DOCSLIB.ORG

MATH 4400, History of Mathematics Turn of the 19Th to 20Th Centuries, the Computer Age

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
MATH 4400, History of Mathematics Turn of the 19Th to 20Th Centuries, the Computer Age MATH 4400, History of Mathematics Turn of the 19th to 20th centuries, The Computer Age Peter Gibson January 14, 2020 Leading figures of 1900 (and their successors) Henri Poincar´e(1854-1912) Professor at the Sorbonne P. Gibson Math 4400 2 / 43 David Hilbert (1862-1943) Professor at G¨ottingen P. Gibson Math 4400 3 / 43 Hermann Minkowskii (1864-1909) Professor at ETH Z¨urich P. Gibson Math 4400 4 / 43 Jacques Hadamard (1865-1963) Professor at Coll`egede France P. Gibson Math 4400 5 / 43 Charles Jean de la Valle-Poussin (1866-1962) Professor at Catholic University of Leuven P. Gibson Math 4400 6 / 43 Tullio Levi-Civita (1873-1941) Professor at University of Rome P. Gibson Math 4400 7 / 43 Albert Einstein (1879-1955) Professor at Institute for Advanced Study, Princeton P. Gibson Math 4400 8 / 43 Hermann Weyl (1885-1955) Professor at Institute for Advanced Study, Princeton P. Gibson Math 4400 9 / 43 Minkowski 1872 (aged 8) moved to K¨onigsberg from Russian kingdom 1883 prize of the French Academy of Sciences friendship with David Hilbert, Adoph Hurwitz 1885 doctorate under Ferdinand von Lindemann appointments at Bonn, K¨onigsberg, Z¨urich,G¨ottingen geometry of numbers Minkowski space time P. Gibson Math 4400 10 / 43 Hadamard List of things named after Jacques Hadamard - Wikipedia https://en.wikipedia.org/wiki/List_of_things_named_after_Jacques... List of things named after Jacques Hadamard From Wikipedia, the free encyclopedia These are things named after Jacques Hadamard (1865–1963), a French mathematician. (For references, see the respective articles.) Cartan–Hadamard theorem Cauchy–Hadamard theorem Hadamard product: entry-wise matrix multiplication an infinite product expansion for the Riemann zeta function Hadamard code Hadamard's dynamical system Hadamard's inequality Hadamard's method of descent Hadamard finite part integral Hadamard's lemma Hadamard manifold Hadamard matrix Hadamard's maximal determinant problem Hadamard space Hadamard three-circle theorem Hadamard Transform and Hadamard gate Hadamard–Rybczynski equation Ostrowski–Hadamard gap theorem Retrieved from "https://en.wikipedia.org /w/index.php?title=List_of_things_named_after_Jacques_Hadamard&oldid=679491174" P. GibsonCategories: Lists of things named after mathematiciansMath 4400 11 / 43 This page was last modified on 4 September 2015, at 21:37. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. 1 of 1 17-02-14 4:47 PM Poincar´e Born in 1854 in Nancy, to a prominent family Top prizes in the concours g´en´eral Graduated from the Ecole Polytechnique, then the Ecole des Mines and worked as a mining engineer 1879 doctorate in mathematics from University of Paris under Charles H´ermite 1881 Professor at the Sorbonne (University of Paris) worked in many different areas, including on the three body problem pioneering work in geometry and topology carried out early work on relativity was active in philosophy, and wrote several widely-read popular works P. Gibson Math 4400 12 / 43 Hilbert 1885 doctorate under Ferdinand von Lindemann 1886-1895 lecturer at K¨onigsberg 1895 professor at G¨ottingen 1900 Paris address 1910 Bolyai prize pre-eminent mathematician of his day P. Gibson Math 4400 13 / 43 One sometimes reads of rivalry and dispute between Hilbert and Poincar´e, the leading mathematicians of 1900. This tends to be overstated. Hilbert contributed to many fields, including mathematical physics|his ideas on the foundations of mathematics are sometimes emphasized at the expense of his many other fundamental contributions. Poincar´e'srejection of Cantor's ideas have not been born out by history. P. Gibson Math 4400 14 / 43 The Institute for Advanced Study in Princeton, New Jersey (established 1930) P. Gibson Math 4400 15 / 43 \spaghetti and Levi-civita" P. Gibson Math 4400 16 / 43 P. Gibson Math 4400 17 / 43 According to Einstein, the theory of relativity relies on the work of: Bernhard Riemann (1826-1866) Hermann Minkowski Tullio Levi-civita Hermann Weyl P. Gibson Math 4400 18 / 43 To a certain extent, Hermann Weyl brought Hilbert's legacy and tradition to the US. P. Gibson Math 4400 19 / 43 The Mathematical Origina of Computers Mathematics is sometimes popularly conceived as ethereal and impractical. In certain instances this is true. P. Gibson Math 4400 20 / 43 Radio waves, microwaves Time dilation (Digital electronic) computers Nuclear fission Wireless communication networks Antiparticles Quantum computers The Higgs boson Yet mathematics has a profound power to make predictions about the world that has been manifest again and again. The existence of each of the following was predicted using mathematics (long) before it was confirmed experimentally. P. Gibson Math 4400 21 / 43 Yet mathematics has a profound power to make predictions about the world that has been manifest again and again. The existence of each of the following was predicted using mathematics (long) before it was confirmed experimentally. Radio waves, microwaves Time dilation (Digital electronic) computers Nuclear fission Wireless communication networks Antiparticles Quantum computers The Higgs boson P. Gibson Math 4400 21 / 43 What is a computer? The word computer has a revealing etymology (as illustrated in the historical uses cited by the Oxford English Dictionary, for example). It's meaning has evolved substantially in the last century. P. Gibson Math 4400 22 / 43 Of course the idea of building a machine to carry out computation was not new|but Turing's mathematical analysis revealed unexpected possibilities, which would take many years to realize. Computers The computer revolution is one of the most dramatic transformations of the late 20th century. It's origins are mathematical, and were largely effected by a single publication, A.M. Turing. On comutable numbers with an application to the Entscheidungsproblem. Proceedings of the London Philosophical Society, S2-42(1):230-265, 1937. P. Gibson Math 4400 23 / 43 Computers The computer revolution is one of the most dramatic transformations of the late 20th century. It's origins are mathematical, and were largely effected by a single publication, A.M. Turing. On comutable numbers with an application to the Entscheidungsproblem. Proceedings of the London Philosophical Society, S2-42(1):230-265, 1937. Of course the idea of building a machine to carry out computation was not new|but Turing's mathematical analysis revealed unexpected possibilities, which would take many years to realize. P. Gibson Math 4400 23 / 43 Major scientific developments of the first part of the 20th century include: special and general relativity quantum mechanics the theory of computing Each of these is deeply mathematical. Aside What were some of the internationally important events of the first half of the twentieth century? P. Gibson Math 4400 24 / 43 Aside What were some of the internationally important events of the first half of the twentieth century? Major scientific developments of the first part of the 20th century include: special and general relativity quantum mechanics the theory of computing Each of these is deeply mathematical. P. Gibson Math 4400 24 / 43 Back to Turing Let's look at Turing's paper directly in some detail. Alan Turing (1912-1954) P. Gibson Math 4400 25 / 43 Exercise Question How many Turing tables are there corresponding to a machine having m states and an alphabet of n symbols? P. Gibson Math 4400 26 / 43 Strangely, the ghost of Cantor emerges to tell us: Theorem (Turing) Almost all real numbers are not computable. Recap Theorem (Turing) There exists a universal computing machine. P. Gibson Math 4400 27 / 43 Recap Theorem (Turing) There exists a universal computing machine. Strangely, the ghost of Cantor emerges to tell us: Theorem (Turing) Almost all real numbers are not computable. P. Gibson Math 4400 27 / 43 A Turing complete electronic computer called the ENIAC (=Electronic NumericalIntegratorAndComputer) was completed in 1946. Other, roughly contemporaneous projects include the Electronic Discrete Variable Automatic Computer (EDVAC) (1951) the Colossus (1944) the Z3, developed by Konrad Zuse (∼1943) Physical devices corresponding to Turing machines can be built out of electronic circuits, using vacuum tubes or transistors. A computing machine is said to be Turing complete if, apart from the restriction of finite memory, it is universal. P. Gibson Math 4400 28 / 43 the Electronic Discrete Variable Automatic Computer (EDVAC) (1951) the Colossus (1944) the Z3, developed by Konrad Zuse (∼1943) Physical devices corresponding to Turing machines can be built out of electronic circuits, using vacuum tubes or transistors. A computing machine is said to be Turing complete if, apart from the restriction of finite memory, it is universal. A Turing complete electronic computer called the ENIAC (=Electronic NumericalIntegratorAndComputer) was completed in 1946. Other, roughly contemporaneous projects include P. Gibson Math 4400 28 / 43 Physical devices corresponding to Turing machines can be built out of electronic circuits, using vacuum tubes or transistors. A computing machine is said to be Turing complete if, apart from the restriction of finite memory, it is universal. A Turing complete electronic computer called the ENIAC (=Electronic NumericalIntegratorAndComputer) was completed in 1946. Other, roughly contemporaneous projects include the Electronic Discrete Variable Automatic Computer (EDVAC) (1951) the Colossus (1944) the Z3, developed by Konrad Zuse (∼1943) P. Gibson Math 4400 28 / 43 The ENIAC was used in the development of the hydrogen bomb under the auspices of the Manhatten Project. All the early electronic computers were developed for military purposes. They provided the impetus for computer science as an independent subject. Most early computer science departments at universities grew out of the local mathematics department. Computers are now ubiquitous, and affect daily life in myriad ways. This is just one example of the predictive power of mathematics and its material consequences.
Load more

Recommended publications
  • Arnold Sommerfeld in Einigen Zitaten Von Ihm Und Über Ihn1
    K.-P. Dostal, Arnold Sommerfeld in einigen Zitaten von ihm und über ihn Seite 1 Karl-Peter Dostal, Arnold Sommerfeld in einigen Zitaten von ihm und über ihn1 Kurze biographische Bemerkungen Arnold Sommerfeld [* 5. Dezember 1868 in Königsberg, † 26. April 1951 in München] zählt neben Max Planck, Albert Einstein und Niels Bohr zu den Begründern der modernen theoretischen Physik. Durch die Ausarbeitung der Bohrschen Atomtheorie, als Lehrbuchautor (Atombau und Spektrallinien, Vorlesungen über theoretische Physik) und durch seine „Schule“ (zu der etwa die Nobelpreisträger Peter Debye, Wolfgang Pauli, Werner Heisenberg und Hans Bethe gehören) sorgte Sommerfeld wie kein anderer für die Verbreitung der modernen Physik.2 Je nach Auswahl könnte Sommerfeld [aber] nicht nur als theoretischer Physiker, sondern auch als Mathematiker, Techniker oder Wissenschaftsjournalist porträtiert werden.3 Als Schüler der Mathematiker Ferdinand von Lindemann, Adolf Hurwitz, David Hilbert und Felix Klein hatte sich Sommerfeld zunächst vor allem der Mathematik zugewandt (seine erste Professur: 1897 - 1900 für Mathematik an der Bergakademie Clausthal). Als Professor an der TH Aachen von 1900 - 1906 gewann er zunehmendes Interesse an der Technik. 1906 erhielt er den seit Jahren verwaisten Lehrstuhl für theoretische Physik in München, an dem er mit wenigen Unterbrechungen noch bis 1940 (und dann wieder ab 19464) unterrichtete. Im Gegensatz zur etablierten Experimen- talphysik war die theoretische Physik anfangs des 20. Jh. noch eine junge Disziplin. Sie wurde nun zu
    [Show full text]
  • 50 Mathematical Ideas You Really Need to Know
    50 mathematical ideas you really need to know Tony Crilly 2 Contents Introduction 01 Zero 02 Number systems 03 Fractions 04 Squares and square roots 05 π 06 e 07 Infinity 08 Imaginary numbers 09 Primes 10 Perfect numbers 11 Fibonacci numbers 12 Golden rectangles 13 Pascal’s triangle 14 Algebra 15 Euclid’s algorithm 16 Logic 17 Proof 3 18 Sets 19 Calculus 20 Constructions 21 Triangles 22 Curves 23 Topology 24 Dimension 25 Fractals 26 Chaos 27 The parallel postulate 28 Discrete geometry 29 Graphs 30 The four-colour problem 31 Probability 32 Bayes’s theory 33 The birthday problem 34 Distributions 35 The normal curve 36 Connecting data 37 Genetics 38 Groups 4 39 Matrices 40 Codes 41 Advanced counting 42 Magic squares 43 Latin squares 44 Money mathematics 45 The diet problem 46 The travelling salesperson 47 Game theory 48 Relativity 49 Fermat’s last theorem 50 The Riemann hypothesis Glossary Index 5 Introduction Mathematics is a vast subject and no one can possibly know it all. What one can do is explore and find an individual pathway. The possibilities open to us here will lead to other times and different cultures and to ideas that have intrigued mathematicians for centuries. Mathematics is both ancient and modern and is built up from widespread cultural and political influences. From India and Arabia we derive our modern numbering system but it is one tempered with historical barnacles. The ‘base 60’ of the Babylonians of two or three millennia BC shows up in our own culture – we have 60 seconds in a minute and 60 minutes in an hour; a right angle is still 90 degrees and not 100 grads as revolutionary France adopted in a first move towards decimalization.
    [Show full text]
  • The Ubiquity of Phi in Human Culture & the Natural World
    John Carroll University Carroll Collected Masters Essays Master's Theses and Essays 2020 THE UBIQUITY OF PHI IN HUMAN CULTURE & THE NATURAL WORLD Jennifer Bressler Follow this and additional works at: https://collected.jcu.edu/mastersessays Part of the Mathematics Commons THE UBIQUITY OF PHI IN HUMAN CULTURE & THE NATURAL WORLD An Essay Submitted to the Office of Graduate Studies College of Arts & Sciences of John Carroll University In Partial Fulfillment of the Requirements For the Degree of Master of Arts By Jennifer L. Bressler 2020 Table of Contents I. Introduction…………………………………………………………………………. 2 II. The Early Greeks…………………………………………………………………… 4 III. Algebraic Properties of the Golden Ratio………………………………………….. 11 IV. The Golden Rectangle…………………………………………………….……….. 20 V. Architecture & Design……………………………………………………………… 22 VI. Art………………………………………………………………………………….. 30 VII. Music……………………………………………………………………………….. 38 VIII. The Natural World………………………………………………………………….. 43 IX. Human Anatomy…………………………………………………………………… 52 X. Geometry…………………………………………………………………………… 56 XI. Conclusion……………………………………………………………………………65 1 I. INTRODUCTION What do rabbit breeding, tornadoes, the Chambered Nautilus, a pentagram, the rhythm of a heartbeat, apple seeds, the shape of a credit card, a pinecone, the human ear, DaVinci’s Last Supper, the structure of DNA, a light switch cover, and the structure of galaxies all have in common? Each relates to an extraordinary ratio that is highly efficient in nature, profoundly attractive to the human eye, and some claim, even divinely inspired. This special ratio is referred to as the “Golden Ratio” and is also known as the divine proportion, golden section, and golden mean. The Golden Ratio has a constant numeric value called “phi” (pronounced “FEE,” or “FI”) which is thought to be the most beautiful and astounding of all numbers.
    [Show full text]
  • The Story of Π
    And of its friend e Wheels Colin Adams in the video “The Great π/e Debate” mentions the wheel “arguably the greatest invention of all times,” as an example of how π appeared already in prehistoric times. But square wheels are possible. If the surface of the earth were not flat but rilled in a very special way. For this to work each little rill (arc) has to have the shape of a hyperbolic cosine, a so called cosh curve. By definition, the hyperbolic cosine is ex e x coshx 2 Another appearance by e. As we shall see, π and e are closely related, even though the relationship is far from being well understood. NOTATION In these notes r = radius of a circle d= its diameter, d = 2r C = its circumference (perimeter) A = its area When did people discover that C A ? d r 2 The Story Begins… There are records (skeletons, skulls and other such cheerful remains) that indicate that the human species existed as long as 300,000 years ago. Most of this was prehistory. The following graph compares history to prehistory: The green part is prehistory, the red history. The vertical black line indicates the time to which some of the oldest records of human activity were dated. Ahmes, the scribe Scribes were a very important class in ancient Egypt. The picture shows a statue of a scribe. Ahmes, the scribe of the Rhind papyrus (c. 1650 BC) may have looked much like this guy. In the Rhind papyrus, Ahmes writes: Cut off 1/9 of a diameter and construct a square upon the remainder; this has the same area of the circle.
    [Show full text]
  • Carathéodory, Constantin
    Constantin Carathéodory (September 13, 1873–February 2, 1950) by HEINZ KLAUS STRICK, Germany In 1994, the Greek postal service issued a double stamp devoted to two Greek mathematicians: CONSTANTIN CARATHÉODORY und THALES OF MILETUS. The name of the Greek scientist from antiquity (THALES was active in the sixth century B.C.E.) may sound familiar, for his name is forever linked with a famous theorem in geometry. But who was CARATHÉODORY? CONSTANTIN CARATHÉODORY was born in 1873 in Berlin, the son of a diplomat of Greek origin serving in the Ottoman Empire’s embassy in that city. At that time, a large portion of what is today the country of Greece was under the dominion of the Ottomans. After a temporary sojourn in Constantinople, the family moved to Brussels, where the father assumed the position of ambassador. After the death of CONSTANTIN’s mother, his grandmother took over the care of the boy and his sister, LOULIA. A German servant girl was engaged so that in addition to French and their native Greek, the children would become fluent in German. CONSTANTIN attended primary school in Brussels, but he also spent part of the year in Berlin. The family spent winters on the Italian Riviera. It was during his secondary-school years that his interest in mathematics developed. He twice won the first prize of the Concours généreaux, the Belgian national mathematics competition for advanced secondary-school pupils. CONSTANTIN CARATHÉODORY completed engineering studies at the École Militaire de Belgique and then worked as a civil engineer on Lesbos until the outbreak of the Greco-Turkish War in 1896.
    [Show full text]
  • Indiana Pols Forced to Eat Humble Pi: the Curious History of an Irrational Number
    The History of the Number \π" On Lambert's Proof of the Irrationality of π House Bill #246: the \Indiana Pi Bill" Indiana Pols Forced to Eat Humble Pi: The Curious History of an Irrational Number Edray Herber Goins D´ıade Pi Instituto de Matem´aticas Pontificia Universidad Cat´olica de Valpara´ıso(PUCV) Department of Mathematics Purdue University March 14, 2018 PUCV Pi Day Celebration Indiana Pols Forced to Eat Humble Pi The History of the Number \π" On Lambert's Proof of the Irrationality of π House Bill #246: the \Indiana Pi Bill" Outline of Talk 1 The History of the Number \π" Introduction What is \π"? Approximations to π 2 On Lambert's Proof of the Irrationality of π Bessel Functions Laczkovich's Theorem Lambert's Theorem 3 House Bill #246: the \Indiana Pi Bill" Lindemann's Theorem Squaring the Circle A Bill for an Act Introducing a New Mathematical Truth PUCV Pi Day Celebration Indiana Pols Forced to Eat Humble Pi The History of the Number \π" On Lambert's Proof of the Irrationality of π House Bill #246: the \Indiana Pi Bill" Abstract In 1897, Indiana physician Edwin J. Goodwin believed he had discovered a way to square the circle, and proposed a bill to Indiana Representative Taylor I. Record which would secure Indiana's the claim to fame for his discovery. About the time the debate about the bill concluded, Purdue University professor Clarence A. Waldo serendipitously came across the claimed discovery, and pointed out its mathematical impossibility to the lawmakers. It had only be shown just 15 years before, by the German mathematician Ferdinand von Lindemann, that it was impossible to square the circle because π is an irrational number.
    [Show full text]
  • The Transcendence of Pi Has Been Known for About a Century
    Results in Mathematics Contents 117 J. Bair/F. Jongmans Volume 7/No. 2/1984 Some remarks about recent result Pages 117-250 on the asymptotic cone 119 W. Beekmann/S. C Chang On the structure of summability fields 130 P. Bundschuh/1. Shiokawa A measure for the linear inde- pendence of certain numbers 145 P. L. Butzer/R. J. Nessel/E. L. Stark Eduard Helly (1884-1943) in memoriam 154 A. S. Cavaretta jr./H. P. Dikshit/ A. Sharma An extension of a theorem of Walsh 164 R. Fritsch The transcendence of ir has been known for about a century-but who was the man who discovered it? 184 Y. Hirano/H. Tominaga On simple ring extensions gener- ated by two idempotents 190 J. Joussen Eine Bemerkung zu einem Satz von Sylvester 192 H. Karzel/C. J. Maxson Fibered groups with non-trivial centers 209 H. Meiert G. Rosenberger Hecke-Integrale mit rationalen periodischen Funktionen und Dirichlet-Reihen mit Funk• tionalgleichung 234 G. Schiffels/M. Stemel Einbettung von topologischen Ringen in Quotientenringe Short Communications on Mathematical Dissertations 249 G. BaszenskijW. Schempp TAXT Konvergenzbeschleunigung von Orthogonal-Doppelreihen The Journal Copyright RESULTS IN MATHEMATICS It is a fundamental condition of publication that submitted RESULTATE DER MATHEMATIK manuscripts have not been published, nor will be simulta- publishes mainly research papers in all Heids of pure and applied mathematics. In addition, it publishes summaries of any mathematical neously submitted or published elsewhere. By submitting a field and surveys of any mathematical subject provided they are de- manuscript, the authors agree that the Copyright for their signed to advance some recent mathematical development.
    [Show full text]
  • Abstracts of Talks Presented to the Indiana Section of the Maa
    ABSTRACTS OF TALKS PRESENTED TO THE INDIANA SECTION OF THE MAA 1. Introduction The Spring 2016 meeting of the Indiana Section of the Mathematical Association of America is at Franklin College, March 18–19. The abstracts appearing here are based on text electronically submitted by the presenters. Contributed talks are listed in alphabetical order by presenter. 2. Invited Talks Presenter: Edray Goins, Purdue University West Lafayette Indiana Pols Forced to Eat Humble Pi — The Curious History of an Irrational Number In 1897, Indiana physician Edwin J. Goodwin believed he had discovered a way to square the circle, and proposed a bill to Indiana Representative Taylor I. Record which would secure Indiana’s claim to fame for his discovery. About the time the debate about the bill concluded, Purdue University professor C. A. Waldo serendipitously came across the claimed discovery, and pointed out its mathematical impossibility to the lawmakers. It had only been shown just 15 years before, by the German mathematician Ferdinand von Lindemann, that it was impossible to square the circle because π is a transcendental number. This fodder became ignominiously known as the “Indiana Pi Bill” as Goodwin’s result would force π =3.2. In this talk, we review this humorous history of the irrationality of π.Weintro- duce a method to compute its digits, present Lindemann’s proof of its irrationality (following a simplification by Mikl´os Laczkovich), discuss the relationship with the Hermite-Lindemann-Weierstrass theorem, and explain how Edwin J. Goodwin came to his erroneous conclusion in the first place. Presenter: Colin McKinney, Wabash College Hoosiers, The MAA, and the Indiana Section This talk will chronicle the role some Hoosiers played in the founding of the MAA.
    [Show full text]
  • Mathematicians Timeline
    Rikitar¯oFujisawa Otto Hesse Kunihiko Kodaira Friedrich Shottky Viktor Bunyakovsky Pavel Aleksandrov Hermann Schwarz Mikhail Ostrogradsky Alexey Krylov Heinrich Martin Weber Nikolai Lobachevsky David Hilbert Paul Bachmann Felix Klein Rudolf Lipschitz Gottlob Frege G Perelman Elwin Bruno Christoffel Max Noether Sergei Novikov Heinrich Eduard Heine Paul Bernays Richard Dedekind Yuri Manin Carl Borchardt Ivan Lappo-Danilevskii Georg F B Riemann Emmy Noether Vladimir Arnold Sergey Bernstein Gotthold Eisenstein Edmund Landau Issai Schur Leoplod Kronecker Paul Halmos Hermann Minkowski Hermann von Helmholtz Paul Erd}os Rikitar¯oFujisawa Otto Hesse Kunihiko Kodaira Vladimir Steklov Karl Weierstrass Kurt G¨odel Friedrich Shottky Viktor Bunyakovsky Pavel Aleksandrov Andrei Markov Ernst Eduard Kummer Alexander Grothendieck Hermann Schwarz Mikhail Ostrogradsky Alexey Krylov Sofia Kovalevskya Andrey Kolmogorov Moritz Stern Friedrich Hirzebruch Heinrich Martin Weber Nikolai Lobachevsky David Hilbert Georg Cantor Carl Goldschmidt Ferdinand von Lindemann Paul Bachmann Felix Klein Pafnuti Chebyshev Oscar Zariski Carl Gustav Jacobi F Georg Frobenius Peter Lax Rudolf Lipschitz Gottlob Frege G Perelman Solomon Lefschetz Julius Pl¨ucker Hermann Weyl Elwin Bruno Christoffel Max Noether Sergei Novikov Karl von Staudt Eugene Wigner Martin Ohm Emil Artin Heinrich Eduard Heine Paul Bernays Richard Dedekind Yuri Manin 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Carl Borchardt Ivan Lappo-Danilevskii Georg F B Riemann Emmy Noether Vladimir Arnold August Ferdinand
    [Show full text]
  • MATH 5400, History of Mathematics Lecture 10: 1900
    MATH 5400, History of Mathematics Lecture 10: 1900 Professor: Peter Gibson [email protected] http://people.math.yorku.ca/pcgibson/math5400 February 16, 2017 In 1896 two mathematicians, working independently, proved the prime number theorem. This relied on recent developments in the theory of functions of a complex variable, in particular on results due to Weierstrass. P. Gibson (YorkU) Math 5400 2 / 20 Jacques Hadamard (1865-1963) Professor at Coll`egede France P. Gibson (YorkU) Math 5400 3 / 20 Charles Jean de la Valle-Poussin (1866-1962) Professor at Catholic University of Leuven P. Gibson (YorkU) Math 5400 4 / 20 The end of the 19th century also saw developments in differential geometry, building on, refining and expanding the ideas of Riemann. Just as Maxwell's results rested on the notions and results in vector calculus due to Gauss and others applied to electric and magnetic vector fields, new developments in physics near the turn of the century made essential use of recent ideas in geometry. P. Gibson (YorkU) Math 5400 5 / 20 Tullio Levi-Civita (1873-1941) Professor at University of Rome P. Gibson (YorkU) Math 5400 6 / 20 Hermann Minkowskii (1864-1909) Professor at ETH Z¨urich P. Gibson (YorkU) Math 5400 7 / 20 Minkowski 1872 (aged 8) moved to K¨onigsberg from Russian kingdom 1883 prize of the French Academy of Sciences friendship with David Hilbert, Adoph Hurwitz 1885 doctorate under Ferdinand von Lindemann appointments at Bonn, K¨onigsberg, Z¨urich,G¨ottingen geometry of numbers Minkowski space time P. Gibson (YorkU) Math 5400 8 / 20 Hadamard List of things named after Jacques Hadamard - Wikipedia https://en.wikipedia.org/wiki/List_of_things_named_after_Jacques..
    [Show full text]
  • Carl Louis Ferdinand Von Lindemann
    CARL LOUIS FERDINAND VON LINDEMANN German analyst and geometer Carl Louis Ferdinand von Lindemann (April 12, 1852 – March 6, 1939) was the first to prove that π is transcendental, that is, it is not the root of any algebraic equation with rational coefficients. His methods were similar to those used by Charles Hermite in 1873 to prove that the constant base of the natural logarithms, e, is transcendental. Lindemann’s achievement showed the impossibility of solving the ancient problem of constructing a square with the same area as a given circle using only a straightedge and a compass. Lindemann was born in Hannover, the son of a modern language teacher at the Gymnasium, and his mother was the daughter of the headmaster of the Gymnasium. At the age of two, Ferdinand’s father moved his family to Schwerin, where the young Lindemann attended school. He commenced his mathematical studies at Göttingen in 1870, where he was greatly influenced by Alfred Clebsch, the founder of a branch of algebraic geometry. Lindemann later published his notes from Clebsch’s geometry lectures. As it was the practice of the time for German students to move from one university to another, Lindemann also attended the University at Munich and took his doctorate from Erlangen for a dissertation on non-Euclidean line geometry and its connection with non-Euclidean kinematics and statics, under the direction of Felix Klein. Lindemann toured the great mathematical centers of Europe, visiting Oxford, Cambridge and London in England and spending time in Paris with Michel Chasles, Charles Hermite, and Camille Jordan.
    [Show full text]
  • History of Mathematics the Early Years
    The History of Mathematics From the Egyptians to Archimedes Michael Flicker OLLI Winter 2011 1 Egyptian and Babylonian • 3000 BC to 260 AD • Essentially empirical • Early number systems • Simple arithmetic, practical geometry • Egyptian papyri & Babylonian cuneiform tablets – Mathematical tables – Collections of mathematical problems 2 3 Hieroglyphic & Hieratic Numerals 4 Hieratic & Hieroglyphic 5 Egyptian Arithmetic • The Egyptians could add, subtract, multiply and divide • Multiplication of whole numbers used the method of doubling Example: 57 x 117 1+ 117 2 234 4 468 8+ 936 16+ 1872 32+ 3744 57 6669 6 Primary Egyptian Sources • Rhind Mathematical Papyrus (RMP) – About 1650 BC from writings made 200 years earlier (18 ft x 13 in) – The Recto Table and 84 (87) mathematical problems • Moscow Mathematical Papyrus – – 1850 BC, (18 ft x 1.5 to 3 in) – 25 problems 7 The Recto Table • The division of 2 by the odd numbers 3 to 101 with the answers expressed as the sum of unit fractions • The entrance into the knowledge of all existing things and all obscure secrets. This book was copied in the year 33, in the 4th month of the inundation season, under the majesty of the king of Upper and Lower Egypt, A-user-Re (Aweserre Apopi), endowed with life, in likeness to writings of old made in the time of Upper and Lower Egypt, Ne-ma-et-Re (Nemare Ammenemes III). It is the scribe Ah-mose who copies this writing. 8 Egyptian Fractions & Algebra • Except for 2/3 and possibly 3/4 the Egyptian arithmetic notation only permitted fractions with unity in the numerator • 2/n equivalents in the RMP Recto table 5: 3 15 7: 4 28 9: 6 18 11: 6 66 13: 8 52 104 15: 10 30 17: 12 51 68 19: 12 76 114 21: 14 42 23: 12 276 25: 15 75 … 97: 56 679 776 … • Could multiply and divide mixed numbers • Simple Algebra – A quantity and its seventh, added together give 19.
    [Show full text]