Reading, 1962) M. Kline, Mathematics, the Loss of Certainty (Oxford University Press, New York, 1980) M. Kline, Mathematics and the Physical World (Dover, New York, 1981) M. Kline, Mathematical Thought from Ancient to Modern Times, 2nd edn. (The Clarendon Press, New York, 1990) I.L. Kushyar, Principles of Hindu Reckoning (University of Wisconsin Press, Madison, 1966) D.F. Lach, Asia in the Making of Europe, vol. 2 (Chicago University Press, Chicago, 1965) V. Lakshmikantham, The Origin of Human Past (Children of Immortal Bliss) (Bharateeya Vidya Bhavan, Bombay, 1999) V. Lakshmikantham, S. Leela, J. Vasundhara Devi, The Origin and History of Mathematics (Cambridge Scientific Publishers, Cambridge, 2005) 458 Bibliography

V. Lakshmikantham, J. Vasundhara Devi, What India Should Know (Bharateeya Vidya Bhavan, Bombay, 2006) L.Y. Lam, A Critical Study of the Yang Hui Suan Fa, a 13th Century Mathematical Treatise (Singapore University Press, Singapore, 1977) L.Y. Lam, T.S. Ang, Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China (World Scientific, Singapore, 1992) J.P. LaSalle, L. Solomon (eds.), Recent Soviet Contributions to Mathematics (Macmillan, New York, 1962) Y. Li, S.R. Du, Chinese Mathematics: A Concise History, Translated from the Chinese and with a preface by J.N. Crossley and A.W.C. Lun (The Clarendon Press, New York, 1987) U. Libbrecht, Chinese Mathematics in the Thirteenth Century (MIT Press, Cambridge, 1973) A. Macfarlane, Lectures on Ten British Mathematicians of the Nineteenth Century (Wiley, New York, 1916) D. MacHale, George Boole. His Life and Work (Boole Press, Dublin, 1985) M.S. Mahoney, The Mathematical Career of Pierre de Fermat, 1601–1665 (Princeton University Press, Princeton, 1973) E. Maor, E: The Story of a Number (Princeton University Press, Princeton, 1998) J.C. Martzloff, The History of Chinese Mathematics, Translated by S. Wilson (Springer, New York, 1994) K.O. May, Bibliography and Research Manual of the History of Mathematics (University of Toronto Press, Toronto, 1973) E.A. Maziarz, T. Greenwood, Greek Mathematical Philosophy (Frederick Ungar, New York, 1968) J. McLeish, Number: The History of Numbers and How They Shape Our Lives (Fawcett Columbine, New York, 1991) K. Menninger, Number Words and Number Symbols: A Cultural History of Numbers (Dover, New York, 1992) J. Merz, Leibniz (Hacker Press, New York, 1948) H. Meschkowski, Ways of Thought of Great Mathematicians (Holden-Day, San Francisco, 1964) H.O. Midonick, The Treasury of Mathematics (Philosophical Library, New York, 1965) Y. Mikami, The Development of Mathematics in China and Japan (Chelsea, New York, 1913/1974) R.E. Moritz, On Mathematics and Mathematicians (Dover, New York, 1958) J. Muir, Of Men and Numbers: The Story of Great Mathematics (Dover, New York, 1996) T.S.B. Murthy, A Modern Introduction to Ancient Indian Mathematics (Wiley Eastern, New Delhi, 1992) P.J. Nahin, An Imaginary Tale (Princeton University Press, Princeton, 1998) S.H. Nasr, Science and Civilization in Islam (Harvard University Press, Cambridge, 1968) J. Needham, Science and Civilization in China (Cambridge University Press, Cambridge, 1959) R. Netz, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Ideas in Context, vol. 51 (Cambridge University Press, Cambridge, 1999) O. Neugebauer, The Exact Sciences in Antiquity, 2nd edn. (Dover, New York, 1969) O. Neugebauer, A History of Ancient Mathematical Astronomy, vol. 3 (Springer, New York, 1975) J.R. Newman (ed.), The World of Mathematics (Simon and Schuster, New York, 1956) O. Ore, Niels Henrik Abel (University of Minnesota Press, Minneapolis, 1957) O. Ore, Number Theory and Its History (Dover, New York, 1988) L.M. Osen, Women in Mathematics (MIT Press, Boston, 1974) M.D. Pandit, Mathematics as Known to the Vedic Samhitas (Sri Satguru Publications, New Delhi, 1993) T. Pappas, The Joy of Mathematics (Wide World Publishing/Tetra, San Carlos, 1989) T. Pappas, Mathematical Scandals (Wide World Publishing/Tetra, San Carlos, 1997) S. Paramesvaran, The Golden Age of Indian Mathematics (Swadeshi Science Movement, Kerala, 1998) D. Pedoe, Geometry and the Visual Arts (Dover, New York, 1976) T. Perl, Women and Numbers (Wide World Publishing/Tetra, San Carlos, 1993) J.-P. Pier, Developments in Mathematics 1900–1950 (Birkhäuser, Boston, 1994) Bibliography 459

D. Pingree, Census of the Exact Sciences in Sanskrit, vol. 4 (American Philosophical Society, Philadelphia, 1970–1981) K. Plofker, Mathematics in India (Princeton University Press, Princeton, 2008) G. Polya, How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, Princeton, 1945) G. Polya, Mathematical Discovery, vol. 2 (Wiley, New York, 1962/1965) G. Prasad, Mathematical Research in the Last Twenty Years (Walter de Gruyter, Berlin, 1923) G. Prasad, Some Great Mathematicians of the Nineteenth Century, Their Lives and Their Works, vol. 2 (Benares Mathematical Society, Benares, 1933–1934) C.T. Rajagopal, M.S. Rangachari, On medieval keralese mathematics. Arch. Hist. Exact Sci. 35, 91–99 (1986) S. Ranganathan, Ramanujan: The Man and the Mathematician (Asia Publishing House, Bombay, 1967) S.B. Rao, Indian Mathematics and Astronomy: Some Landmarks (Jnana Deep Publications, Bangalore, 1994) C. Reid, Hilbert (Springer, New York, 1970) C. Reid, Courant in Göttingen and New York: The Story of an Improbable Mathematician (Springer, New York, 1976) E. Rosen, Three Imperial Mathematicians (Abanis, New York, 1986) R. Rucker, Infinity and the Mind (Bantam Books, New York, 1983) B. Russell, The Autobiography of Bertrand Russell, vol. 2 (Little, Brown & Co., Boston, 1951) S. Saliba, A History of Arabic Astronomy (New York University Press, New York, 1994) T.A. Sarasvati, Geometry in Ancient and Medieval India (Motilal Banarsidass, Delhi, 1979) K.V. Sarma, A History of the Kerala School of Hindu Astronomy (Viveshvarand Institute Publica- tions, Hoshiarpur, 1972) G. Sarton, The Study of the History of Mathematics and the Study of the History of Science (Dover, New York, 1957) W.L. Schaaf, A Bibliography of Recreational Mathematics. A Guide to the Literature, 3rd edn. (National Council of Teachers of Mathematics, Washington, DC, 1970) J.F. Scott, The Scientific Work of René Descartes (Taylor & Francis, London, 1952) J.F. Scott, A History of Mathematics from Antiquity to the Beginning of the Nineteenth Century (Taylor & Francis, London, New York, 1969) J.F. Scott, The Mathematical Works of John Wallis, D.D., F.R.S. (1616–1703) (Chelsea, New York, 1981) A. Seidenberg, The origin of mathematics. Arch. Hist. Exact Sci. 18, 301–342 (1978) C. Seife, Zero: The Biography of a Dangerous Idea (Viking, New York, 2000) G.E. Sen, The Pageant of Indian History (David McKay Co., New York, 1948) S.K. Sen, R.P. Agarwal, ; e;  with MATLAB: Random and Rational Sequences with Scope in Supercomputing Era (Cambridge Scientific Publishers, Cambridge, 2011) S.N. Sen, A.K. Bag, The Sulbasutras (Indian National Science Academy, New Delhi, 1983) K. Shen, J.N. Crossley, A.W.C. Lun, The Nine Chapters on the Mathematical Art (Oxford University Press and Science Press, Beijing, 1999) K.S. Shukla, Aryabhatiya of Aryabhata with the Commentary of Bhaskara I and Somesvara (Indian National Science Academy, New Delhi, 1976) G.F. Simmons, Calculus Gems: Brief Lives and Memorable Mathematics (McGraw-Hill, New York, 1992) J. Singh, Great Ideas of Modern Mathematics: Their Nature and Use (Dover, New York, 1959) S. Singh, J. Lynch, Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem (Bantam Books, New York, 1998) D.E. Smith, L.C. Karpinski, The Hindu–Arabic Numerals (Ginn, Boston, 1911) D.E. Smith, Y. Mikami, A History of Japanese Mathematics (Open Court, Chicago, 1914) D.E. Smith, History of Mathematics, vol. 2 (Dover, New York, 1958) D.E. Smith, A Source Book in Mathematics (Dover, New York, 1959) 460 Bibliography

D.E. Smith, J. Ginsburg, A History of Mathematics in America Before 1900 (Arno, New York, 1980) D. Solow, How to Read and Do Proofs (Wiley, New York, 1990) D.A. Somayaji, A Critical Study of the Ancient Hindu Astronomy (Karnataka University, Dharwar, 1971) N. Spielberg, B. Anderson, Seven Ideas that Shook the Universe (Wiley, New York, 1987) L.A. Steen, On the Shoulders of Giants: New Approaches to Numerary (National Academy Press, Washington, DC, 1990) L.A. Steen (ed.), Mathematics Today (Springer, New York, 1978) S. Stein, Archimedes: What Did He Do Besides Cry Eureka? (MAA, Washington, DC, 1999) S. Stein, Mathematics: The Man Made Universe (Dover, New York, 2000) J. Stillwell, Mathematics and Its History (Springer, New York, 1989) D.J. Struik, A Sourcebook in Mathematics, 1200–1800 (Princeton University Press, Princeton, 1986) D.J. Struik, A Concise History of Mathematics, 4th edn. (Dover, New York, 1987) B.V. Subbarayappa, K.V. Sarma (eds.), Indian Astronomy, a Source Book (Nehru Center, Bombay, 1985) J.W.N. Sullivan, The History of Mathematics in Europe, from the Fall of Greek Science to the Rise of the Conception of Mathematical Rigour (Oxford University Press, New York, 1925) J. Suzuki, A History of Mathematics (Prentice Hall, Upper Saddle River, 2002) F.J. Swetz, T.S. Ang, A brief chronological guide to the history of Chinese mathematics. Hist. Math. 11, 39–56 (1984) F.J. Swetz (ed.), From Five Fingers to Infinity (Open Court, Chicago, 1994) I. Todhunter, A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace (Chelsea, New York, 1949) H.W. Turnbull, The Great Mathematicians (New York University Press, New York, 1969) B.L. van der Waerden, Science Awakening, Translated by A. Dresden (Kluwer, Dordrecht, 1975) B.L. van der Waerden, Geometry and Algebra in Ancient Civilizations (Springer, Berlin, 1983) B.L. van der Waerden, A History of Algebra (Springer, Berlin, 1985) B. van Nooten, Binary numbers in Indian antiquity. J. Indian Philos. 21, 31–50 (1993) V.S. Varadarajan, Algebra in Ancient and Modern Times (American Mathematical Society, Providence, 1998) K. Venkatachalam, Bharateeya Sakamula (Arya Vijnanadeepa Publications, Vijayawada, 1950) K. Venkatachalam, The Plot in Indian Chronology (Arya Vijnanadeepa Publications, Vijayawada, 1950) F. Viéte, The Analytic Art, Translated by T.R. Witmer (Kent State University Press, Kent„ 1983) A. Weil, Number Theory: An Approach Through History: From Hammurabi to Legendre (Birkhäuser, Boston, 1983) D.G. Wells, You Are a Mathematician: A Wise and Witty Introduction to the Joy of Numbers (Wiley, New York, 1997) R.S. Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge University Press, Cambridge, 1980) H. Weyl, Philosophy of Mathematics and Natural Science (Princeton University Press, Princeton, 1949) E. Whittaker, From Euclid to Eddington (Dover, New York, 1958) N. Wiener, I Am a Mathematician: The Later Life of a Prodigy (Doubleday, New York, 1956) R.L. Wilder, The Foundations of Mathematics (Wiley, New York, 1965) R.L. Wilder, The Evolution of Mathematical Concepts: A Historical Approach (Wiley, New York, 1968) M. Williams, A History of Computing Technology (Prentice-Hall, Englewood Cliffs, 1995) E. Zebrowski, A History of the Circle: Mathematical Reasoning and the Physical Universe (Rutgers University Press, Piscataway, 1999) M.C. Zeller Sr., The Development of Trigonometry from Regiomontanus to Pitiscus (Edwards Brothers, Ann Arbor, 1946) Name Index

A Apollo, 71, 156 al-Mamun (786–833), 105, 106, 108 Apollonius of Perga (around 262–200 BC), al-Mansur/Messala/Messahalla, Caliph 83–84 (714–775), 105 Appel, K. (1932–2013), 35, 36 al-Mutasim (around 794–842), 108 Appell, P.É. (1855–1930), 327 al-Mutawakkil (822–861), 108 Aquinas, S. (1225–1274), 163 al-Rashid, H. (766–809), 105 Arago, D.-F.-J. (1786–1853), 233, 262 al-Shatir, A. (1304–1375), 125 Aratus (around 315–240 BC), 85, 94 al-Tusi, N. (1201–1274), 121 Archimedes of Syracuse (287–212 BC), 78–80 al-Wafa, A. (940–998), 10 Archytas of Tarentum (around 428–347 BC), al-Wathiq (816–847), 108 68 Ammal, J., 369 Argand, J.-R. (1768–1822), 221 Ammal, P., 376 Ariosto (1474–1533), 151 Ammannati, G. (1538–1620), 151 Aristaeus of Croton (about 400 BC), 71 Ampére, A.-M. (1775–1836), 251, 280 Aristaeus the Elder (around 370–300 BC), 74 Amyclas, 70 Aristarchus of Samos (310–250 BC), 77–78 Anaxagoras of Clazomanae (500–428 BC), 61 Ariston of Chios (flourished about 250 BC), Anaximander of Miletus (around 610–547 81 BC), 52–53 Aristotle (around 384–322 BC), 72–73 Anaximenes of Miletus (around 585–525 BC), Arsinoe (around 305–248 BC), 81 54 Artin, E. (1898–1962), 320 Anderson, B., 18 Aryabhatta (born 2765 BC), 7, 12, 21, 41–43, Anderson, C.A. (1940–), 401 86, 109 Andrews, G. (1938–), 370 Askey, R. (1933–), 370 Andrews, P.B. (1937–), 401 Asmussen, O., 326 Andronicus II (1259–1332), 124 Asoka, 87 Andronov, A.A. (1901–1952), 413 Atanasoff, J.V. (1903–1995), 28 Anne, F., 270 Athari, M. (740–815), 105 Anne, O., 357 Athenaeus (flourished about 200), 81 Anne, Q. (1665–1714), 184 Atiyah, E. (1903–1964), 436, 437 Anthemius of Tralles (around 474–558), 99 Atiyah, M.F. (1929–), 436–437 Anthony, H.D., 368 Aubrey, J. (1626–1697), 176 Antiphon of Rhamnos (around 480–411 BC), Auguste, de Thou (1553–1617), 146 64 Augustine, S. (354–430), 52 Apastamba, 40, 41 Autolycus of Pitane (360–290 BC), 96

© Springer International Publishing Switzerland 2014 461 R.P. Agarwal, S.K. Sen, Creators of Mathematical and Computational Sciences, DOI 10.1007/978-3-319-10870-4 462 Name Index

Ayyangar, C.N.S., 368 Bernoulli, Jacob (1654–1705), 12, 125, 158, Ayyar, C.S. (1885–1960), 415 189, 197 Bernoulli, Johann (1667–1748), 12, 193, 201–203 B Bernoulli, N. (1695–1726), 199 Babbage, C. (1791–1871), 240–241 Bernstein, F. (1878–1956), 294 Babuška, I.M. (1926–), 434 Bernstein, J. (1945–), 422 Bach, J.S. (1685–1750), 427 Bernstein, S.N. (1880–1968), 272 Bachmann, P.G.H. (1837–1920), 289 Berthollet, C.C.L. (1748–1822), 237 Backus, J.W. (1924–2007), 432 Besant, A. (1847–1933), 364 Bacon, F. (1909–1992), 17 Bessarion, C. (1403–1472), 130 Bacon, R. (1214–1294), 15–17 Bessel, F.W. (1784–1846), 234 Bailly, J.-S. (1736–1793), 211 Betti, E. (1823–1892), 288, 316 Baire, R. (1874–1932), 317, 332 Bézout, É. (1730–1783), 232 Bairstaw, U. (1880–1963), 352 Bhabha, H.J. (1909–1966), 16, 395, 430 Bairstow, L. (1880–1963), 352 Bhagavantam, S. (1909–1989), 378 Baker, H.F. (1866–1956), 369 Bhaskara I (before 123 BC), 9, 11, 86, 88, 91, Baker, W.R.G. (1892–1960), 448 108, 128 Bakhshali Manuscript (about 200 BC), 84 Bhaskara II/Bhaskaracharya (working 486), 7, Balakrishnan, S. (1891–1931), 415 10, 13, 89, 100–102, 128, 137, 168 Ball, W.W.R. (1850–1925), 21 Bhatnagar, P.L. (1912–1976), 417–418 Balzan, E. (1874–1953), 435, 444 Bhatnagar, S.S. (1894–1955), 428, 450 Banach, S. (1892–1945), 382–383, 389 Bhattathiri, M.N. (1559–1632), 127, 150 Banarsidass, M., 365 Bianchi, L. (1856–1928), 303 Banneker, B. (1731–1806), 210 Bianconi, M.-L. (1880–1950), 331 Barrow, I. (1630–1677), 175, 176, 181, 182 Bias of Priene (about 600 BC), 50 Barry, G. (1894–1986), 336 Bidder, G.P. (1806–1878), 280 Bartels, J.C.M. (1769–1836), 223–224, 241 Bieberbach, L.G.E.M. (1886–1982), 374 Bashforth, F. (1819–1912), 269 Bienaymé, J. (1796–1878), 271 Bass, H. (1932–), 421 Biham, E., 448 Bateman, H. (1882–1946), 357 Bille, B. (1526–1605), 147 Battaglini, G. (1826–1894), 314 Binet, J.P.M. (1786–1856), 235 Baudhayana (born 3200 BC), 40, 41 Bingham, C., 381 Bauer, G., 329 Biot, J.B. (1774–1862), 235 Becker, R. (1887–1955), 392 Birkhoff, G. (1911–1996), 352, 363, 397 Bedé, V. (673–735), 104 Birkhoff, G.D. (1884–1944), 351, 362–363 Beg, U. (1393–1449), 128, 129 Blackwell, D.H. (1919–2010), 429 Bell, E.T. (1883–1960), 4, 17, 29, 168 Bliss, G.A. (1876–1951), 341–342, 358 Bellarmino, C.R. (1542–1621), 153 Blumenthal, L.O. (1876–1944), 321 Bellavitis, G. (1803–1880), 188, 251 Bôcher, M. (1867–1918), 8, 329 Beltrami, E. (1835–1900), 77 Bode, J.E. (1747–1826), 227 Bénard, H.C. (1874–1939), 413 Boethius, A.M.S. (around 475–526), 99–100, Bendixson, I.O. (1861–1935), 14, 316–317 120 Benedetti, G. (1530–1590), 153 Bohr, A. (1922–2009), 368 Benedict XIV, Pope (1675–1758), 155, 206, Bohr, C. (1855–1911), 367 209 Bohr, E.A. (1860–1930), 367 Berenice, 75 Bohr, H.A. (1887–1951), 367 Berkeley, B.G. (1685–1753), 183 Bohr, N.H.D. (1885–1962), 367–368 Bernays, P.I. (1888–1977), 353 Bolibruch, B., 321 Berndt, B.C. (1939–), 370 Boltzmann, L.E. (1844–1906), 311 Berners-Lee, T.J. (1955–), 32 Bolyai, F.W. (1775–1852), 229, 250 Bernoulli, D. (1700–1782), 200, 201, 203, 208, Bolyai, J. (1802–1860), 229, 250, 404, 446 222 Bolza, O. (1857–1942), 342 Name Index 463

Bolzano, B.P.J.N. (1781–1848), 233–234 Bunsen, R.W.E. (1811–1899), 246, 280 Bombelli, R. (1526–1573), 143–144 Burali–Forti, C. (1861–1931), 300 Bombieri, E. (1940–), 444 Bürgi, J. (1552–1632), 150 Bonaparte, N. (1769–1821), 212 Buridan, J. (around 1300–1358), 154 Boncompagni, B. (1821–1894), 106 Busby, R. (1606–1695), 176 Boole, G. (1815–1864), 265 Bush, G.W., 428 Boole, J. (1777–1848), 265 Bush, V. (1890–1974), 31 Boole, M.E. (1832–1916), 241 Buxton, J. (1707–1772), 280 Borel, A. (1923–2003), 431 Byron, L. (1788–1824), 264 Borel, F.É.J.É. (1871–1956), 232–233 Born, M. (1882–1970), 391 Borromeo, C.F. (1564–1631), 164 C Borsuk, K. (1905–1982), 376 Caccini, F.T. (1574–1648), 153 Bortolotti, E. (1866–1947), 143 Caddenhead, 178 Bose, A., 385 Cahn, A. (1922–1999), 434 Bose, Satyendra N. (1894–1974), 385–387 Calabi, E. (1923–), 447 Bose, Surendra N., 385 Callimachus (around 310–240 BC), 81 Boškoviæ, R.J./Roger J.B. (1711–1787), 206 Callippus of Cyzicus (around 370–300 BC), 74 Bosse, A. (1602–1676), 160 Campanus of Novara (around 1220–1296), 122 Bossut, C. (1730–1814), 214 Campbell, J.F. (1821–1885), 270 Bothwell, A. (around 1527–1593), 148 Cannon, J. (1943–), 445 Bott, R. (1923–2005), 438 Cantelli, F.P. (1875–1966), 332 Bouquet, J.-C. (1819–1885), 314 Cantor, G. (1845–1918), 298–301 Bourbaki, N. (1939–), 443–444 Carathéodory, C. (1873–1950), 253, 336, 342, Boussinesq, J.V. (1842–1929), 297 354, 372, 373 Bouvelles, C. (around 1470–1553), 152 Cardano, F. (1444–1524), 137 Bowditch, N. (1779–1838), 217 Cardano, G. (1501–1576), 7, 137–140 Boyle, R. (1627–1691), 176 Carmichael, R.D. (1879–1967), 350–351 Braga, G.M., 449 Carnap, R. (1891–1970), 302 Brahe, O. (1518–1571), 147 Carnot, L. (1753–1823), 220 Brahe, T. (1546–1601), 147 Carr, G.S. (1837–1914)), 368 Brahmagupta (born 30 BC), 7, 8, 10, 11, Cartan, É.J. (1869–1951), 258, 296, 402 88–89, 91, 104, 107, 109 Cartan, H. (1904–2008), 402–403, 421, 434, Brauer, R.D. (1901–1977), 355 443 Breit, G. (1899–1981), 395 Carter, J. (1924–), 442 Brianchon, C.J. (1785–1864), 234–235 Casorati, F. (1835–1890), 288–289 Briggs, H. (1561–1630), 148 Cassini, G.D. (1625–1712), 191, 196 Brioschi, F. (1824–1897), 288 Cassini, J. (1677–1756), 196 Briot, S., 314 Castelli, B. (1578–1643), 164 Brömmel, L., 281 Castillon, J. (1704–1791), 202 Brougham, L. (1778–1868), 231 Cataldi, P.A. (1552–1626), 149 Brouncker, W.V. (1620–1684), 12, 101, 171, Catherine, Queen, 147, 171, 205, 416 190 Cauchy, A.-L. (1789–1857), 237–239 Brouwer, L.E.J. (1881–1966), 353–354 Cavalieri, B.F. (1598–1647), 164–165 Brown, L., 437 Cayley, A. (1821–1895), 273–274 Brown, R. (1773–1858), 347 Celsius, A. (1701–1744), 201 Bruce, C.W. (1816–1900), 416 Celsius, M. (1621–1679), 201 Bruce, E., 269 Celsius, N. (1658–1724), 201 Bruhat, F.G.R. (1929–2007), 424 Cesáro, E. (1859–1906), 314–315 Bruno, G. (1548–1600), 129 Cesi, M.F., 153 Brusentsov N. (1925–), 30 Challis, J., 268 Bryson of Heraclea (about 450 BC), 68 Chanakya, 18 Buddha, Gautama (1887–1807 BC), 17, 45, 59 Chandra, H. (1923–1983), 395, 430–431 Buniakovski, V.J. (1804–1899), 254 Chandrasekhar, S. (1910–1995), 415–416 464 Name Index

Chapman, S. (1888–1970), 400 Copernicus, N. (1473–1543), 133–134 Charak, A. (before 600 BC), 53 Copley, G. (1653–1709), 233 Charles I, 164 Cotes, R. (1682–1716), 197 Charles II, King of Britain (1630–1685), 164, Coulomb, J. (1904–1999), 443 169, 171, 190 Countess of Lovelace (1815–1852), 256, 264 Charles V, Holy Roman Emperor, 141 Courant, R. (1888–1972), 379–380 Charles V, King of France (1338–1380), 125 Coxeter, H.S.M. (1907–2003), 315 Chasles, C.-H., 243 Crafoord, H. (1908–1982), 426 Chasles, M.F. (1793–1880), 243, 296 Craig, J. (1663–1731), 193 Chastellet, F.C., 202 Cramer, A.M., 201 Chatterjee, S.K., 378, 379 Cramer, G. (1704–1752), 201–202 Chauvenet, W. (1870–1920), 342 Cramér, H. (1893–1985), 429 Chebyshev, P.L. (1821–1894), 271–272 Cramer, J., 201 Chennus, P., 84 Crelle, A.L. (1780–1855), 248 Cheops (flourished about 2680 BC), 43 Cremona, L. (1830–1903), 314 Chern, S–S. (1911–2004), 410, 447 Croesus, 51 Chevalley, C. (1909–1984), 291 Cromwell, O. (1599–1658), 164 Chih, Tsu Chih/Chongzhi (429–500), 98–99 Crookes, 311 Chilon of Sparta (about 600 BC), 51 Crosio, C., 313 Chitrabhanu (about 1530), 144 Cross, W.L. (1862–1948), 468 Chiu-Shao, Ch’in (around 1202–1261), Ctesibius of Alexandria (working 285–222 121–122 BC), 81 Cholesky, A.-L. (1875–1918), 337 Cuneiform Tablets (about 2000 BC), 4, 6, 7, Christina, Queen (1626–1689), 162 43–45 Christoffel, E.B. (1829–1900), 227, 283–284 Curie, Madame (1867–1934), 386 Chrystal, G. (1851–1911), 358 Cyzicenus, 70 Chudnovsky, G.V. (1952–), 320 Chuquet, N. (around 1445–1488), 131–132 Church, A. (1903–1995), 401 D Cimabue (1240–1302), 163 da Coi, Z.T. (about 1530), 144 Ciompa, P., 18 da Vinci, L. (1452–1519), 137, 160 Clairaut, A.C. (1713–1765), 207, 233 d’Alembert, J.R. (1717–1783), 208, 213, 216, Clasen, B.I., 296 226, 239 Clavius, C. (1537–1612), 145 Damo, 60 Clebsch, R.F.A. (1833–1872), 287 Damodara (around 1410–1510), 131, 136 Clement VIII, Pope (1536–1605), 103 Dán, K., 399 Cleobulus of Lindos (about 600 BC), 50–51 Dandelin, G.P. (1794–1847), 242 Cleomedes (about 20), 80 Dante, 123, 163, 338 Clifford, W.K. (1845–1879), 298 Dantzig, G.B. (1914–2006), 363 Cock, C., 176 Dantzig, T. (1884–1956), 363 Cohen, A., 440 Darboux, J.G. (1842–1917), 296 Cohen, M., 440 Darley, R., 169 Cohen, P.J. (1934–2007), 14, 319, 440 Darwin, C.R. (1809–1882), 15, 177 Colburn, Z. (1804–1840), 280 Darwin, F. (1848–1925), 1 Cole, A.L., 414 Dase, J.M.Z. (1824–1861), 279–280 Cole, F.N. (1861–1926), 337 Davenport, H. (1907–1969), 390 Colladon, J.-D. (1802–1893), 251 Davidov, A. (1823–1885), 301 Collins, J. (1625–1683), 175 Davis, M.D. (1928-), 401 Colson, J. (1680–1760), 209 de Bardi, N., 232 Conant, L.L. (1857–1916), 450 de Bessy, B.F. (around 1605–1675), 166 Conon of Samos (about 245 BC), 83 de Buffon, C. (1707–1783), 201 Converse, W., 292 de Bure, A., 238 Conway, J. (1937–), 443 de Condorcet, M. (1743–1794), 213 Cooley, J.W. (1926–), 32 de Coulomb, C.-A. (1736–1806), 395 Name Index 465 de Fermat, P. (1601–1665), 165–168 Dicaearchus of Messana (around 350–285 de Giorgi, E. (1928–1996), 321 BC), 74–75 de Grouchy, S. (1764–1822), 213 Dickson, L.E. (1874–1954), 336–337 de La Hire, L. (1606–1656), 179–180 Diderot, D. (1713–1784), 205, 208 De la Hire, P. (1640–1719), 179–180 Dieck, A., 365 de la Ramée, P. (1515–1572), 142 Dieudonné, J. (1905–1992), 443 de la Roche, E. (about 1480), 131 Dijkstra, E.W. (1930–2002), 437 de la Vallée–Poussin, C. (1866–1962), 219, Dini, U. (1845–1918), 314, 338 226, 343 Dinostratus (around 390–320), 71 de Lacaille, A.N.L. (1713–62), 211 Diocles (around 240–180 BC), 84 de Lespinasse, J. (1732–1776), 208 Diocletian (284–305), 96 de Maupertuis, P.L.M. (1698–1759), 201 Diodorus (florished about 60 BC), 79 de Méziriac, C.G.B. (1581–1638), 158–159 Dionysodorus of Caunus (around 250–190 De Moivre, A. (1667–1754), 194, 195, 201 BC), 7 De Morgan, A. (1806–1871), 24, 205, Diophantus of Alexandria (about 250), 95–96 256–257, 262, 264, 265, 273, 274, 294, Dirac, F., 394 303, 323 Dirac, P.A.M. (1902–1984), 395 de Possel, R. (1905–1974), 443 Dirichlet, P.G.L. (1805–1859), 4, 236, de Prony, M.R. (1755–1839), 220 254–255, 259, 270, 274, 277, 278, 283, de Rham, G. (1903–1990), 410 285, 286, 324 de Richelieu, D., 202 Dodgson, C.L./Lewis Carroll (1832–1898), 8, de Roberval, G.P. (1602–1675), 12, 169 285–286 de Saint-Lambert, M., 203 Doll, W.R.S. (1912–2004), 381 de Saint-Venant, A. (1797–1886), 287, 297 Donaldson, S.K. (1957–), 437 de Saint-Vincent, G. (1584–1667), 287, 297 Donnan, F.G. (1870–1956), 292 de Tencin, Madame (1682–1749), 208 Donsker, M.D. (1925–1991), 444, 445 de Thou, J.A. (1553–1617), 146 Dora, 334 de Torquemada, T., 143 Doraiswamy, L., 415 de Véretz, C.O. (died 1905), 297 Dorodnow, A.W., 66 de Villa Dei, A., 106 D’Ovidio, E. (1842–1933), 313 De Witt, J. (1625–1672), 175 Draper, C.S. (1901–1987), 432 Debreu, G. (1921–2004), 439 Dreyfus, A., 327 Debye, P. (1884–1966), 392 Droppers, J.G., 362 Dedekind, J.L.U., 284 du Bois–Reymond, E. (1818–1896), 311 Dedekind, J.W.R. (1831–1916), 14, 15, 71, Dubost, A. (1842–1921), 330 167, 255, 278, 282, 284–285 Duhem, P.-M.-M. (1861–1916), 292 Dehn, M. (1878–1952), 319, 321 Duke Wilhelm of Cleve (1516–1592), 141 del Ferro, S. (1465–1526), 132–133, 135, 136 Dvoretzky, A. (1916–2008), 396 Delambre, J.B. (1749–1822), 235 Dwaipayana, Krishna/Veda Vyasa (born 3374 Democritus of Abdera (around 460–362 BC), BC), 38–40 66–67 Demylus, 62 Denjoy, A. (1884–1974), 339, 388 E Desargues, G. (1591–1661), 160, 179 Earl of Bothwell (1534–1578), 148 Descartes, R. (1596–1650), 8, 12, 15, 83, 98, Eckertm, J.A.P. Jr. (1919–1995), 29, 30 117, 125, 150, 158–165, 169, 170, 172, Eddington, A.S. (1882–1944), 348 173, 181, 182, 189, 221 Edward VI, King (1537–1553), 140 Desestre, M.-M., 237 Egorov, A.D., 400 Deslartes, J. (1903–1968), 443 Egorov, D.F. (1869–1931), 360 Destouches, C.L.-C. (1668–1726), 208 Ehresmann, C. (1905–1979), 443 Devi, S. (1929–2013), 280 Eickemeyer, R., 326 Dewey, J. (1859–1952), 334 Eileen, R., 381 di Agnesi, P., 208 Eilenberg, S. (1913–1998), 420–421 Diamond, F. (1964–), 168 Einstein, A. (1879–1955), 346–350 466 Name Index

Einstein, H. (1847–1902), 346 Fibonacci/Leonardo of Pisa (around Einstein, P. (1858–1920), 346 1170–1250), 118–119 Eisenhart, L.P. (1876–1965), 342, 358 Fields, J.C. (1863–1932), 424 Eisenhower, D.D. (1890–1969), 30, 397 Filippa, 132 Eisenlohr, 49 Finch, E. (1900–1978), 335 Eisenstein, F.G. (1823–1852), 167, 235, 254, Finé, O. (1494–1555), 134 283, 410 Fiore, A.M. (about 1506), 133, 135, 136 Elizabeth, B., 269 Fischer, E.K.B. (1824–1907), 311 Elizabeth II Queen, 381 Fisher, G., 380 Elizabeth, Margaret, 363 Fisher, K., 380 Elizabeth, Marnie, 357 Fisher, R.A. (1890–1962), 380–381, 428 Elizabeth Protestant Queen, 141, 194 Flaccus, Q.H., 151 Émilie, M.C.-L. (1706–1749), 202–203 Flamsteed, J. (1646–1719), 187, 190, 192 Encke, J.F. (1791–1865), 274 Florensky, P.A. (1882–1937), 360 Epicureans (founded around 307 BC), 77 Fontana, N./Tartaglia (1500–1557), 7, 135–136 Eratosthenes of Rhodes (around 276–194 BC), Fontenelle, 201 81–82 Föppl, A.O. (1854–1924), 340 Erdös, P. (1913–1996), 351, 419–420 Forsyth, A.R. (1858–1942), 16, 274 Etienne, 172, 232, 327 Fourier, J.B.J. (1768–1830), 221–223, 245, Eubulides (about 400 BC), 308 251, 252 Euclid of Alexandria (around 325–265 BC), Fowler, R.H. (1889–1944), 415 75–77 Fowler, W.A. (1911–1995), 415 Euclid of Megara (around 435–365 BC), 75 Francis, Grand Duke of Tuscany, 206 Eudemus of Rhodes (around 350–290 BC), 83 Franck, J. (1882–1964), 391 Eudoxus of Cnidus (around 400–347 BC), Frankel, A.H. (1891–1965), 14 70–71 Franklin, B. (1706–1790), 213 Euler, L. (1707–1783), 4, 10, 13, 66, 101, 162, Fréchet, M.R. (1878–1973), 346 166, 167, 196, 197, 199, 201, 203–205, Frederick II, Emperor (1194–1250), 118 208, 209, 211, 213, 217, 222, 226, 235, Fredholm, E.I. (1866–1927), 8, 258, 316, 328 246, 248, 258, 272, 281, 342, 420 Frege, F.L.G. (1848–1925), 300–302, 333 Euphorbus, 59 Frend, S., 257 Eurytas of Metapontum (around 400 BC), 69 Frend, W., 264 Eutocius of Ascalon (around 480–540), 68 Frenet, J.F. (1816–1900), 223 Euwe, M. (1901–1981), 354 Fresnel, A.J. (1788–1827), 174 Everest, G. (1790–1866), 241, 265 Frey, G. (1944–), 167 Exner, F. (1849–1926), 371 Fricke, R. (1861–1930), 303 Friedrichs, K.O. (1901–1982), 380 Frisius, G. (1506–1555), 141 F Frobenius, F.G. (1849–1917), 8, 266, 336, 342 Fahrenheit, G.D. (1686–1736), 198 Fuchs, I.L. (1833–1902), 287–288 Fairfax, M.C., 231–232 Fuchs, W.H.J. (1915–1997), 443 Fairfax, W.G. (1739–1813), 231 Fuks, D.B., 422 Fatou, L.P.J. (1878–1929), 345 Fulkerson, D.R. (1924–1976), 450 Faulhaber, J. (1580–1635), 158 Fuller, T. (1710–1790), 280 Fechner, G. (1801–1887), 18 Furtwängler, P. (1869–1940), 390, 408 Feige, U., 448 Feigenbaum, M.J. (1944–), 446 Fejér, L. (1880–1959), 336, 351–352 G Fekete, M. (1886–1957), 396 Gabriel-Philippe (1677–1719), 180 Ferguson of Raith (1723–1816), 215 Gadbled, C. (1734–1782), 216 Fermi, E. (1901–1954), 398 Galenus, C. (129–217), 115 Ferrari, L. (1522–1565), 7, 136, 138, 142–143 Galilei, G. (1564–1642), 151–155 Feynman, R. (1918–1988), 292, 399, 412 Galilei, V. (1521–1591), 151 Fiat, A. (1957–), 448 Gallai, T. (1912–1992), 264 Name Index 467

Galöis, E. (1811–1832), 260–261 Gram, J.P. (1850–1916), 304–305 Galton, F. (1822–1911), 276–277 Grandi, L.G. (1671–1742), 195–196 Gamba, M., 154 Grassmann, H.E., 258 Gamow, G., 322 Grassmann, H.G. (1809–1877), 257–258 Gandhi, M.K. (1869–1948), 6 Graunt, J. (1620–1674), 170–171 Ganea, T. (1922–1971), 421 Great Pyramid at Gizeh (erected around 2600 Garfield, J.A. (1831–1881), 22 BC), 43 Garga, 87 Green, B.J. (1977), 451 Gause, G.F., 252 Green, G. (1793–1841), 242–243 Gauss, K.F. (1777–1855), 225–231 Gregory, D.F. (1813–1844), 273 Gay-Lussac, 218 Gregory, J. (1638–1675), 177–179 Geiser, K.F. (1843–1934), 373 Greig, C.S., 231 Geissler, J.H.W. (1814–1879), 246 Grimaldi, Jesuit, 186 Gelfand, I.M. (1913–2009), 421–422 Grimm, P., 203 Gelfand, S., 422 Gromov, M.L. (1943–), 445–446 Gelfond, A.O. (1906–1968), 404 Gross, E.P. (1926–1991), 418 Gelfond, O.I., 404 Gudermann, C. (1798–1852), 266 Gelon, King (around 230 BC), 78 Guggenheim, 431 Geminus of Rhodes (around 10 BC-60 AD), 89 Guldin, P. (1577–1643), 96 Genocchi, A. (1817–1889), 313 Gunter, E. (1581–1626), 158 Gentzen, G. (1909–1945), 319 Gutenberg, J. (around 1400–1468), 132 George VI, King (1895–1952), 335 Guy, W.A. (1810–1885), 428 Gerbert d’Aurillac (945–1003), 114 Gergonne, J. (1771–1859), 237 Germain, M.-S. (1776–1831), 224–225 H Gershgorin, S.A. (1901–1933), 408 Haar, A. (1885–1933), 339 Gerson, L. (1288–1344), 172 Hadamard, A., 326 Gherardo of Cremona (around 1114–1187), 42 Hadamard, J.S. (1865–1963), 326–328 Ghosh, A. (1872–1950), 364 Hadley, J. (1682–1744), 182 Ghosh, J.C. (1894–1959), 385 Hahn, H. (1879–1934), 375 Ghosh, U., 385 Haken, W. (1928–), 36 Gibbs, J.W. (1839–1903), 291–292 Hakim, Caliph (985–1021), 115 Gilbert, W.S. (1836–1911), 304 Halayudha (about 975), 61 Ginsburg, J., 111 Haldane, J.B.S. (1892–1964), 18 Ginzburg, V.L. (1916–2009), 412 Hales, T.C. (1958–), 320 Girard, A. (1595–1632), 160 Halley, E. (1656–1742), 190–192 Glauert, 341 Halsted, G.B. (1853–1922), 336 Gleason, A. (1921–2008), 319 Hamel, G.K.W. (1877–1954), 319 Glyde, S. (1619–1695), 169 Hamilton, J. (1512–1571), 139 Gödel, K.F. (1906–1978), 404–407 Hamilton, W. (1788–1856), 17 Gödel, R., 404 Hamilton, W.D. (1936–2000), 381 Gokhale, G.K. (1866–1915), 364 Hamilton, W.R. (1805–1865), 255–256 Goldbach, C. (1690–1764), 199 Hamming, R.W. (1915–1998), 422–423 Goleniscev, V. (1856–1–947), 49 Hammurabi, King (1792–1750 BC), 43 Gonzalo, C.F., 143 ha-Nasi, A.B.H. (1070–1136), 117 Goode, H.H. (1909–1960), 441 Hankel, H. (1839–1873), 258 Gopala, 103 Hardy, G.H. (1877–1947), 343–345 Gordan, P.A. (1837–1912), 287 Hardy, I., 343 Gosselin, G. (1536–1600), 144 Hardy, S.H., 343 Goursat, É.J.-B. (1858–1936), 296 Harnack, C.G.A. (1851–1888), 305 Govindasvami/Govindasv¯ amin/Govindaswami¯ Harnack, T. (1817–1889), 305 (around 800–860), 108 Harriot, T. (1560–1621), 150 Gräffe, K.H. (1799–1873), 242 Harvey, W. (1578–1657), 163 Grafius, M.E., 363 Hasse, H. (1898–1979), 389–390 468 Name Index

Hausdorff, F. (1868–1942), 330 Holmboe, B.M. (1795–1850), 249 Hawking, S. (1942–), 395 Homer (around 800–700 BC), 80 Heath, R., 205 Hooke, R. (1635–1703), 176–177 Heaviside, O. (1850–1925), 291 Hopf, H. (1894–1971), 412 Hecataeus of Miletus (around 550–476 BC), Hopper, G.M. (1906–1992), 407–408 52 Horace (65–8 BC), 25 Hecke, E. (1887–1947), 321 Horner, W.G. (1786–1837), 121 Hegel, G.W.F. (1770–1831), 225 Horowitz, 245 Heine, H.E. (1821–1881), 270–271 Householder, A.S. (1904–1993), 402 Heisenberg, K.E.A., 390 Hui, Liu (around 220–280), 93–94 Heisenberg, W.K. (1901–1976), 390–393 Hui, Yang (1238–1298), 123–124 Hempel, C.G. (1905–1997), 321 Hull, M.D., 415 Heng, Z. (78–139 AD), 91–92 Hurewicz, W. (1904–1956), 401–402 Henkin, L.A. (1921–2006), 401 Hurwitz, A. (1859–1919), 266 Henrion, D. (1580–1632), 58 Hutton, J. (1726–1797), 216 Henry III, King (1551–1589), 145 Huxley, A. (1894–1963), 185 Henry IV, King (1553–1610), 145 Huygens, C. (1629–1695), 173–174 Henry VIII (1491–1547), 124 Hypatia of Alexandria (370–415), 97–98 Hensel, K. (1861–1941), 278 Hypsicles (around 190–120 BC), 83 Hera in Tarentum, 59 Herglotz, G. (1881–1953), 380 Hermann, J. (1678–1733), 197 I Hermeas, King, 72 Iamblichus (around 245–325), 94–95 Hermite, C. (1822–1901), 275–276 ibn Ezra, A.M. (around 1090–1167), 118 Hermotimus, 70 ibn Luqam, Q. (died 912), 123 Hero of Byzantium, 81 ibn Tariq, Y. (died about 796 AD), 106 Herodotus (around 484–425 BC), 43 ibn Tibbon, J.M. (around 1236–1304), 123 Heron of Alexandria (about 75 AD), 90–91 Ignacy, 372 Herrejoni, 110 Inaudi, J. (1867–1950), 280 Herschel, C. (1750–1848), 231 Innocent XIII, Pope (1655–1724), 103 Herschel, F.W. (1738–1822), 241 Isidore of Seville (560–636), 103 Hertz, H. (1857–1892), 8 Isidorus of Miletus (about 540), 102 Hesse, L.O. (1811–1874), 261 Iyer, R.C. (born 1866), 376 Hevelius, J. (1611–1687), 190 Heydrich, R.T.E. (1904–1942), 392 Hiero II (around 307–216 BC), 78 J Hilbert, D. (1862–1943), 318–323 Jacobi, C.G.J. (1804–1851), 252–253 Hilbert, F. (1893–1969), 318 Jaimani, 38 Hildebrandt, T.H. (1888–1980), 438 James VI, King (1566–1625), 148 Hill, A.B. (1897–1991), 381 James, W. (1842–1910), 294 Hill, G.W. (1838–1914), 290 Jamesome, M., 178 Himmler, H. (1900–1945), 392 Janiszewski, Z. (1888–1920), 374–375 Hipparchus (around 190–120 BC), 84–85 Jarden, D., 23 Hippasus of Metapontum (about 500 BC), 61 Jeanne, 297 Hippias of Elis (about 460 BC), 66 Jefferson, T. (1743–1826), 210 Hippocrates of Chios (about 470 BC), 65–66 Jelinek, F. (1932–2010), 443 Hitler, A. (1889–1945), 332 Jerosch, K., 318 Hittorf, J.W. (1824–1914), 246 Jing-Run, C. (1933–1996), 439 Hoare, C.A.R. (1934–), 441 Johannes Widman of Eger (1460–1500), 221 Hobbes, T. (1588–1679), 170 John of Seville (about 1125), 106 Hobson, E.W. (1856–1933), 369 John Paul II, Pope (1920–2005), 155 Hodge, W.V.D. (1903–1975), 434 John, St., 149, 394 Hoecke, V., 140 Jones, P.S., (Not cited in the text) Hölder, O.L. (1859–1937), 315 Jones, W.W., 41 Name Index 469

Jordan, M.E.C. (1838–1922), 290–291 Kneser, A. (1862–1930), 266 Jordan, W. (1842–1899), 295–296 Kneser, H. (1898–1973), 321 Joseph, G.G., 127 Knuth, D.E. (1938–), 441–442 Joseph, H., 365 Kolmogorov, A.N. (1903–1987), 399–400 Jourdain, P.E.B. (1879–1919), 308 Komalatammal, 368 Julia, G.M. (1893–1978), 383 König, J. (1849–1914), 300 Julia, P.G., 435 König, R. (1885–1979), 321 Justinian, Emperor (483–565), 69 Koppelman, L., 243 Jyesthadevan (around 1500–1600), 136–137 Kornfield, K., 434 Korteweg, D.J. (1848–1941), 353 Kossuth, L. (1802–1894), 404 K Kotarbinski, T. (1886–1981), 393 Kaczmarz, S. (1895–1939), 372 Kothari, D.S. (1905–1993), 418 Kagan, V.F. (1869–1953), 319 Kovalevskaya, S.V. (1850–1891), 304 Kaiser Rudolph II, Emperor (1552–1612), 155 Kövesi, M., 399 Kakutani, S. (1911–2004), 397 Kowa, S. (1642–1708), 180 Kale, L., 431 Kowalewski, W.H.G. (1876–1950), 341 Kalmár, L. (1905–1976), 403 Krai, C., 147 Kamil, A. (850–930), 112 Kramers, H.A. (1894–1952), 368 Kanaka, 107 Krishnamurthy, E.V. (1934–2012), 440–441 Kanellakis, P.C. (1953–1995), 448 Krishnan, K.S. (1898–1961), 378 Kanigel, R. (1946–), 370 Kronecker, I., 277 Kant, I. (1724–1804), 225 Kronecker, L. (1823–1891), 277–279 Kapitsa, P. (1894–1984), 411 Krook, M. (died 1985), 418 Karmarkar, N. (1957–), 449 Kummer, E.E. (1810–1893), 259–260 Karnaugh, M. (1924–), 433 Kummer, M., 297 Kasiski, F. (1805–1881), 240 Kuratowski, K. (1896–1980), 388–389 Kästner, A.G. (1719–1800), 223 Kurdyka, K., 419 Katyayana, 6, 40, 41 Kursunoglu, B. (1922–2003), 395 Kayal, N., 33 Kutta, M.W. (1867–1944), 329–300 Keatinge, R., 263 Keller, A., 457 Kemeny, J.G. (1926–1992), 401 L Kemp, C., 249 Lacroix, S.F. (1765–1843), 220–221 Kempe, A.B. (1849–1922), 302 Ladyzhenskaya, O.A. (1922–2004), 429 Keng, Tsu /Zu Gengzhi (450–520), 99 Lagadha, Sage (before 1350 BC), 50 Kepler, J. (1571–1630), 155–156 Lagrange, J.L. (1736–1813), 211–213 Key, M.M., 360 Laguerre, E.N. (1834–1886), 288 Khan, Khublai (1216–1294), 120 Lalla (around 720–790), 104 Khayyám, Omar (1048–1131), 116–117 Lalouvére, A. (1600–1664), 165 Khinchin, A.Y. (1894–1959), 272 Lambert, J.H. (1728–1777), 209–210 Khufu (2589–2566 BC), 43 Lamé, G. (1795–1870), 244, 246 Khwajah Nizami of Samarkand, 117 Lanchester, F.W. (1868–1946), 340 Kielhau, M., 249 Landau, E. (1877–1938), 285, 342–343, 373, Kirchhoff, G.R. (1824–1887), 280–281 390 Kirillov, A.A. (1936–), 422 Landau, H. (1877–1938), 342–343 Klammer, 340 Landau, L.D. (1908–1968), 411–412 Kleene, G.A., 414 Lane, L., 298 Kleene, S.C. (1909–1994), 414–415 Langlands, R.P. (1936–), 431 Klein, F.C. (1849–1925), 303 Laplace, P.S. (1749–1827), 216–218 Kleiner, A. (1849–1916), 347 Larmor, J. (1857–1942), 270 Kline, M. (1908–1992), 413 Lasker, E. (1868–1941), 321 Knaster, B. (1893–1980), 376 Latadeva, 86 Kneschke, A. (1902–1979), 341 Laurent, P.-A. (1813–1854), 228 470 Name Index

Lax, H., 434 Lorenz, E.N. (1917–2008), 425–426 Lax, P.D. (1926–), 434 Lotka, A.J. (1880–1949), 351 Le Bouteiller, J., 297 Lotze, R.H. (1817–1881), 301 le Canu, P., 216 Louis IX, King (1214–1270), 120 Le Monnier, R., 212 Louis XVI, King (1754–1793), 212 Le Verrier, U.J.J. (1811–1877), 262, 268 Louis-Francois (1760–1848), 237–239 Lebesgue, H.L. (1875–1941), 338–339 Louis-Philippe (1773–1850), 235 Lebovitz, N.R., 416 Louvois, 188 Leelavati, 100, 126, 137, 440 Lowndes, T. (1692–1748), 268 Lefévre, J. (1455–1536), 132 Lubin, J.D. (1936–), 434 Lefschetz, S. (1884–1972), 310 Lucas, F.É.A. (1842–1891), 294 Legendre, A.-M. (1752–1833), 218–220 Lucas, H. (1610–1663), 175 Leibniz, G.W. (1646–1716), 185–187 Lucius, 90, 151 Lenin, V.I. (1870–1924), 379 Lukasiewicz, J. (1878–1956), 345–346 Lenobu, S.T. (1662–1712), 180 Lun, Tshai (around 50–121), 132 Leo X, Pope (1475–1521), 134 Luther, M., 311 Leodamas (about 380 BC), 70 Luzin, N.N. (1883–1950), 360 Leon (about 375 BC), 70 Lysanias of Cyrene, 81 Lerch, M. (1860–1922), 278 Lesniewski, S. (1886–1939), 393 Leucippus (about 440 BC), 66 M Levens, J., 436 MacColl, H. (1837–1909), 294 Lévi, P., 432 MacLane, S. (1909–2005), 421 Levi-Civita, T. (1873–1941), 227 Maclaurin, C. (1698–1746), 199–200 Levitan, B. (1914–2004), 422 Macropedius, 141 Lévy, M.-H., 424 MacWilliams, J. (1917–1990), 443 Lévy, P.P. (1886–1971), 424 Madhava of Sangamagramma (1340–1425), Lewis, D.K. (1941–2001), 396 126–127 Lewy, H. (1904–1988), 380 Magnus, A. (around 1193–1280), 120 L’Hôpital, G.F.A. (1661–1704), 13, 192 Mahalanobis, P.C. (1893–1972), 385 L’Huilier, S.A.J. (1750–1840), 128 Maharaja, B.K.T. (1884–1960), 364–365 Li, Chih (1192–1279), 120 Maharaja, T.T., 364 Li, Y., 120 Mahavira (817–875), 109–111 Lian, Bong, 447 Mahavira, V. (around 1894–1814 BC), 45–48 Liapunov, A.M. (1857–1918), 310–311 Mainardi, G. (1800–1979), 288 Libri, G. (1803–1869), 238 Maitrayana, 40 Lichtenberg, G.C. (1742–1799), 223 Malthus, T.R. (1766–1834), 221 Lie, S. (1842–1899), 295 Manava, 40 Liénard, A.M. (1869–1958), 331 Mandelbrojt, S. (1899–1983), 443 Lifshitz, E.M. (1915–1985), 412 Mandelbrot, B. (1924–2010), 432–433 Lily, 324, 431, 437 Manzur, S. (1905–1981), 383 Lincoln, A. (1809–1865), 325 Mar, G., 401 Lindelöf, E.L. (1870–1946), 310 Marangoni, C.G.M. (1840–1925), 292 Liouville, J. (1809–1882), 258–259 Marcellus (266–208 BC), 78 Lipschitz, R.O.S. (1832–1903), 286 Marconi, G. (1874–1937), 449 Listing, J.B. (1808–1882), 240 Maria, H. (1609–1669), 164 Littlewood, J.E. (1885–1977), 21 Maric, M. (1875–1948), 347 Liu, Kefeng (1965–), 447 Marina, 399 Livia (born 1601), 154 Markov, Andrei A. (1856–1922), 308–309 Lobachevsky, N.I. (1792–1856), 241–242 Markov, Andrey A. (1903–1979), 308–309 Lokasundari, 376 Markov, Vladimir A. (1871–1897), 308 Lomnicki, A.M. (1881–1941), 382 Marolois, S. (1572–1627), 160 London, F.W. (1900–1954), 412 Maro,P.V. (70–19 BC), 151 Lorentz, H.A. (1853–1928), 324 Marre, A., 131 Name Index 471

Martha, 232 Montgomery, D. (1909–1992), 421 Mary, Queen (1516–1558), 140, 148 Moore, E.H. (1862–1932), 337 Mascheroni, L. (1750–1800), 218 Moore, G.E. (1873–1958), 333 Mathieu, 291, 327 Moore, J. (1646–1714), 190 Mathieu, É.L. (1835–1900), 291 Moore, J.C. (1923–), 421 Matiyasevich, Y.V. (1947–), 320 Moore, R.L. (1882–1974), 359–360 Matteucci, C. (1811–1868), 379 Moray, R. (1608–1673), 178 Mauchly, J.W. (1907–1980), 29 Mordell, L.J. (1888–1972), 410 Maupetuis, 202 Morgenstern, O. (1902–1977), 397 Maurice of Nassau (1567–1625), 147 Morley, F. (1860–1937), 357 Maurolico, F. (1494–1575), 135 Morse, C.P., 325 Maurya, King (1472–1436 BC), 87 Morse, H.C.M. (1892–1977), 325 Maximilian I, Emperor (1459–1519), 130 Moschopulus, M. (around 1350–1450), 179 Maxwell, J.C. (1831–1879), 228 Moscow, P. (about 1850 BC), 48–50 Mazurkiewicz, S. (1888–1945), 375–376 Moser, J. (1928–1999), 434 McCarthy, J. (1927–2011), 435–436 Moses, 141 McClintock, B. (1902–1992), 292 Mostowski, A. (1913–1975), 418–419 McCluskey, E.J. (1929–), 414 Mostowski, T., 419 McDowell, W.W., 432 Moulton, F.R. (1872–1952), 33 Meeks, W.H., 447 Mukherjee, A. (1864–1924), 377 Melissus, 64 Müller, W., 392 Menaechmus of Proconnesus/Alopeconnesus Murarka, N.P., 440 (around 375–325 BC), 73–74 Murray, F.J. (1911–1996), 398 Mendel, G.J. (1822–1884), 275 Musa, B. (around 800–860), 106 Menelaus of Alexandria (around 70–140 AD), Mussolini, 344 90 Myllias, 59 Menger, K. (1902–1985), 274 Myrica, G., 141 Mengoli, P. (1625–1686), 125 Myson of Chene, 51 Menzel, D.H. (1901–1976), 418 Mercator, G. (1512–1594), 141–142 Mercator, Nicolaus/Kauffmann (1620–1687), N 171 Nagata, M. (1927–2008), 320 Mersenne, P.M. (1588–1648), 159 Naimark, M.A. (1909–1978), 422 Mertens, F. (1840–1927), 278 Namboodri, P. (around 1370–1460), 128 Metrodorus (about 500), 92 Napier, A. (1534–1608), 148 Meyer, T. (1882–1972), 340 Napier, J. (1550–1617), 148–149 Michael VIII, P. (1223–1282), 124 Nash, J.F. (1928–), 321 Michelangelo, 151 Naucrates, 75 Micheria, C., 137 Naur, P. (1928–), 436 Midas, Phrygian King, 59 Navakshethra, 128 Milgram, A.N. (1912–1961), 434 Nave, H., 132 Mill, J.S. (1806–1873), 161 Navier, C.-L. (1785–1836), 222 Millbanke, A. (1792–1860), 264 Nearchus, 63 Milman, V.D. (1939–), 396 Nemorarius, J. (1225–1260), 123 Minkowski, H. (1864–1909), 324 Neocleides, 70 Minos, King, 71 Neugebauer, O. (1899–1990), 23 Mitra, S.K., 428 Neumann, F.E. (1798–1895), 280 Mittag-Leffler, S.G. (1846–1927), 266 Neumann, K.G. (1832–1925), 287 Mnesarchus, 54, 60 Neumann, N., 379 Möbius, A.F. (1790–1868), 239–240 Nevanlinna, R.H. (1895–1980), 409 Mohr, D.G. (1640–1697), 218 Newton, H.A. (1623–1679), 180 Moisieva, 241 Newton, I. (1642–1727), 181–185 Monge, G. (1746–1818), 214–215 Neyman, J. (1894–1981), 429 Montel, P. (1876–1975), 388 Nicholas IV, Pope (1227–1292), 122 472 Name Index

Nicholas of Cusa (1401–1464), 129–130 Paul II, Pope (1417–1471), 130 Nick, P., 443 Paul III, Pope (1468–1549), 138 Nicolas, J. (1685–1727), 180 Pauli, W.E. (1900–1958), 430 Nicolette, 410 Peacock, G. (1791–1858), 2221 Nicomachus of Gerasa (around 60–120 AD), Peano, G. (1858–1932), 313–314 89–90 Pearl, R. (1879–1940), 252 Nicoteles of Cyrene (about 250 BC), 83 Pearson, K. (1857–1936), 311 Nightingale, F. (1820–1910), 263 Peirce, B. (1809–1880), 15 Nikodym, O.M. (1887–1974), 382 Peirce, C.S. (1839–1914), 293–294 Nilakanthan, S. (around 1444–1544), 382 Pell, J. (1610–1685), 86 Nisanku, 86 Pelletier/Peletier, J. (1517–1582), 142 Nissen, R. (1896–1981), 349 Pericles, 63 Noether, A.E. (1882–1935), 354–356 Perrin, J. (1870–1942), 348 Nonni, G., 338 Perron, O. (1880–1975), 352 Nørlund, M., 367 Pestalozzi, J.H. (1746–1827), 244 Nrpatunga, Rastrakuta King Amoghavarsa Péter, R. (1905–1977), 403 (814–877), 109 Petersen, J.P.C. (1839–1910), 292–293 Petrarch, F. (1304–1374), 151 Pettis, B.J. (1913–1979), 422 O Peyrard, F., 75 Obama, B. (1961–), 445 Pfaff, J.F. (1765–1825), 223 Odlyzko, A. (1949–), 443 Phaedrus (around 444–393 BC), 49 Ogilvie, A., 357 Pherecydes of Syros (about 600 BC), 54 Ohm, G.S. (1789–1854), 235–236 Phidias, 78 Omar I, Caliph (579–644), 97 Philip of Macedonia, King (382–336 BC), 72 Onsager, L. (1903–1976), 292 Philipp II (1527–1598), 146 Oppenheimer, J.R. (1904–1967), 395 Philippus, 70 Oresme, N. (1320–1382), 125–126 Phillippe XIV, Louis (1638–1715), 165 Osgood, W.F. (1864–1943), 325 Philo of Byzantium (about 250 BC), 81 Ostrogradsky, M.V. (1801–1862), 245–246 Philo of Gadara, 94 Ostrowski, A.M. (1893–1986), 328 Philolaus of Croton (around 480–405 BC), Oughtred, W. (1575–1660), 157 64–65 Ourisson, A., 363 Philoponus (about 490), 71 Piazzi, G. (1746–1826), 227 Picard, C.E. (1856–1941), 309–310 P Picard, C.M.J. Pacioli, L. (1446–1517), 133 Picard, J. (1620–1682), 135 Paganini, B.N.I., 112 Pick, G.A. (1859–1942), 297 Paila, 38 Pierre, 327 Painlevé, P. (1863–1933), 287, 308 Pingala (about 500 BC), 60–61 Pais, A. (1918–2000), 386 Pisharati, T.A. (1550–1621), 149 Palit, T.N., 377 Pittacos of Mytilene (around 640–568 BC), 50 Panaetius of Rhodes (around 185–109 BC), 85 Plancherel, M. (1885–1967), 431 Pandit, N. (1340–1400), 126 Planck, M. (1858–1947), 268 Panini (about 500 BC), 60 Planudes, M. (1260–1330), 124 Pappus of Alexandria (around 290–350), Plato of Athens (around 427–347 BC), 68–70 96–97 Plato of Tivoli (around 1132–1146), 117 Parmenides (about 480 BC), 62 Playfair, J. (1748–1819), 215–216 Parry, W.E. (1790–1855), 232 Playfair, J.G., 216 Parseval, M.-A. (1755–1836), 220 Pliny the Elder (23–79), 104 Parusinski, A., 419 Plouffe, S. (1956), 443 Pascal, B. (1623–1662), 171–173 Plücker, J. (1801–1868), 246–247 Pascal, É. (1588–1651), 172 Plume, T. (1630–1704), 197 Pasteur, L. (1822–1895), 73 Plutarch (around 46–120), 51 Name Index 473

Pococke, E., 59 Rayleigh, J.W.S. (1842–1919), 242 Poincaré, J.H. (1854–1912), 306–309 Recorde, R. (around 1510–1558), 140–142 Poisson, S.D. (1781–1840), 232–233 Regiomontanus/Johann Müller (1436–1476), Poitou, G. (1926–1989), 434 130–131 Polkinghorne, J.C. (1930), 395 Reid, C.B. (1918–2010), 426 Polya, G. (1887–1985), 372–374 Reinhardt, K.A. (1895–1941), 320 Poncelet, J.-V. (1788–1867), 236–237 Rhind, A.H. (1833–1863), 49 Pond, J., 247 Rhind Papyruses (about 1650 BC), 48–50 Pontryagin, L.S. (1908–1988), 412–413 Ribet, K. (1948–), 167 Porkert, A., 406 Riccati, F. (1676–1754), 196 Posidonius of Apamea (135–51 BC), 85 Riccati, V. (1707–1775), 196 Post, E. (1897–1954), 405 Ricci, M. (1552–1610), 127 Prandtl, L. (1875–1953), 340–341 Ricci, O. (1540–1603), 151 Prausnitzer, F., 277 Ricci-Curbastro, G. (1853–1925), 227 Prausnitzer, J., 277 Richard, L.-P.-É. (1795–1849), 260 Prithuyasas, 87 Richard of Wallingford (1292–1336), 124 Proclus, D. (410–485), 16 Richardson, L.F. (1881–1953), 433 Protagoras of Abdera (around 484–414 BC), Richelot, C., 280 63–64 Richelot, F.J. (1808–1875), 280 Ptolemaeus, A.C. (around 90–168 AD), 92 Riemann, G.F.B. (1826–1866), 281–282 Ptolemy I, 75 Riesz, F. (1880–1956), 346 Ptolemy II Philadelphus, King (around Rivest, R.L. (1947–), 447 283–246 BC), 81 Robert of Chester (about 1150), 106 Ptolemy III Euergetes, 81 Robespierre, 222 Ptolemy, King, 77 Robinson, J.H.B. (1919–1985), 426–427 Puranic, 88 Robinson, R.M. (1911–1995), 426 Pürbach, G. (1423–1461), 130 Robison, J. (1739–1805), 216 Purser, M., 274 Roch, G. (1839–1866), 285 Pushkin, A.S. (1799–1837), 308 Rockefeller, J. (1839–1937), 373 Pythagoras (around 582–481 BC), 54–60 Rodrigues, O. (1794–1851), 243 Pythais, 54 Rogers, H. (1926), 401 Pythonax of Crete, 60 Rohn, K. (1855–1920), 303 Rolle, M. (1652–1719), 188–189 Roosevelt, F.D. (1882–1945), 349 Q Rosen, F., 106 Quincke, G.H. (1834–1924), 311 Rossby, C.G. (1898–1957), 426 Quine, W.V.O. (1908–2000), 414 Rosser, J.B. (1907–1989), 401 Qurra, T. (826–901), 111–112 Rowe, D. (1950), 410 Rudolff, C. (1499–1545), 168 Ruffini, P. (1765–1822), 120 R Rumford, C. (1753–1814), 269 Rabin, M.O. (1931), 401 Runge, C.D.T. (1856–1927), 309 Rajagopal, C.T. (1903–1978) Runge, N., 379 Raleigh, W. (1552–1618), 150 Runkle, J.D. (1822–1902), 290 Ramachandran, G.N.I. (1922–2001), 440 Russell, B.A.W. (1872–1970), 333–335 Raman, C.V. (1888–1970), 376–379 Ruth, 324, 381 Ramanujan, S. (1887–1920), 368–370 Rutherford, E. (1871–1937), 367 Ramsey, F.P. (1903–1930), 396 Rao, B., 429 Rao, C.R. (1920), 428 S Rao, N.R., 449 Saccheri, G. (1667–1733), 77 Raphson, J. (1648–1715), 187 Sachs, A. (1915–1983), 23 Rapoport, A., 18 Sacrobosco, J. (around 1195–1256), 132 Rashevsky, N., 18 Sadleir, M. (died 1706), 273 474 Name Index

Safford, T.H. (1836–1901), 280 Shakespeare, W. (1564–1616), 151 Sagan, C.E. (1934–1996), 416 Shamir, A. (1952), 448 Saha, M. (1893–1956), 385 Shannon, C.E. (1916–2001), 425 Sahl, I. (940–1000), 157 Shastri, V.V., 364 Saks, S. (1897–1942), 338 Sheffer, H.M. (1883–1964), 362 Salam, A. (1926–1996), 395 Shelley, P.B. (1792–1822), 333 Salem, R. (1898–1963), 450 Shi Huang, Emperor (213 BC), 93 Salmon, G. (1819–1904), 270–271 Shih-Chieh, Chu (about 1300), 124–125 Salvatorus, S., 142 Shilov, G.E. (1917–1975), 422 Salviati, 153 Shimura, G. (1930), 167 Samuel, 357, 420 Shirakatsi, A. (610–685), 103 Samuelson, P.A. (1915–2009), 292 Shrautasutras, 40 Sarte, J.-P. (1905–1980), 163 Siegel, C.L. (1891–1981), 410 Satkhandagama, 48 Sierpinski,´ K., 341 Saunderson, N. (1682–1739), 194 Sierpinski,´ W.F. (1882–1969), 358–359 Savile, H. (1549–1622), 148 Simonis, E. (1810–1893), 148 Savio, M. (1942–1996), 439 Simplicio, 153 Sawyer, W.W. (1911–2008), 16 Simplicius (about 520), 89 Saxena, N. (1981), 33 Simpson, T. (1710–1761), 205–206 Scarlatti, G.D. (1685–1757), 427 Singh, H.K., 418 Schauder, J.P. (1899–1943), 383 Siu, Yum-Tong (1943), 447 Scheffers, G. (1866–1945), 295 Sixtus IV, Pope (1414–1484), 130 Schering, E.C.J. (1824–1897), 301 Skolem, A.T. (1887–1963), 332 Scheutz, E., 28 Slater, J.C. (1900–1976), 368 Scheutz, P.G. (1785–1873), 28 Sloan, A.P. (1875–1966), 431 Schlömlich, O.X. (1823–1901), 279 Sloane, N.J.A. (1939), 442–443 Schmidt, E. (1876–1959), 304 Smale, S. (1930), 438–439 Schneider, T. (1911–1988), 320 Smith, B., 180 Schnirelmann, L.G. (1905–1938), 403 Smith, D.E. (1860–1944), 111 Schoen, R. (1950), 447 Smith, H.J.S. (1826–1883), 111 Schöenflies, A.M. (1853–1928), 291 Smith, J., 242 Scholasticus, S. (380–450), 97 Smith, P.A. (1900–1980), 447 Schoute, P. (1846–1923), 315 Smith, R. (1689–1768), 197 Schröder, E. (1841–1902), 294 Smith, W., 242 Schrödinger, E. (1887–1961), 371 Smullyan, R.M. (1919), 427–428 Schubert, H. (1848–1911), 427 Snell, W. (1580–1626), 157 Schumacher, E., 393 Sobolev, S.L. (1908–1989), 30 Schur, I. (1875–1941), 339–340 Socrates (around 469–399), 64 Schwartz, J.T. (1930–2009), 437–438 Sohncke, L. (1842–1897), 243 Schwartz, L.-M. (1915–2002), 424 Solomon, L., 310 Schwarz, K.H.A. (1843–1921), 297–298 Solon (around 638–559 BC), 50 Sciama, D.W.S. (1926–1999), 395 Somayaji, N. (around 1444–1544), 131 Scott, C.A. (1858–1931), 312–313 Somayaji, P. (around 1600–1740), 165 Scott, D.S. (1932), 401 Somerville, M.F. (1780–1872), 231–232 Segal, I.E. (1918–1998), 422 Somerville, W. (1771–1860), 231 Seifert, H. (1907–1996), 341 Sommerfeld, A. (1868–1951), 306 Selberg, A. (1917–2007), 421 Speiser, A. (1885–1970) Senator, F.M.A.C. (490–585), 102 Spence, P., 334 Seneca (4 BC-65 AD), 151 Spole, A. (1630–1699), 201 Senff, K.E. (1810–1849), 223 Sponius, 140 Serre, J.-P. (1926), 434–435 Sporus of Nicaea (around 240–300), 94 Serret, J.A. (1819–1885), 223 Sridhara (before 486), 100 Shafarevich, I.R. (1923), 434 Sripati (around 1019–1066), 116 Shah, S.M. (1055–1092), 116 Stabius, J., 141 Name Index 475

Steenrod, N.E. (1910–1971), 421 Theaetetus (around 417–369 BC), 70 Stein, E.M. (1931), 45 Theano of Crotona (about 546 BC), 60 Steiner, J. (1796–1863), 244 Theodoric (King) (454–526), 99, 102 Steinhaus, H.D. (1887–1972), 372 Theodorus of Cyrene (about 431 BC), 68 Steinmetz, C.P. (1865–1923), 325–326 Theodosius of Bithynia (around 160–100 BC), Stevin, S. (1548–1620), 147–148 96 Stieltjes, T.J. (1856–1895), 339 Theon of Alexandria (about 390), 75 Stifel, M. (1486–1567), 134 Theophrastus (around 371–287 BC), 75 Stirling, J. (1692–1770), 199 Theudius (about 350 BC), 70 Stobaeus (about 500), 73 Theuth, 49 Stokes, G.G. (1819–1903), 269–270 Thibaut, G. (1848–1914), 40 Stolz, O. (1842–1905), 315 Thiele, R., 321 Stone, M.H. (1903–1989), 383 Thiele, T.N. (1838–1910), 289 Stott, A.B. (1860–1940), 315–316 Thom, R. (1923–2002), 419 Stott, W., 315 Thomson, J.J. (1856–1940), 367 Straus, E.G. (1922–1983), 407 Thomson, W./Lord Kelvin (1824–1907), 15 Stroock, D.W. (1940), 445 Thrasyllus of Mendes (around 50 BC-36 AD), Strutt, J.W., 242 87–88 Sturm, J.C.F. (1803–1855), 250–251 Threlfall, W. (1888–1949), 341 Sudhrut, A. (before 600 BC), 53 Thucydides, 64 Sulbasutras (about 3200 BC), 40–41 Thymaridas of Paros (around 400–350 BC), 8 Sullivan, A. (1842–1900), 304 Tiberius, Emperor (42 BC-37 AD), 88 Sumanthu, 38 Timaeus of Locri (around 420–380 BC), 69 Sushruta (before 800 BC), 53 Tippett, L.H.C. (1902–1985), 381 Swami, P., 86 Todd, J. (1911–2007), 408 Sylvester II, Pope (945–1003), 114 Todd, O.T. (1906–1995), 408–409 Sylvester, J.J. (1814–1897), 262–264 Toeplitz, O. (1881–1940), 373 Szabó, Á. (1913–2001), 21 Tokugawa, L.S. (1662–1712), 180 Szegö, G. (1895–1985), 373 Tomlinson, R.S. (1941), 32 Szemerédi, E. (1940), 422 Tooke, M., 191 Szilard, L. (1898–1964), 349 Toomer, G.J. (1934), 105 Torricelli, E. (1608–1647), 168 Trénel, L.-A., 326 T Trilokaprajnapti, 48 Takagi, T. (1875–1960), 321 Tschebatorew, N.G., 66 Talmud, M., 347 Tsetlin, 422 Tamagawa, T. (1925), 410 Tsu, Sun (about 400), 98 Taniyama, Y. (1927–1958), 167 Tukey, J.W. (1915–2000), 423 Tao, Terence Chi-Shen (1975), 450–451 Turán, P. (1910–1976), 351 Tarski, A. (1902–1983), 393–394 Turing, A.M. (1912–1954), 416–417 Tasso, 152, 202 Turing, J.M. (1873–1947), 416 Tate Jr., J.T. (1925), 453–454 Turing, S. (1881–1976), 417 Tauber, A. (1866–1942), 384 Turnbull, H.W. (1885–1961), 366–367 Tayler, R.J. (1929–1997), 416 Tzitzéica, G. (1873–1939), 296 Taylor, B. (1685–1731), 198 Tzu, Mo (around 470–391 BC), 154 Taylor, R. (1962), 167 Telauges (about 500 BC), 60 Teller, E. (1908–2003), 349 U Teresa, 325 Ulam, S.M. (1909–1984), 389 Thales of Miletus (around 625–545 BC), Unguru, S. (1931), 410 50–51 Urban IV, Pope (1195–1264), 122 Thasus, 70 Urysohn, P.S. (1898–1924), 360 476 Name Index

V von Tschirnhaus, E.W. (1651–1708), 188 Vaisampayana, 38 von Walterhausen, S. (1809–1876), 230 Valmes, P., 143 van Beethoven, L. (1770–1827), 225 van Ceulen, L. (1539–1610), 145 W van der Pol, B. (1889–1959), 380 Wabewski, T. (1896–1972), 388 van der Waals, J. (1837–1923), 292 Wallace, A.R. (1823–1913), 381 van der Waerden, B.L. (1903–1996), 355 Wallace, W. (1768–1843), 231 van Roomen, A. (1561–1615), 146 Wallis, J. (1616–1703), 169–170 van Schooten, F. (1615–1660), 168–169 Wallman, H. (1915–1992), 401 van Waveren Hudde, J. (1629–1704), 174–175 Wallmarks, V.A., 328 Vandermonde, A.-T. (1735–1796), 210–211 Wantzel, P. (1814–1848), 262 Varadhan, S.R.I.S. (1940), 444–445 Ward, S. (1617–1689), 176 Varaha, 38, 40 Waring, E. (1736–1798), 212 Varahamihira, D. (working 123 BC), 86–87 Warner, W. (1563–1643), 150 Variar, S. (around 1500–1600), 137 Waterman, A.T. (1892–1967), 450 Varignon, P. (1654–1722), 189 Watson, G.N. (1886–1965), 369 Varman, S. (1800–1838), 245 Weaver, W. (1894–1978), 387–388 Veblen, O. (1880–1960), 342 Weber, E. (1795–1878), 18 Venn, J. (1834–1923), 288 Weber, H. (1842–1913), 390 Verdet, É. (1824–1866), 297 Weber, S.V., 373 Verhulst, P.F. (1804–1849), 252 Weber, W. (1804–1891), 228 Vidhula, 40 Wecklein, A., 390 Viéte, F. (1540–1603), 145–146 Wedderburn, J.H.M. (1882–1948), 357–358 Vijayanandi (around 940–1010), 113–114 Wéfá, A. (940–997), 113 Vikramaditya (102 BC-18 AD), 86–87 Weierstrass, K.T.W. (1815–1897), 265–268 Vincent of Beauvais (around 1190–1264), Weil, A. (1906–1998), 409–410 120 Weil, S. (1909–1943), 409 Vincenzio (born 1606), 154 Weinberg, W. (1862–1937), 343 Vinogradov, I.M. (1891–1983), 381–382 Weldon, W. (1860–1906), 312 Virahanka (about 600 AD), 103 Wendroff, B. (1930), 434 Virasenachary, 47 Wendt, H., 341 Virgil (70–19 BC), 151, 202, 204, 238 Wessel, C. (1745–1818), 221 Virginia (1600–1634), 154 Weyl, H. (1885–1955), 365–366 Vitali, G. (1875–1932), 338 Weyl, L., 365 Vitruvius (around 75–15 BC), 81 Whately, R. (1787–1863), 280 Voltaire, F. (1694–1778), 80 Whewell, W. (1794–1866), 232 Volterra, V. (1860–1940), 316 Whiston, W. (1667–1752), 194 von Dyck, W.F.A. (1856–1934), 329 White, L.A. (1900–1975), 15 von Eötvös, L.B. (1848–1919), 373 Whitehead, A.N. (1861–1947), 317–318 von Goethe, J.W. (1749–1832), 16 Wiberg, M. (1826–1905), 28 von Harnack, A. (1851–1930), 305 Widmann, J. (1462–1500), 140 von Helmholtz, H. (1821–1894), 278 Wien, W.J. (1864–1928), 391 von Humboldt, A. (1769–1859), 218 Wiener, N. (1894–1964), 384–385 von Kármán, T. (1881–1963), 340 Wigler, M. (1947), 438 von Lindemann, C.L.F. (1852–1939), Wigner, E. (1902–1995), 349 305–306 Wigner, M. (1904–2002), 394 von Mises, H.G. (1893–1973), 361 Wilder, R.L. (1896–1982), 412 von Mises, R.E. (1883–1953), 361 Wiles, A. (1953), 167 von Neumann, J.L. (1903–1957), 396–399 Wilkes, M.V. (1913–2010), 30 von Peuerbach, G. (1423–1461), 130 Wilkie, 215 von Seidel, P.L. (1821–1896), 274–275 Wilkins, J. (1614–1672), 176 von Staudt, K.G.C. (1798–1867), 251 Wilkosz, W. (1891–1941), 382 von Strasznicky, L.R.S. (1803–1852), 279 Wilks, S.S. (1906–1964), 423 Name Index 477

William of Moerbeke (1215–1286), 122 Y William, W. (1667–1752), 194 Yahweh, Lord, 44 Wilowski, M.J., 394 Yamabe, H. (1923–1960), 319 Wilson, E. (1879–1964), 292 Yau, Shing-Tung (1949), 447–448 Wingate, E. (1596–1656), 164 Young, G.C. (1868–1944), 303 Wittegenstein, L.J. (1889–1951), 302 Young, W.H. (1863–1942), 323 Woepcke, F., 117 Yu (Yii), Great Emperor (around 2200–2100 Wolf, J.R. (1816–1893), 403 BC), 94 Wolff, C. (1675–1715), 202 Wolfskehl, P.F. (1856–1906) Woodhouse, R. (1773–1827), 224 Z Wren, C. (1632–1723), 157 Zaremba, S. (1863–1942), 323–324 Wright, E. (1561–1615), 151 Zariski, O. (1899–1986), 409 Wright, E.M. (1906–2005), 410–411 Zenarchus, 75 Wright, S.G. (1889–1988), 18 Zeno of Citium (around 334–262 BC), 81 Wronski, J.M.H. (1776–1853), 255 Zeno of Elea (around 495–435 BC), 62–63 Zenon, 99 Zermelo, E. (1871–1953), 331–332 X Zhukovski, N.Y. (1847–1921), 301 Xenocrates of Chalcedon (around 396–314 Zippin, L. (1905–1995), 319 BC), 72 Zoccolanti, F., 136 Xenophon, 18 Zuse, K. (1910–1995), 415–416 Xylander, G. (1575), 144 Zygmund, A. (1900–1992), 376 Subject Index

A Algoritmi de numero Indorum, 106 Abaci, construction of, 26, 114, 236 Altars, precisely measured, 5 Abacus Amphetamines, 420 Chinese, 25 Analysis, quantitative, 26, 284 Russian, 236 Anatomy, 53, 200, 286 wax, 25 Anchor Ring, 342 Abdominal aortic aneurysm, 349 Androgyny, 56 Aberration, spherical, 115 Anecdote, 51, 146, 200, 230, 322, 344, 349, Abodes of different devatas, 39 352, 374, 380, 384 Abraham–Lorentz–Dirac force, 395 Anemia, pernicious, 295 Abstract, shortest possible, 37 Anemometer, 177 Accident, carriage, 173 Anesthesia, 53 Accounting, 89 Angina pectoris, 184 Acoustical diaphragms, 224 Angula, 48, 110 Acoustics, 10, 159, 208, 222, 278, 328, 377 Anthropology, 372 Actuarial science, 13, 18, 191 Antichrist, 149 Adda in Bengali, 387 Anti-electron, 395 Adjoint, 218, 337, 395 Antikythera, 26, 89 Aerodynamics, 301, 329, 340, 341, 361 Antilogies, 64 Aerostatics, 216 Antinomies, 14 Aesthetics, 18, 92, 363, 442 Antinomy, Russell’s, 333 Agarwal–Kayal–Saxena (AKS) primality test, Antiquity, 2–4, 9–11, 21, 50, 78, 82, 84, 85, 33, 34, 36 96, 146, 218 Ages, seven, 56 Anti-typhoid vaccines, 383 Agnesi, witch of, 209 Apameia, 85 Agni (15,400 verses), 38 Apeiron, 52 Airfoil design, 363 Aphorism, Einstein’s often-quoted, 334 Alchemical writings, Newton’s, 184 Aplanatic surface, 115 Alchemy, 140, 149, 185 Apocryphal story, 154, 205 Algebra, computer, 8 Apoplexy, 188 Algorithm Appendix, ruptured, 324 non-numerical, 27 Approximation, 9, 12, 13, 23, 41, 42, 44, 78, oldest known, 23 83, 86, 92–94, 99, 115, 127, 128, 154, semi-numerical, 27 171, 195, 207, 242, 271, 272, 279, 297, ALGOrithmic Language (ALGOL) 68, 31 310, 340, 341, 348, 370

© Springer International Publishing Switzerland 2014 479 R.P. Agarwal, S.K. Sen, Creators of Mathematical and Computational Sciences, DOI 10.1007/978-3-319-10870-4 480 Subject Index

Aqen, the ferryman, 3 Atom, motion of the, 67 Arabic numerals, 365 Automatic Computing Engine (ACE), 28 Aranyakas (theologies), 38 Automatic sequence controlled calculator Aratus’ Phaenomena,94 (ASCC), 29, 407 Archaeology, 66 Automotive engineering, 340 Archimedes’ axiom, 20, 79 Axiom, 14, 18, 20, 21, 75, 79, 241, 250, 285, Archimedes’ death, 80 301, 302, 313, 318–320, 322, 332, 359, Archimedes’ number, 79 374, 405, 406, 421, 440 Archimedes’ paradox, 79 Axiom of Archimedes,20 Architecture, von Neumann, 28, 398 Ardhacheda, 47, 48 Ardha-jya, 42 B Arithmetic(s) Baboon’s fibula, 2 of algebras, 337 Backus–Naur form (BNF), 31, 432, 436 binary, 28, 186 Ballistics, 29, 245, 333, 390, 397 computational, 118 Bamboo sticks, 25 infinite, 314 Bark fibers thread, 53 multiple-modulus residue, 98, 450 Barometer, 168, 177, 187, 198 operations (Ganit), 38 Baudhayana, 6, 40, 41 p-adic, 450 Beads, mounted, 26 ARPANET, 32 Belief(s) Arthashastra, 18 Aristotelian, 103 Artificial intelligence, 25, 294, 398, 425, 435, in Gods, 67 436 religious, 37 Art of Computer Programming, 442 in spirits, 54 Aryabhatteeyabhashya,86 Bell curve, 277 Aryabhattiyam, 21, 42 Bhagavad Gita, 38, 409 Asanna, 42 Bhagavata (18,000 verses), 38 ASCC. See Automatic sequence controlled Bhagavata Purana, 38, 150 calculator (ASCC) Bhagvati Sutra, 45, 47 Assassination, 199 Bhatnagar–Gross–Krook (BGK) model, 418 Asteroid, 156, 187, 227, 291, 380, 416, 433, Bhavishya,38 436 Bijaganitam, 100 Asthadhyayi,60 BINAC, 30 Astigmatism, 247 Binary system, 28, 186 Astrology Bindu, 39 Hindu, 87 Bioinformatics, 361, 438 horoscopic, 105 Biologist, evolutionary, 312, 380, 381 predictive, 87 Biometrics, 18 Astronomer Birch barks, 84 Bible of planetary, 227 Black body radiation, 280 Yavana (not Greek), 87 Black holes, 416, 447 Astronomy Blood transfusion, 407 Aristotle’s view of, 152 Blueness of the sea, 377 descriptive, 224 BNF. See Backus–Naur form (BNF) Greek, 87 BNF notation (Backus–Naur form), 31 Indian, 87 Body, seven parts of the, 56 Atharvaveda, 38, 39, 365 Bohr–Einstein debate, 367 Atlas Coelestis, 187 Bone Atlas, Farnese, 85 dead, 163 Atmosphere, 115, 190, 191, 206, 222, 376, Ishango, 2 385, 415, 422 Lebombo, 2 Atomic collisions, 412 tumor, 432 Atomic model, Bohr’s, 367, 393 Bosons, 386 Subject Index 481

Boyle’s law, 176 Christ, horoscope of, 139 Brahma (24,000 verses), 38 Chromatic aberration, 228 Brahmanas (rituals), 38 Chudamani Maheshvar, 100 Brahmanda (12,000 verses), 38 Cipher, undecipherable, 240 Brahmavaivarta (18,000 verses), 38 Circle squaring, 41, 88, 94, 96, 259, 305 Bridges, arches of, 152 Clay tablet, 2, 6, 23 Bronchial trouble, 239 Clerk, accounts, 369 Brotherhood, secret,55 COBOL, validation software for, 408 Bugs, 73 Cock-fight, 110 Bull-choking sandwich, 78 Collar, leather, 180 Bushel, 104 Colleague, vindictive, 177 Butterfly effect, 425–426 Colon, double, 157 Color mixing, 413 Colors of flower, 378, 379 C Combination, candle and mirror, 155 Calculator, pocket, 26 Combinatorics, 61, 72, 264, 373, 420, 449, 450 Calculus Comets, 4, 147, 153, 156, 181, 192, 197, 206, absolute differential, 338 207, 211, 219, 268, 269, 292, 436 of finite differences, 186, 198 Comets, artificial, 181 fluxional, 181–183 Communion, 238 lambda, 401 Compass, Geometric and Military, 152 Calendar, Gregorian, 180, 201 Complexity Canal, building of, 93 computational, 442, 446 Cancer, 150, 381, 383, 393, 399, 426, 427, 438 theory, 400, 449 Cannonball, 136, 154, 294 Composite numbers, 20, 82 Canon, Buddhist, 94 Compressible flow, 340 Canons, five astronomical, 87 Computability, 28, 401, 406, 414 Capillarity, 347 Computation Captured (married), 420 error-free, 98, 450 Cardinality for infinite quantities, 299 mental, 225 Cards Computer IBM, 29 analog, 26, 31, 89 punched, 28 Leelavati, 440 Cartography, 10, 75, 210 mechanical, 27, 240 Cataracts, 53, 154 program-controlled, 28 Caterpillar vehicle, 225 proofs, 35, 36 CAT scans, 11 security, 446–448, 450 Causality, 67, 396 simulation, 26 CDC 6600, 434 stored-program, 28, 30 Chakravala method, cyclic, 7, 101 virus, 446 Chakra-yantra, 43 Computing platform, distributed, 27 Chalk and slate, 25 Computing, time-sharing and parallel, 435, 438 Chandas (meter), 39 Concentration Chandrasekhar limit, 416 camp, 330, 388, 419 Chaos, 16, 18, 40, 52, 91, 217, 307, 426, 446 intense, 37, 78 Charcoal ink, 25 Congruence, 33, 175, 283, 319, 410 Chariot, mechanical South Pointing, 99 Conics, 76, 83, 97, 135, 200, 243, 312, 365 Cheapest science, 374 Conjecture, 20, 32, 35, 96, 129, 133, 167, 168, Cheating methods, 140 170, 177, 199, 219, 249, 254, 258, 272, Chemical castration, 417 289, 320, 322, 344, 360, 366, 373, 381, Chhandah-shastra, 60, 61 398, 401, 410, 419, 421, 431, 434–436, Chhatra-yantra, 43 438, 439, 444, 447 Chhaya-yantra, 43 Conjecturing, Art of, 158, 189, 208 Chou (literally, “calculating sticks”), 25 Consciousness, 163, 411, 427 482 Subject Index

Consistency, 15, 319, 405, 406, 413, 440 Cyclone, anti, 276 Constellations, 57, 85, 91, 250 Cylinder, volume of the smallest, 11, 79 Constructive proof, 23 Cylindrical helix, 83 Continued fractions, 78, 127, 143, 149, 159, 170, 171, 180, 204, 210, 324, 352, 369 Continuity, 156, 206, 234, 239, 267, 271, 277, D 284, 286, 292 Dancing, 235, 269 Continuum-hypothesis, 330, 332, 359, 406, Danda, 48 440 Dark Things,49 Contradiction, proof by, 23–24 DARPA/ISTO, 438 Convolutions, 189 Darwinism, 311 Coordinates Dasha, 110 of latitudes, 107 Data polar, 189, 197 census, 252 rectangular, 162, 246 statistical, 263 Coprime, 33, 219 structures, 442 Corollary, 20, 34 Deacon, 164, 187 Correctness of computer programs, 435 Dead, Book of the,3 Correlation, 53, 276, 277, 381 Deadlock avoidance, 437 Cosmography, 48, 101, 103 Death Cosmology, 45, 46, 48, 317 with clubs, 100 Cosmos, 39, 55, 80 freezing to, 236 Counterexample, 20, 32, 35, 36, 320 threats, 37 Counter-reformation, 155 Debugging, 408 Counting boards, 26, 122 Decad, 56 Counting, zig-zag glyph for, 3 Decidability, 414 Cow-catcher, 241 Decimal fractions, 93, 147 Craft, underwater, 149 Deductive science, 21 Cray XE6 Hopper supercomputer, 408 Delta, Kronecker’s, 278 Creation, process of, 56 Despicable teachers, 373 Cricket match, 344 Determinant, 8, 180, 186, 210, 211, 225–227, Criminology, 277 239, 253, 263, 264, 273, 274, 286, 326, Crowing roosters, 140 328, 341, 366 Cryptanalysis, 109, 417, 448 Deterministic chaos, 426 Cryptography Devil public-key, 448 pact with the, 114 visual, 448 soul to the, 114 Cryptology, 109 wife of the, 209 Crystal diodes, 29 Devouring, 161 Crystallography, 10, 257, 291 Dhanur-yantra, 43 Cube(s), 7, 23, 38, 42, 44, 47, 56, 58, 70, 71, Dharmic life, 39 88, 94, 96, 102, 133, 146, 148, 155, Dhavala commentary, 47 156, 166, 183, 262, 315, 322, 370 Dhikotidakarana, 116 doubling, 68, 84, 262 Dhruvamanasa, 116 of sums, 110 Diabetes, 53, 253 Cubits, 44, 101 Diagram, polar-area, 263 Cuneiform tablets, 4, 6, 7, 11, 43–45 Dialogue on Ancient and Modern Music, 151 Curve Dials, 190 bell-shaped, 209 Dice, 49, 137, 348 catenary, 193 Dictionary, New Hacker’s, 414 fitting, 226 Dictionary of Scientific Biography, 243 Cybernetics, 384 Differences, finite, 186, 198, 214, 232, 265 Cycloid, 152, 165, 169, 171, 173, 174, 179, Differentiability, 319 192 Differentiable curve in space, 253 Subject Index 483

Differentiation Earthquakes, discourse of, 177 fractional, 258 Easter, date of, 202, 226 logarithmic, 189 Eccentric orbits, 83 Diffusion processes, 445 Eclipse Digital signatures, 446 lunar, 86, 88, 91, 104, 113, 116 Diophantus identity, 182 projection of, 113 Dioptra,91 solar, 5, 85, 101, 104, 113, 149 Diphtheria, 306 Ecology, 400 Discourse on Method, 161 Econometrics, 18, 428 Discrete Fourier transform, 32 Ecuador, 26 Discriminant, 263 Edo period, 180 Disease EDSAC 1. See Electronic delay storage bladder, 216 automatic calculator (EDSAC 1) liver, 171 Education, desultory, 231 Dislocations, 53 EDVAC. See Electronic Discrete Variable Dispensator, 26 Automatic Computer (EDVAC) Disposition, affectionate, 156 Egg, yolk of the, 91 Dispute, Newton-Leibniz, 194 Egypt, 5, 18, 21, 43, 49, 50, 54, 58, 59, 66, 67, Distribution of primes, 272, 315, 344, 444 69, 70, 73, 75, 79, 81, 82, 88, 92, 96, Divergence, 125, 193, 228, 245 97, 112, 115, 214, 222, 327, 336, 436 Divinity, 124, 158, 200, 270, 291 Egypt, jewel of, 67 Divisible, infinitely, 73 Eigenvalues, locations of the, 408 Division by two, 2 Eka, 110 DNA as a computational system, 446–447 Elasticity of air, 81 Doctrine of Chances, 195 Elastic vibrations, 233 Dodecahedron, 56, 58, 70, 83, 155 Electric discharge, 246 Dogs, howling, 140 Electricity and magnetism, 216, 228, 233, 242, Door and key to the sciences, 15 278 Double siphon, 81 Electric sparks, 214 Dove, wooden, 68 Electromagnetic radiation, 368 Dragon heads, 91 Electromagnetic waves, 8, 270 Draughts (checkers), 15 Electronic delay storage automatic calculator Dreamer, 163 (EDSAC 1), 30 Drink only water, 55 Electronic discrete variable automatic Drone, 156 computer (EDVAC), 29, 30 Duality, 56, 97, 174, 237, 246, 413, 434, 435 Electronic numerical integrator and computer Duel, forced into a, 261 (ENIAC), 29 Duplication of a cube, 71, 73, 96, 146 Electronic valves (vacuum tubes), 29 Dwarfism, 325 Electron pulses, 28 Dynamic energy, 39 Elements, Latin translations of the, 75 Dysplasia, hip, 325 Elephant, order of the, 367 Elimination, method of, 232 Ellipse, super, 246 E Ellipsoid, 207, 218, 219, 227, 233, 310, 416 Earth Email communication, 32 axis, tilt of the, 82 Embrace, parents, 171 circumference, 42, 82, 85 Embryology, 53, 311 diameter, 46, 78, 234 Empirical rules, 108 hollow, 191 Empty locations, gaps, or discontinuities, to the Moon, distance from the., 78 284 period of the, 156 Encyclopedia, compiler of an, 103 radii, 92 Enemy of Torricelli’s, personal, 169 shadows of, 157 Energy, conservation of, 228 to the Sun, distance from the, 78 Engine, difference, 28, 240 484 Subject Index

ENIAC. See Electronic numerical integrator Fanatics, savage and merciless, 97 and computer (ENIAC) Fascism, 316 Entertainment media, 25 Fast Fourier transform (FFT), 32, 423 Enumeration and comparison of relations, 15 Father of Algebra, 95 Environmental hostility, 37 Fatigue, 237 Epernon, 243 Feminine Divine, 39 Epicycloids, 179 Feminine, union of the first, 56 Epidemiologist, 381 Fencing, 145, 266 Epigrams, 92, 335 Fertile human-land, 38 Epilepsy, 279 Feud, Abusive public, 193 Episode, blind man, 17 Fever, violent, 197 Epistemology, 353 FFT. See Fast Fourier transform (FFT) Epsilon, 84, 420 Fig tree, 282 Equation(s) Fingerprints, 277 determinate, 222 Finger’s breadth, 48 Diophantine, 42, 88, 98, 101, 144, 309, 320 Fire of London, great, 190 for the electron, relativistic, 395 Firmware, 25 integer solution to, 42 Fixed points of recursive programs, 448 logistic, 252 Flatulence, 55 natural, 341 Fluid mass, rotating, 200 solvability of, 277 Fluorescence, 269, 378 using radicals, 252, 262, 317 Fluxions, Doctrine and Application, 197 Equilibria, stable and unstable, 148 Flywheel Masses in Crank Drives, 361 Equinox, spring, 74 Foci, 99, 156 Equivalence of matter and energy, 347 Focused minds, 37, 38 Errors Force conceptual, 152 centrifugal, 174, 207 in reasoning, 76 centripetal, 174 Essential singularity, 310 supernatural, 54 Ether in magnetic fields, 347 Forest management, 304 Etymology, 39 Formalism, Ostrogradsky, 245 Eudoxus, 12, 67, 69–71, 73, 74, 76, 85, 284 Formal language, 18, 31, 394 Eudoxus, Phaenomena of, 85 Formulas, mnemonic for, 148 Eugenics, 277, 312 FORmula TRANslator (FORTRAN), 31, 432 Eunuchs, 47 Fortification, 145, 147, 202, 214 Eureka, 79 Fortune teller, 205 Europe, medieval, 106 Fossil record, 177 Evolutionary approaches, 34 Fractal, 314, 359, 383, 424, 433, 446 Excavation, 202 Fraction Exhaustions, method of, 71, 76 continued, 78, 127, 143, 147, 149, 159, Exile, dreary, 157 171, 180, 204, 324, 352, 369 Exodus of the Israelites, 88 of a point, 62 Expiatory rites, 59 Fractures, 53 Explosion, primus stove, 412 France, Newton of, 216 Exponents, prime, 260 Frauds, 159 Extraordinarily subtle insight, 19 Free speech movement, 439 Extraterrestrial life, 174 Freezing point, 201 Eye of the mind, 69 Frequency components, spectrum of its, 222 Frustum, 11, 45, 49, 91, 93 Functional programming, 31, 401 F Functions Fable of the Bees, 203 calculus of, 240 Fallacies, 20, 76, 249 characteristic, 310 Famine, 156, 271 elementary, 258, 272 Subject Index 485

logarithmic, 48, 178 Graphical computer program, 433 notion of a, 234 Graphical Statics, 340 primitive recursive, 403 Gravitation, universal law of, 212 Fundamental concepts of deduction, 21 Gravity, universality of, 262 Greatest creations of mankind, 18 Grhasthas, 39 G Grid, 162 Gambling, 137, 138, 161, 202, 361 Grooves, carved, 26 Game, lottery, 252 Guitar, 59 Game of Logic, 286 Gun, rapid-fire, 149 Games of chance, 173, 208 Guruvayur, 150 Gang of four, 439 Gynecologist, 342 Ganitasara (Essence of Mathematics), 100 Gyroscope, 140, 325 Ganitatilaka, 116 Ganymede, 152 Garuda (19,000 verses), 38 H Gear mechanism, oldest known complex, 26 Habits, methodical, 156 Gears, ratchet, 81 Hall of Fame for Great Americans, 292 Generalizations, empirical, 339 Hall of Fame, National Inventor’s, 326 Generalized inverse of a matrix, 428 Hall of Fame of India’s National Institution, Generation, spontaneous, 73 429 Genesis 11:4, 45 Hands, using the, 104 Genetics, 18, 308, 312, 361, 381 Harappan period, 42 Genius, universal, 185 Hard disk space, 33 Genomics, 361 Hardware, 25, 27, 29, 33, 414 Geodesy, 11, 227, 269, 284, 289, 295, 337 Harivamsa (16,000 verses), 38 Geography, universal, 96 Harmony of the Worlds, 156 Geologic timescale, 82 Harvard Mark I computer, 28, 407 Geology, 140, 185, 223, 306, 329, 400 Harvest, sheaves of a good, 93 Geometrical paradoxes, 96 Hawk, 86 Geometry Head, large, 16 computational, 6 Health, state of, 56 higher dimensional, 263 Heart attacks, 230, 255, 309, 314, 343, 358, projective, 6, 160, 172, 215, 240, 244, 251, 368, 387, 418, 419, 431 258, 287, 449 Heavenly bodies, position of, 88 German cipher machine, 417 Heaven, map of the, 91 Giddiness, 177 HEC 2M. See Hollerith Electronic Computer Glassblowing, 198 2M (HEC 2M) Glaucoma, 154 Helium II, a liquid, 412 Global communication, 32 Hell, location of, 152 Globe of the stars, 141 Hemoglobin, 384 Glycerin, 378 Heptad, 56 God Herbs, 67 existence of, 73, 205 Heredity, 275–277, 312, 361 Invariable, 101 Hero of the revolution, 439 mind of, 89, 157 Hiker and climber, 415 Goddess Athena, virgin, 56 Hindu–Arabic numeral, 106, 118, 119, 131 Goladhyaya, 100 Hindu Art of Reckoning, 106 Golden mean, 60 Hindustani classical music, 377 Gold pieces, 110 History, chronology of ancient, 82 Gout, 186, 256 Hoax, 115 Govardhan Matha Monastery in Puri, 364 Hollerith Electronic Computer 2M (HEC 2M), Grahaganitam, 100 387 Grantham, 181 Homosexual relationship, 417 486 Subject Index

Honeybee, 275, 420 Internet, 32, 103, 159, 294 Hora Saara,87 Interpolation, 9, 10, 87, 88, 99, 128, 131, 178, Hormone therapy, 417 183, 199, 289, 339, 341, 384 Horoscopes of prominent persons, 107 Intervention, divine, 67, 217, 369 Horse’s hair, 53 Intuition, spirit of, 173 Human-land, fertile, 38 Invasion, Aryan, 21 Hunchback, 325 Irrationals, 3, 23, 34, 41–43, 58, 61, 67, 68, 71, Hydraulic organ, 79 77, 83, 101, 112, 117, 131, 134, 144, Hydrogen bomb, 398 210, 258, 267, 277, 278, 284, 289, 320, Hygrometer, 177 404 Hymn, 38, 39 Itihasa-Purana, 39 Hypercomplex numbers, 255, 358 Hyper-computing facilities in India, 418 Hypertext transfer protocol (http), 32 J Hypotenuse, 6, 41, 58, 96 Jacobites, 199 Hypothesis, generalized continuum, 330, 406 Jain monk, 109 Jambudvipa, 48 Jaundice, 171, 396 I Java, 31 IBM 704 computer, 432 Jaws of animals, 53 Icosahedron, 56, 58, 70, 83, 155, 303 Jesuit priest, 206 Identity, 119, 163, 182, 235, 253, 271, 296 Jewels, nine, 86 Immunology, 446 Jupiter, satellites of, 211 Imposter, 344 Jyotisha, 39, 50 Imprisonment, life, 153, 327 Incommensurable magnitudes, 70 Indestructible part of a line, 62 K Indestructible part of time, 62 Kalpa (ritual), 39 Indian numeral, 118 Karana Padhhathi, 165 India’s first second generation computer, Karmic, finite, 14 ISIJU, 30, 440 Katyayana, 6, 40, 41 Induction, mathematical, 24, 114, 135, 256 Keyboard, octave, 174 Inequalities, 9, 55, 150, 191, 206, 239, 247, Khandakhadyaka (Edible Bite), 88, 104 254, 271, 292, 297, 305, 308, 315, 322, Kidney failure, 147 323, 326, 328, 366, 373, 381, 382, 445, Kithara, 59 446 Knife, stealing a, 262 Infallibility of the Church, 270 Knots, 25, 26, 170, 437 Infinite amount of sex, 66 Knowledge-based systems, 433 Infinite dimensional case, 254 Knowledge, erroneous, 104 Infinite, paradox of the, 109 Knucklebones, 2 Infinitesimals, 12, 71, 101, 125, 129, 156, 165, Kosmos, 59 174, 185, 190, 209, 251, 288, 295, 296, Kronecker’s opposition to Cantor’s work, 267 313, 314, 338 Kuttaka, 7, 42, 137 Infinity of infinities, 14 Influenza, 253, 260, 304, 335, 375 Insane, 115, 225 L Instability, 35 Ladies’ Diary, 205 Integers Laghubhaskariya,86 complex, 227 Lalla’s teachings, 116 smallest, 56 Lamp, shaded, 230 sums of powers of, 158 Lancets, 53 Integrals, volume, 258 Lands, measuring of, 106 Integration, numerical, 12, 29, 269, 333, 398 Land surveying, 11, 114, 117, 241 Intercourse, 60 Languages, four thousand, 3 Subject Index 487

Law Madhyaloka, 48 of continuity, 156, 206 Maga Brahmin, 86 of large numbers, 189, 233, 271 Magic square, pandiagonal, 87 natural, 197 Magnetism, terrestrial, 228 Planck’s, 386 Magnetohydrodynamics, 416 Snell’s, 157 Mahabharata, 38 Stokes’, 269 Mahabhaskariya, 86, 108 Laws of nature, ten, 162 Mahakshobha, 110 Laws of Thought, 265 Mahayuga, 42 Learning, Perverse, 69 Maitrayana, 40 Learning, Revival of, 16 Majority decisions, 213 Least action, principle of, 91 Male and female, both, 55 Lenses, focal length of, 164 Manava, 40 Letters, enciphered, 170 Manchester Mark I, 28 Leukemia, 427 Mango fruits, 110 Life, aristocratic, 196 Manhattan Project, 349, 367, 398, 422 Lightning, 52 Mannheim, Baden, Germany, 294 Light Quantum Hypothesis, 386 Man, primitive, 3–5 Light, speed of, 126, 154 Man, small, 162, 176 Light-years, 234 Manyakheta, 109 Lilavathi Bhasya, 13, 128 Maps Limits conformal, 284, 297, 301, 325, 379 narrower, 262 weather, 276 variable, 228 Maragha, 121 Linear combination, 144, 290 Marbles, gravity-driven, 28 Linga (11,000 verses), 38 Markandeya (9,000 verses), 38 Lobsters, 424 Markov chains, 308, 327 Loci, surface, 76 Marriage and morals, 334 Logarithm Mars, occultation of, 190 common, 158 Martyrs, 163 device called the, 148 Marvelous Merchiston, 148 Napierian, 204 Maryland, 29, 210, 363, 397, 398, 440 natural, 171, 298 Massacre, St. Bartholomew’s Day, 142 Logic Massless rod or cord, 174 computational, 438 Mathematical Analyzer, Numerical Integrator intuitionistic, 400 and Computer (MANIAC), 398 programming, 31 Mathematical art, 8, 93 symbolic, 256, 288, 394, 401, 419 Mathematical Explorations and Excursions, Longitude at sea, 191 404 Lotus flower, 39, 101, 102, 421 Mathematical proof, 19–21, 25, 34, 36, 93, Loudspeakers, 224 131, 205, 299 Love knot, 170 Mathematical puzzles, 342 Lunar year, 65 Mathematician(s) Lune, 11, 65 blind, 194 Lungs, action of the, 200 hyper-pure, 370 and machine, 32 Vedic, 46, 365 M Mathematics Machine computer, 413 general-purpose, 29–31 faulty, 14, 300 learning, 447 prince of, 184, 230 theoretical/hypothetical turing, 28 queen of, 4, 230 Machine-independent programming languages, Sanksrit sutras in, 364 408 uncivilized continent of, 4 488 Subject Index

Mathematics in War Perspective, 334 Mobile phones, 448 Matrimony, 156 Molding, 38 Matrix algebra, 273, 358, 428 Molecular Computation of Solutions, 446 Matsya (14,000 verses), 38 Monads, 186 Matter, first principle and basic form of, 54 monas, One, the, 55 Maxima, 12, 13, 200, 336 Mongol invasion, 120 Mayan ziggurat, 402 Monk, 69, 104, 109, 127, 133, 135 Meat broth, 73 Monsoon season, rainy, 5 Mechanics, quantum, 273, 276, 287, 295, 348, Moon 367, 395, 397, 412 mountains on the, 152 Medallist, youngest gold, 450 waxing and waning of the, 4 Medical imaging, 11 Morality, victorian notion of, 334 Medication, potency of their, 109 Motion Medicinal plants, 53 elastic, 224 Meditation, 39, 161, 184, 322, 364, 379 laws of planetary, 147, 191 Melancholy temperament, 298 six types of, 70 Memory, photographic, 396 Motorized pogo stick, 425 Memory, re-circulating mercury-delay line, 29 Mountaineering accident, 327 Meningitis, 368 Movie Sneakers, 447 Mental calculation, 170, 279 Mozambique, 2 Mental illness, undiagnosed, 318 Mridangam, 377 Mercator charts, 151 Mug, quart, 180 Merchants, three, 110 Mule, 51, 77, 119, 442 Mercury, 29, 77, 155, 156, 190, 191, 198, 206, Multimedia authoring tools, 438 348 Multiplication, rules for the, 143 Meridian at Greenwich, Prime, 247 Muscle contraction, 193 Meruprastaara, 60, 61 Muses, 44, 56, 72 Metalanguage, 394 Mushrooms, poisonous, 198 Metal insert, 147 Music therapy, 59, 109 Metals to gold, 184 Mustard seeds, 46 Metaphysics, 14, 121, 122, 185, 186, 203, 299, Myriad, 79, 102 311, 317, 335, 364 Mystery, unsolved, 365 Metempsychosis, 59 Mystic, number, 155 Meteor shower, Leonid, 269 Mythological monster, 80 Method, “chakravala” (cyclic), 7, 101 Method, least squares, 219 Methods, heuristic (self-educating) search, 433 N Metric spaces, 346, 389 Naked, stripped, 97 Microscope, reflecting, 182 Namagiri, family goddess, 369 Microwave ovens, 33 Naming convention for large numbers, 142 Migraine headaches, 173 Napier’s bones, 29, 148 Milky Way, 152 Narada (25,000 verses), 38 Millennium BC Narayaneeyam Dinam, 150 first, 3 Natural inheritance, 276 second, 5 Natural Knowledge, Principles of, 317 Mimamsa (rituals and spiritual philosophy), 39 Nature, Concept of, 317 Minds as vital tools, 37 Nature, good, lucky celestial, 55 Minerals and plants, properties of, 67 Navaratnas, 86 Minimal cost telephone networks, 442 Navayoni Chakra, 39 Minimal surfaces, 444, 447 Navigation, 11, 141, 147, 148, 150, 217, 414 Minute arc, 130, 151, 158 Navigation instructor, 414 Mirror, Burning, 83, 84, 99, 149 Nazi years, 305 Misnomers, historical, 365 Nearsightedness, 192 Mlechchas, 87 Nebulae, 4, 189 Subject Index 489

Necklace, beautiful pearl, 101 Oil stoves, 286 Negative wealth, 441 Old Testament, 44, 132 Neomartyr, 360 Olive crop, 51 Neoplatonism, Syrian, 94 Olympic soccer (football) player, 367 Neo-positivist, 361 One-third man, 66 Nephritis, 275 Ontology, 353 Neptune, 153, 227, 231, 262, 268 Operating systems, 437 Nerve action potential, 311 Operations, fixed- and floating-point, 29, 34 Netherworld, 3 Opinion, two stood for, 56 Neural networks, 443 Opium, overdose of, 176 Neurosurgery, 432 Optical illusions, 348 Newton, Correspondence of Isaac, 366 Optics, physiological, 180, 214, 278 Newton’s work, plagiarized, 183 Orbits of Jupiter and Saturn, 207 Nile, periodical inundations of the, 50 Organisms, 177, 417 Nirukta (etymology), 39 Origin, “barbaric,” 236 Nitrous acid, 214 Orphic philosopher, 60 Nomad, academic, 362 Overheated room, 223 Nonconstructive proof, 23 Oyster shell, 97, 110 Non-deterministic polynomial time (NP)-hard problem, 34 Nose, prominent, 162 P Notation, good, 318 Padma (55,000 verses), 38 Notion of compactness, 346 Paganism, twilight of, 163 Nuclear fission, 282 Painter, mathematical, 234 Nuclear fusion, 393 Paleontology, 177 Nude, 285 Palm leaves, 2 Number(s) Panava, 86 of atoms, infinite, 66 Panchangam, 43 decomposition of, 260 Pancha-Siddhanta,87 distribution of prime, 444 Paper tape, punched, 29 feminine, even, 55 Parable, 17, 253 first masculine, 56 Parabola, focal properties of a, 83 irrational (illogical or unreasonable), 3 Parabolic reflector, 80 law of large, 189, 233 Paradox not a, 55, 134 liar’s, 308 perfect, 57, 105, 131, 163 Russell’s, 14, 333 theory Paradoxes of the Infinite, 234 computational, 4, 449 Parallax, 107, 129, 152, 234 probabilistic, 4 Parallel zero-knowledge proof, 448 transfinite, 318, 319 Paralysis, 150 Numbering rods, 148 Paramour Pink, 191 Number: The Language of Science, 363 Paranoia, 184 Numerical calculations, lacks any, 76 Parody of the metric system, 442 Nursing, modern medical, 263 PASCAL, 31 Nyaya (law of nature), 39 Pascaline, calculating machine, 25, 186 Patiganita (Mathematics of Procedures), 100 Patrimony, 372 O Peashooters, 247 Oath not to reveal, 55 Pebble, common, 116 Objects beyond our world, 4 Pellets, pierced, 25 Obscurity of the subject, 64 Pendulum in a resisting medium, 232 Occultation, 90, 190 Pensees (Thoughts), 173 Octahedron, 56, 58, 70, 155 Pentagram, the beautiful star, 55 Octave, 119, 174 Periodical, world’s first, 248 490 Subject Index

Persecution, 37, 64, 175, 340, 389 Potential infinity, 12, 73 Personality, vivacious, 176 Power, French unit of, 237 Person of the century, 349 Prakrit language, 300 Perturbations of the planetary orbits, 232 Pressure, barometric, 191 Pharaonic practice, 81 Prime, Mersenne, 32 Philosopher, Neoplatonist, 97 Primes, infinite number of, 24, 77, 219 Philosopher’s death, 82 Primordial female, 39 Philosophy Primordial male, 39 experimental, 197 Princeton Cemetery, 401 founder of, 163 Principle of Maximum Plastic Dissipation, of science, 51, 361 361 Photoelectricity, 347, 349 Principles of Analytical Calculation, 224 Photons, 349, 367, 378, 386 Prisms, volumes of, 11, 45 Physical weakness, 161 Prism, truncated triangular, 11, 93 Physicochemical phenomena, 291 Probability, negative, 395 Physico-mathematics, 208 Problem Physics, elementary particle, 446 birthday, 361 Physiological optics, 180, 214, 278 intractable, 32 Piano keyboard, 119 kissing, 443 Pipe organ, 81 traveling salesman, 446–447 Pirates, 176 Problem, Cattle,79 Plagiarism, Leibniz of, 183 Processor speed, 33 Plague, bubonic, 181 Prodigy, child, 255, 342, 396, 411, 450 Plague, Great, 181 Programming as a scientific discipline, 437 Plane Loci, 83 Progression Planet(s) arithmetic, 48, 49, 96, 144, 195, 254, 385, innermost, 155 405, 451 latitudes of the, 101 with fractional numbers, 100 longitudes of the, 86, 104, 113 geometric, 41, 96, 144 Plant genetics, 361 harmonic, 96 Platonic realm of objects, 353 Projective transformation, 32, 34, 303, 449 Platonist school, 97 Proof Plato’s Academy, 69, 72, 81 direct, 21, 22, 90 Pleuritis, 281 fallacious, 302 Plimpton 322 (a Babylonian clay tablet), 6 geometric, 143 Pneumonia, 162, 250, 265, 267, 334 methods of, 70 Pocket compass, 347 and program verification systems, 438 Points, infinitely close, 12 of the transcendence of e; 276 Poisoning, methods of, 53 ugly, 25 Polarization of the sunlit sky, 415 Proportion, rule of, 164 Polio, 355 Proposition Polish notation, 346 false, 19, 35 Polish underground army, 383 infinite list of, 24 Polyhedron, 155 Protestant sentiment, antipsychic, 155 Polymath, 129, 206, 340 Psychology, differential, 26, 60 Polynomial-time, 32–34, 449 Psychometrics, 277 Polytope, 315 Pump Population hydraulic, 165 dynamics, 351 piston, 81 flour beetle, 252 pressure, 81 fruit fly, 252 suction, 81 Porcelain, inventor of, 188 Puranic view, 88 Postulates, three, 76 Putha-gorus, 59 Potato, 150 Puthumana Illam (Kerala), 165 Subject Index 491

Pyramid, volume of a, 11 Rocket-powered Frisbee, 425 Pythagoreans, fanatic, 61 Roman numeral, 118 Romantic era, 308 Rooster, psychic, 149 Q Roots, recomposition of imaginary, 160 Quadrivium, 55, 56, 69, 102, 114 Rope stretchers, 6, 41, 67 Quantities, impossible, 215 Rotating mass of fluid, 307 Quantum computing, 441 Rotating universes, 406 Quarrel, acrimonious, 193 Rotation, diurnal, 104 Quartan fever, 177 Rote learning, 347 Qubits, 441 Rounding and truncation, 35 Quicksort, 441 RSA data security, 447 quipu (an Inca word meaning “knot”), 26 Ruler and compasses, 66 Russia, invasion of, 236 Russian cipher, 375 R Raasi-gola-sphuta-neeti, 149 Rabbit, pair of, 118 S Radical group, 261 Sadhu (saint), 364 Rajju,48 Sadratnamala, 127 Raleigh’s ship, 150 Sages and Rishis of history, 19 Raman effect, 378 Saint of computers, patron, 103 Rao Paradox, 429 Saint of the Internet, patron, 103 Rarefied gases, 246 Sakhas (recessions)., 38 Rasa, 53, 377 Sakti, 39 Rasi, 300 Sam (United States), 420 Reality, 4, 17, 66, 69, 70, 175, 253, 267, 268, Samadhi, Maha, 364 317, 334, 344, 347, 349, 441 Samaveda,38 Reasoning through a process, 55 Samhita Rebirth, 105 Brihat, 87 Rectangle Charak, 53 square equal to a, 6, 40 Sushrut, 53 triangle equal to a, 6, 40 Samhitas (hymns), 38 Reductio ad absurdum, 23, 65, 90, 300 Samuha, 300 Refraction, atmospheric, 43, 115 Samurai warrior, 180 Regression, linear, 226 Sanatana Dharma, 39, 87 Reincarnation, 59 Sanatorium, 406 Relativity priority dispute, 322 Sand Reckoner, 78, 170 Religion of the Soul, Eternal, 364 Sand-Reckoner, Archimedes, 78 Religious cults, 54 Sangamagramma, 13, 126–127 Renaissance, 112, 121, 122, 144, 164 Sanitation in hospitals, 263 Respiration, 179 Sanskrit scientific manuscripts, 106 Retardation, equatorial, 190 Sanyas, 364 Revelation, whole, 149 Satan, Cantor, and infinity, 427 Revolution, French, 211, 213, 217, 219, 220, Satellite-artificial, 43 222, 235 Satkhandagama, 48 Rheumatic fever, 426 Saturn’s rings, 304 Rhombus, triangle equal to a, 6, 40 Savior, tomb of the, 163 Right-angle triangle, archetypal, 56 Scarlet fever, 426 Rigveda, dictionary for the, 257 Scattering of x-rays by liquid, 378 Rise of divorce, 381 Scholastics, first of the, 100 Rishis, 19, 87 School, Digambara, 48 Ritual sacrifice, 5, 40 School of astronomy and mathematics, Kerala, Robotics, 438 127, 137, 149, 150 492 Subject Index

School of Economics, London, 333 Sightless, 203 School of Mathematics, Jain, 14, 300 Signal processing, 226, 450 Schools of thought, 14, 300 Silicon chip, 31 Science and Humanism, 371 Sine table, construction of a, 87, 108 Science, molecular and microscopic, 231 Singular value decompositions, 291 Science of love, 110 Skanda (81,100 verses), 38 Science of measurement and number, 15 Skating, ice, 235 Science of nonexistent things, 372 Slavery, 210 Science of self-evident things, 15 Slaves to women, 67 Sciences Slide rule, principle of the, 164 exact, 52, 173, 312 Smallpox, 200, 253 queen of the, 230 Smoker, inveterate, 176 Scientific computing, 27 Smoking cigars, 325 Sea-Mirror of the Circle Measurements, 120 Smoothing of Stationary Time Series, 384 Secretiveness, 192 Snake, black, 110 Secrets-military, 327 Soap, film analogy, 341 Seismology, 11, 70 Socrates, pupil of, 68 Self-realized saint, 364 Software, 25, 27, 33, 103, 408, 436, 438 Self-replicating spacecraft, 398 Solar year, Length of the, 89, 111 Semitic Babylonians, 43 Solids, perfect tetrahedron, 70 Sequences, fourteen types of monotone, 14 Solitonic physics, 434 Series Solutions-existence and uniqueness of, 286 divergent, 249, 315, 332 Son Nilakanthan’s arctangent, 179, 186 drowning, 315 summability of, 315 illegitimate, 208 Series of functions, infinite, 13 Sorcery, 146 Series of squares and cubes-summation of, 42 Sorting algorithms, 441 SETL programming language, 438 Soul Set-omniscient, 14, 300, 301 parting of the, 282 Set-perfect, 317 purification of the, 55 Sets-transfinite, 14 Sound, ranging equipment, 358 Set topology, 317 Sour, 53, 183, 353 Setun-70, 31 Space-filling curves, 325, 375 Sexagesimal (base 60), 108 Space Shuttle Columbia, 416 Shankaracharya of Sharadapith, 364 Space-time continuum, 273, 324 Shanku-yantra, 42–43 Space–time–matter, 366 Shastras, 50 Spectroscopy of gases, 246 Shiksha (phonetics and phonology), 39 Spheres Shirsa prahelika, 46 celestial, 113, 156 Shishyadhividdhidatantra, 104 gravitational, 290 Shiva (24,000 verses), 38 Spherical harmonics, 270, 287 Shock waves, 284, 340, 434 Sphuta-nirnaya, 149 Siddhanta Spider-black, 149 Aryabhatta, 42 Spiral Paitamaha, 87 equiangular, 189 Paulisa, 87 logarithmic, 187, 197 Romaka, 87 Spirits, departed, 3 Siromani, 13, 100 Spiritual philosophy, 39 Surya, 9, 87 Spyglass, 152 Vasishtha, 87 Square equal to a rectangle, 6, 40 Siddhanta of Brahmagupta, 107 Square n times in area to a given square, 5, 40 Siddhantasekhara, 116 Squaring a figure, 61 Siddhanta Siromani (Crown of Treatises), 100 Srichakra, 39, 40, 43 Sifr, 118 Sriyantra,39 Subject Index 493

Stability Switches, telephone routing, 29 in a chaotic system, 439 Switching circuits, 425 hydrodynamic and hydromagnetic, Symbol of health, 55 415–416 Symbol of the mathematics, 55 of orbits, 307 System Star caste, 116 binary, 234 heliocentric, 85 dead, 234 Hindu–Arabic decimal, 86 Starvation, 82 Hindu place-value, 106 State of silence, the ultimate state, 379 limitations of the Greek numbering, 78 Statistical mechanics, 291 of weights and measures, 3 Statistics System of Numeral, Sanskrit, 108 Bose, 386 Fermi–Dirac, 395 Statistics and Truth, 428 T Stellar atmosphere, 385, 415 Tables, nautical, 178 Stellar Interiors, 418 Tablets, 2, 4, 6, 7, 11, 23, 43–45 Sterility of a cow, 271 Talismans against evil, 87 Sticks-notches cut on wooden, 2 Tangents, for drawing, 12, 166 Stones-scratches on, 2 Tasso, critique of, 152 Storage and control, separation of, 28 Tata Institute of Fundamental Research Story, apocryphal, 205 Research Automatic Calculator Strange dreams, 140 (TIFRAC), 30 Street brawl, 193 Telescope String aerial (tubeless), 174 knotted, 26 Gregorian, 178 vibrations of, 198 Tensor analysis, 227, 284 Strip of carbon and oxygen atoms, 240 Ternary computer, 31 Stroke, 2, 3, 42, 179, 204, 255, 362, 407 Tetrahedral, congruent, 319 Structured programming, 437 Tetrahedron, 12, 56, 58, 70, 93, 136, 155 Student, rowdy, 263 Theorem Submarines, German, 414 of algebra, fundamental, 7, 160, 226, 238 Suicide by taking cyanide, 417 Aryabhatta, 21, 22 Sulbasutra, 40 binomial, 24, 114, 117, 123, 179, 182 Sun of calculus, fundamental, 13, 128 annual eclipses of the, 113 central limit, 271, 310, 373, 416 diameter, 78 Chinese Remainder, 98 distance, 190 divergence, 228, 245 equator of the, 206 famous false, 239 true longitudes of the, 113 Fermat’s Last, 166, 219, 231, 244, 254, 344 true positions of the, 107 four colors, 36, 302 Sunya, 42 Gödel Completeness, 405 Super, computer, 408 prime number, 219, 226, 272, 326, 328, 343 Supersonic nozzle, 341 proof of Fermat’s last, 231, 260, 305, 344 Supersonic shock waves, 340 Theories, undecidable, 394 Superstitious, 54 Theory Supper, Last, 160 algorithmic complexity, 400 Supreme Fascist (God), 420 Bohr–Kramers–Slater (BKS), 367 Surfaces, minimal, 444, 447 of Brownian motion, 289, 415 Surgical operation, 407 of the circulation of blood, 163 Surveying, 5, 11, 50, 89, 90, 114, 117, 145, of complex iteration, fundamental, 345 241, 295, 337 of errors, 251 Surya Prajnapti,45 of the evolution of the sex ratio, 381 Sutra, Buddhist Diamond, 94 fuzzy set, 14 494 Subject Index

Theory (cont.) Universal Automatic Computer (UNIVAC), 30 Maxwell’s electromagnetic, 347 Universal Truth Machine, 405 measure, 330, 332, 336, 389, 397 Universe proof, 321 center of the, 45, 130 of recursive functions, special, 404, 414 infinitude of the, 268 of relativity, general, 348, 355, 371, 416 Unshaken foundation of science, 15 of relativity, special, 154, 307 Upangas, 39 of the structure of the human brain, 399 Upanishads (philosophies), 38 of superconductivity, 412 Uparagakriyakrama on lunar, 149 Theory for Metamathematics, Recursion, 427 URAL (a big-bodied Russian Computer), 387 Theory of Error-Correcting Codes, 443 Uranus, 80, 231, 262, 268 Theory of Numbers, History of the, 337 Uttaradyyana Sutra,45 Thermometer alcohol, 198 mercury, 198 V Thyagaraja Keerthana, 376 Vacuum tubes, 29–31, 246 Tiger of Bengal, 377 Vaisampayana, 38 Time, sharing computer systems, 435 Vamana (10,000 verses), 38 Tomato picker, automatic, 155 Varaha (10,000 verses), 38, 40 Toothache, 173 Vayu (24,000 verses), 38 Topology, chemical, 240 Vedanga Jyotisha, 50 Tragedies, 37, 66, 327 Vedangas, 39 Trajectories, orthogonal, 183 Vedas, 38–40, 50, 364 Trakeacheda, 47, 48 Vedic meters, 60 Transformations, infinitesimal, 295 Vedic Sulvasutras, 48 Transistors, 31 Veena, 376 Transmigration, 59 Vegetarianism, 369 Transmission control protocol/internet protocol Vehicle, tank-like, 149 (TCP/IP), 32 Venn diagram, 14, 288 Transmutations, 52 Venus, transit, 178, 192 Tree, Steiner, 244 Vietnam War, 439 Triad, three the, 56 Vikalpa, 45 Triangle, 5, 6, 9–11, 20, 22, 24, 39–41, 45, 50, Violent way, 67 51, 56–58, 60, 65, , 75, 77, 85–87, 90, Violin, acoustics of the, 328 91, 96, 114, 119–121, 123, 125, 130, Virginity, 56 136, 147, 148, 153, 160, 166, 172, 202, Virtual private networks, 448 219, 242, 297, 359 Viscosity of liquids, 378 Triangle Pascal’s, 24, 114, 119, 123, 125 Vishnu (23,000 verses), 38 Trilokaprajnapti,48 Vishnu Purana, 38 Triloko Sara,48 Vitamin B12, 295 Truth VLSI design, 447 subjective, 19 Voi d, 67 universal, 19, 405 von Neumann Tuberculosis, 53, 124, 161, 201, 248, 281, 289, architecture, 28, 398 298, 331, 338, 369 bottleneck, 398 Tubes, vacuum, 29–31, 246 Vyakarana (grammar), 39 Turing-complete, 28, 29 Vyasa, 38–40 Turing machine, 28, 417 Typhoid fever-plague of eruptive, 71 W Wandering stars, seven, 56 U War, Trojan, 59 Ulcer, bleeding, 407 Waterclock, 181 Uncertainty principle, 392, 395 Wavelets, 222 Subject Index 495

Web browsers, 448 Y Western drums, 377 Yajurveda, 38, 50 Whales, 50 Yasti-yantra, 43 Whispering gallery, 377 Year, length of the, 42, 43, 116 White Jew, 392 Yoga-sadhana, 364 Windmill (for grinding grain), 242 Yojana, 46, 48 Wind tunnel, 341 Yuktibhasa, calculus text, 13 Wisdom, static, 39 Witch’s spell, 171 Wolf, young, 2 Z Woman-rugged, tireless, 162 Z1, 28 Wood-apples, fragrant, 110 Z3, 28 Work, three types of, 72 Zeeman effect, 309 World, map of the ancient, 92, 107, 141 Zeno’s paradoxes, 62, 63, 74 World War I (1914–1918), 309 Zero World War II (1939–1945), 305 division by, 88 World wide web (www), 32 repeated, 88 the void, 186 X Zodiac, signs of the, 113 X-machine, 421 Zoology, descriptive, 179