50 & 100 Years Ago

Jeremy Gray

50 Years Ago Nature, October 13, 1934. Giuseppe Peano. Among the eighteen papers in the Rendiconti del Seminario Math- ematico e Fisico di Milano (7, 1933), the longest, and, to the general reader, most interesting is an account of the scientific works of G. Peano, more than two hundred, ranged over pure and applied mathematics, logic, philosophy, grammar, comparative philology, international languages, and even politics. Some early papers dealt with the algebra of invariants. He then tu rned to calculus and differential equat ions . His "space-filling curve" has been described as one of the most remarkable results in the theory of aggregates. Two investigations of the foundations of geometry and arithmetic are of great importance, but his crowning achievement is his system of mathematical logic, with its elaborate symbolism (the 'Peanese' ridiculed by Poincar6), which has been used in England by Russell and Whitehead. Peano applied his logical methods to grammar, and this led to other linguistic studies, in- cluding the invention of the international language In- terlingua. As a contrast to his abstract work may be mentioned his methods for the approximate solution of problems in practical mathematics. He stands out in the history of science as one of the few modern thinkers who have combined p ro found originality with a wide range of activities.

The Indian Mathematical Society. The jubilee com- memoration volume of the Journal of this Society con- tains, in addition to the usual research papers, an ac- count of the history of the Society. It began in a very modes t way in 1907, w h e n Mr. V. R a m a s w a m y Aiyyar, then deputy Collector at Gooty, formed the "Analytical Club", the object of which was to sub- scribe for mathematical periodicals and circulate them among the members . In 1909 appeared the first number of the Journal. By the end of 1910, the name of the Society had changed twice, first to the "Indian Analytical Club" and then to the "Indian Mathematical

Column Editor: Jeremy Gray, Faculty of Mathematics, The Open University Milton Keynes MK7 6AA, England

Society". The number of members, originally about twenty, is now nearly three hundred. A central library is maintained at Poona, and conferences are held bien- nially in different parts of India. The Society is con- ducting an inquiry into the present conditions of math- ematical teaching and examinations in schools and col- leges, with the view of introducing certain reforms, and is also trying to set up prizes for research. It is considering the advisability of dividing its Journal into two parts, an advanced part for the publication of re- search papers, as at present, and a new elementary part, similar to the Mathematical Gazette or the Amer- ican Mathematical Monthly. The achievement of which the Society is most proud is the discovery of the great Indian mathematician Ramanujan whose contri- butions began to appear in the Journal in 1911. In the present volume, the place of honour is given to two papers developing Ramanujan's results.

Science, November 9, 1934. Dr. Hans Rademacher, formerly professor of mathematics in the University of Breslau, has joined the Faculty of the University of Pennsylvania for one year under a joint grant from the Emergency Committee in Aid of Displaced German Scholars and the Rockefeller Foundation. Dr. Rade- macher served on the faculty at the University of Ham- burg before going to Breslau and is known for his re- search work in the analytic theory of numbers, differ- ential geometry and the theory of functions of a real and complex variable.

Bulletin of the American Mathematical Society, De- cember, 1934. Selections from the Table of Life Mem- bership Fees (Rates for other years may be obtained from the Treasurer.).

Age Fee

25 . . . . . . . . . . . . . . $143.37 30 . . . . . . . . . . . . . . . 137.93 35 . . . . . . . . . . . . . . . 131.48 40 . . . . . . . . . . . . . . . 123.88 45 . . . . . . . . . . . . . . . 115.13 50 . . . . . . . . . . . . . . . 105.24

Age Fee

55 . . . . . . . . . . . . . . . $94.36 60 . . . . . . . . . . . . . . . . . 82.74 65 . . . . . . . . . . . . . . . . . 70.71 70 . . . . . . . . . . . . . . . . . 58.81 75 . . . . . . . . . . . . . . . . . 47.56 80 . . . . . . . . . . . . . . . . . 37.44

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100 Years Ago Nature, O c t o b e r , 1884. Simson's Line. Mr. J. S. Mackay of the Edinburgh Academy, though not able to trace "Simson's line" to Simson's works (see my notice of Dr. Casey's "Euclid," Nature, October 23, p. 607) has furnished me with the following account, which may be of general interest: "The theorem that the orthogonal projections of a point on the circum- ference of a circle upon the sides of an inscribed triangle are collinear is ascribed to Robert Simson by Catalan in his 'Th6or~mes et Probl6ms de G6om6trie E16men- taire, ' and he speaks several t imes of 'la droite de Simson. ' This book of Catalan's is, I fancy, bet ter known in the United Kingdom than many other Con- tinental works where the same statement is made; and I conjecture that we have adopted the name from Cat- alan. It may, however, be the case that we have taken the information from Poncelet 's "Propri6t6s Projec- tives,' w where it is said that Servois attributes the theorem to R. Simson. The passage where Servois makes the acription occurs in Gergonne's 'Annales de Math6matiques,' vol. iv. p. 250, and it is unsatisfactory enough: 'La m6thode qui vent d 'e t re indiqu6 plus haut pour d6terminer le point C repose sur le th6o- r~me suivant, qui est, je crois, de Simson.' I cannot carry the ascription of the theorem to Simson farther back than to Servois, and though I am not positive that Servois has made a mistake, yet I think it highly prob- able. The extension of the theorem to the oblique pro- jections is attributed by Catalan to Chasles. It is due to Poncelet, and is given in the section quoted above." The Writer of the Notice, October 27 [i.e., Anon.], and also:

We are glad to learn that the trustees have appointed Prof. N e w c o m b Professor of Mathemat ics and As- tronomy in the Johns Hopkins University, and that he had agreed to accept the position. The University be- gins the session with 273 students, of whom 160 are graduates , and the a t tendance is d is t r ibuted well through all the departments.

Nature, 31, December 18, 1884. Modern English Math- ematics. An address delivered by Prof. Henrici, F.R.S., at the annual meeting of the London Mathematical So- ciety (November 13), on the occasion of presenting the De Morgan Memorial Medal to Prof. Cayley, F.R.S. [concluded:]

It would be an impertinence for me to say much either in praise of Prof. Cayley's work or in justifica- tion of the Council's choice. Prof. Cayley has invented and worked out the theory of invariants, and in steady life-long work connected it with nearly every branch of mathematics, enriching everything he touches, and everywhere throwing open new vistas of future work.

The Council of the Mathematical Society in selecting Prof. Cayley as the first recipient of the De Morgan

Medal, and thus doing homage to his genius, did so not so much with the idea that it could add honour to his name as that they might add honour to the medal by connecting his great name with it, and thus increase its value for all future recipients. And it is befitting that a b o d y like the London Mathematical Society should give formal expression to the reverence and admiration in which it holds the greatest among its members.

Nature, 31, January 8, 1885. According to the North China Herald there died a few months ago at Peking, the greatest Chinese mathematician of the present cen- tury. His name was Li Shan-lan, and he was Professor of Mathematics at the Foreign College in the Chinese Capital. He differed from the mathematicians of Eu- rope in this respect, that he denied the non-existence of a point. "A point," said Prof. Li, "is an infinitesi- ' mally small cube," and in saying this he only repro- duced the theories of Chinese sophists 2000 years ago. A great writer of that age put into the mouth of a sophistical being, w h o m he called the god of the nor thern sea, the fol lowing theory, which has its bearing on Prof. Li's heterodox views about a mathe- matical point: Subtlety is the occult part of the minute. Be a thing subtle or gross, it seems to me that it must have a form. A formless or unsubstantial thing cannot be dist inguished as gross or subtle, discriminate as minutely as you will. What can be spoken of is the gross or palpable part of an entity; what can be imag- ined only is its subtle part of essence; but I take it that what is neither gross nor subtle can neither be talked of nor imagined.

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