V V 25 TABLE GF CGNTENTS g I. INTRODUCTION: Mathematics from the Time cf the First Learned Academies to the Time of the First Mbdern Mathematical Journal. 7 Advances in the Seventeenth Century. 7 Discussien. .. .. 7 Outstanding Mathemticians. 9 Thomas Harriet. .. .. ...... 9 Galileo. .. .. .. 10 Johann Kepler. .. ...... .. 11 John Napier. .. .. 13 william Oughtred. lk Pierre de Fermat. .. .... 15 Rene Descartes. 18 Gerard Desargues. 20 Blaise Pascal. .. 21 John Wallis. .. .... 23 Christiaan Huygens. ... 2k IseacNevton............. 26 Gottfried Wilhelm Leibniz. 29 Academies. .. .. ... 31 The Accademie dei Lincei. .31 The Royal Society of London. .. 32 French Academy of Sciences. .. 3k ‘ . 3 Advances in the Eighteenth and early part of the Nineteenth Centuries. ... 35 Discussion. .. .. 35 Outstanding Methematicians. 38 Jakob and Johann Bernoulli. 38 Brook Taylor. ... .. #0 Abraham Demoivre. .. .. #0 Colin Maclaurin. .. .. #1 Leonhard Euler. .. #2 Johann ae:mr1eb Lambert........*+3+ Joseph Louis Lagrange. A6 Gaspard Menge. .. .. #7 Pierre Simon Laplace. .. #8 Adrien Marie Legendre. .. 50 Niels Henrik Abel. .. 51 Carl Friedrich Gauss. .. 52 Johann Bolyai. ... .. 55 Nicolai Ivanovitch Lobachevski. .. 56 Augustin Louis Cauchy. .. 57 Evariste Galois. .. .. .. 58 Academies. ... ... 60 Berlin Academy. ..... 60 St. Petersburg Academy. .. 61 Royal Society of Edinburgh. 62 Others................65 N II, THE GROTH OF LEARNED SOCIETIES AND JOURNALS, AND USING THE LITERATURE. .. 67 The Growth of Learned Societies and Journals. .. .. .. 67 Using the Literature. .. .. 73 III, AMERICAN MATHEMATICAL SOCIETY. .. 78 History. .. 78 Membership and Advantages. .. 80 Publications. .82 Bulletin. .83 Transactions. .. .8N Colloquium Publications. 86 Mathematical Reviews. .. .. .. 87 Translations. .. .. 90 Others. .. 91 OTHER LEARNED SOCIETIES AND JOURNALS OF THE IV. rmxrsa srAr1«:s................9*+ — National Academy of Sciences National Research Council. 99 Proceedings. .. 98 Mathematics of Computation. 100 The Mathematical Association of America. .101 National Science Foundation. 106 Society for Industrial and Applied Mathematics. .. 108 American Philosophical Society. .. 110 Industrial Mathematics Society. .. lll I 6 I American Statistical Association. 112 Institute of Mathematical Statistics. 112 Association for Symbolic Logic. .. 113 Mathematics Magazine. .. 11A The Operations Research Society of America. .. 115 The National Council of Teachers of Mathematics, . .. 116 Scripte Mathematica. 119 V. LEARNED SOCIETIES AND JOURNALS OF GREAT HUMHL. .... .... .... .... Lw The London Mathematical Society. .. 120 Glasgow Mathematical Association. .. 121 The Mathemtical Association. 123 Quarterly Journal cf Mechanics and Applied Mathematics. 125 The Quarterly Journal of Mathematics. 126 VI. LEARNED SOCIETIES AND JOURNALS OF MmMmY... ... ... ... ... ... 128 Zentralblatt fur Mathematik. 128 Gesellschaft fur Angewandte Mathematik und Machanik. .. .. .. 129 Mathematischen Zeitschrift. .. 132 Mathematische Annalen. .. .. 133 Numerische Mathematik. .... 13h VII. LEARNED SOCIETIES AND JOURNALS OF OTHER cmmnumh. ... ... ... ... ... 136 L 6 L L Az·gentina...............136Union Mathematica Argentina. .. .. 136 L Austra1ia................137 Australian Mathematical Society. .137 Canada.................138 §8”§ä§€§°§+"’“é2„§ä§? €°’?°?"?”I‘6....138 Royal Society of Canada. .. 139 Canadian bäthematical Congress. 1*+0 H01land................ 1*+1 Composite Mathematica. .. 1*+1 India................. 1*+3 Calcutta Mathematical Society. 1*+3 Mexico.................1*+6 Sociedad Matematica Mexicana. .. 1*+6 Po1and........·.........1*+8 Fundamente Ahthematicae. .. .1*+8 Sweden.................150 Acta Mathematica. ... ... 150 VIII. ACIQHINLEDGELGIIWTS. .. .... .. 152 xx. B1aL1ocaA1=·+1Y...............155 X. mm...................160 7Mathematicsfrom the Time of the First Learned Academies to the Time of the First Modern Mathematical Journal ADVANCES IN THE SEVENTEENTH CENTURY Qlssuaaicu The seventeenth century is often taken by historians as the dawn of modern mathematics. This was the period of great advances, such as, Napier's logarithms, Galileo's science of dynamics, Kepler*s laws of planetary motion, Desargue's and Pascal's new geometry, Descartes•s analytical geometry, the theory of probability, Fermat*s number theory, and the calculus of Newton and Leibniz. This period, more than any other, was marked with men who tcwered head and shoulders above the crcwd. The fruitfulness of this period was not confined to mathematics alone, as other intellectual pursuits enjoyed similar gaius. This increase in attention given to in- tellectual endeavors came largely as a result of political, economic, and social advauces of the time. This was a time of strong gaius in human rights, a time that saw machines become economically important, and a time of in- creased awareness of intellectual efforts. This period was the pre·b1rth era of many cf our periodicals which contain mathemtical articles. By the end of the century only seventeen such periodicals had appeared but the eighteenth century saw the inaguaration S increase can be attri- of 210 new such periodicals. This academies. Scientific buted to the formation of learned hold discussions of men of the period began to gather and such groups grew, mathematical interest. As the number of communication. To satisfy there arose an apparent need for periodicals. The most this need we have the formation of the seventeenth important academies of those appearing in Society of London, century are Accademie dei Lincei, Royal The chief function of and the French Academy of Science. results of research but these academies was to publish the in overcoming the they also played a most important role of the day, religious bigotry and scholarly intolerance activity in America In regard to the mathematical to make a brief state- during this century it will suffice colonies. Very few ment concerning the situation in the time; and in those few, schools were established during this The mathematical little attention was given to methematics. farmer needed merely to needs of the settler were few. The The first mathematicians in knew hew to add and substract. as an aid in the study the New'World looked upon mathematics century America produced no of astronomy. Thus seventeenth more interested mathematicians of note. The settlers were land, religicus quar- in the problems of survival in a new feuds, and devising rels, fighting witchcraft, political than they were in tortures for those whom they hated, 9 furthering the cause of science. 6 century One will note in traversing the seventeenth shifts from Italy that the center of mathematical activity came largely to France and England. This northward shift and heating facilities as a result ef advances in lighting atmosphere and the emergence of a more favorable political in northern Europe. sent Thomas Harriet (1560-1621) was the Englishman and map that part by Sir walter Raleigh in 1585 to survey Carolina, His ef the Virginia colony which is new North equations. His mathematical work·was mostly in theory of contained a "Artis Analyticae Praxis" published in 1631 with pe- section devoted to the formation of an equation between selected roots, a statement ef the relationship and intro- the coefficients and the roots ef an equation, greater than, duced the symbole <, and 7for less than and manuscripta there respectively. In one of his unpublished out in the form is a table of binomial coefficients worked used the triangle thirty of a Pascal triangle. Pascal first was also the first years after the death of Harriet. Harriet te recognize imaginary and negative roots. as the Harriet is often referred to by historians even though founder of the English school of algebraists, a 10 4 it has been established that he received credit for some things he didn't do. For instance Mhrley in his bio- graphy of Thomas Harriot stated that one of his manu- scripts contained a well formed analytical geometry but D. E. Smith later found that this section was not Harriot's writing. He was also falsely given credit for the state- ment that an nth degree polynomial has n solutions and Descartes• “Rule of Signs". Some cf these errors were due to insertions in his manuscripta by later writers. He was also an astronomer having discovered sunspots and observed the satellites of Jupiter independent of Galileo at about the same time. Galileo Galileo (l56M—l6h2), a native of Pisa, started his higher education as a medical student at the University of Pisa, but later secured parental permission to change to science and mathematics. While a medical student at the u¤1veee1ty of Pisa, he observed that the pendulous lamp of the cathedral there oscillated with a period independ- ent of the size of the arc of oscillation. He later showed that the period of a pendulum is independent of the pendul- um's bob. At the age of 25 he ecame Professor of Mathematics at the ua1vers1ty of Pisa and while holding this position he performed his famous leaning tower experiments. Due 11 to local controversies he resigned this position in 1591 to accept a similar position at the University of Padua where he had more freedom in his scientific pursuits. Upon hearing of the discovery cf the telescope in 1607 by Johann Lippershein, he made an instrument of his own with which he observed sunspots, mountains on the moon, the phases of Venus, Saturn*s Rings and the four brighter satellites of Jupiter. His observations contradicted the Aristotelian view that the sun