April 22, 1922] 



NATURE 



521 



reason for Brown's behaviour. An admirable Report 

 has just been published in which it has been thought 

 necessary to emphasise the obvious fact, that an 

 English student who intends to pursue a course in 

 the humanities must, first of all, have a sound and 

 fairly extensive knowledge of his own language and 

 literature. Unless this foundation is well and truly 

 laid, the student's equipment is imperfect, and he is 



III severely handicapped at every turn. 



™ Now, mathematics occupies a precisely similar 

 position with regard to a course in science. To give 

 a full justification of this statement is, of course, 

 impossible here ; but an attempt to do so partially 

 will be made by putting an imaginary case. Let us 

 suppose that progress in mathematics had stopped 

 abruptly at the end of the 15th century, a compara- 

 tively recent date in the history of the science. The 

 result would be that physics would be almost entirely 

 empirical ; there would be no theories at all to account 

 for the motions of the heavenly bodies, for the trans- 

 formations and indestructibility of energy ; no general 

 theories, capable of verification, in physical optics, 

 heat, or electricity. It is extremely unlikely, not to 

 say impossible, that instruments like modern tele- 

 scopes, microscopes, spectroscopes, or electric and 

 electromagnetic meters of various kinds, could have 

 been invented. Some, at least, of the consequences 

 involved in this can be seen by everyone who considers 

 the matter. 



To turn to more banausic or, if the reader prefer 

 it, practical considerations : a single example must 

 suffice. Let us suppose that " practical " engineers 

 had succeeded in constructing a steel steamship, 

 approximating to the modern type. (This in itself 

 is taking a good deal for granted.) The induced 

 variations of its compass would have to be corrected 

 by a blind and tedious process of trial ; the skipper 

 would have no Nautical Almanack, no means of deter- 

 mining the exact local time (and consequently his 

 true longitude), no rules to guide him in keeping a 

 great circle course from one given port to another. 

 Similarly biologists and chemists are indebted to 

 physicists and mathematicians for the perfection of 

 their instruments ; and such topics as heredity and 

 Mendelism require for their full discussion a good deal 

 of mathematics. Physiology, too, is becoming daily 

 more dependent on physical theory and mathema- 

 tical formulae ; for instance, a full explanation of the 

 rise of sap in trees must involve a mathematical 

 theory. 



Such examples might be multiplied indefinitely. 

 Let us now turn to another aspect of the question. 

 Benjamin Disraeli, who was by no means the charlatan 

 which some people suppose him to have been, is 

 reported to have said that the best way of gauging 

 the commercial prosperity of a country was to find 

 out the condition of the chemical market. We may 

 venture to assert that the intellectual state of a country 

 may be estimated fairly well by its attitude towards 

 mathematics and its progress therein. In this respect 

 England is much inferior to other and smaller nations. 

 For instance, in England many private libraries have 

 been either given to the nation or placed at the dis- 

 posal of genuine students : very few of these are 

 wholly or mainly mathematical. Contrast with this 



NO. 2738, VOL. 109] 



the Mittag-Leffler endowment, of which an account 

 will be found in Nature of July 6, 1916, p. 384. The 

 founders expressly emphasised the supreme importance 

 of pure mathematics from a national point of view. 

 Again, no one can dispute the practical efficiency of 

 the American nation ; compare their treatment of 

 mathematical professors with ours. An American 

 university teacher may be a specialist devoted to the 

 most abstract and " unpractical " parts of his science ; 

 he is left perfectly free to pursue his researches ; h.. 

 is provided with a sufficient staff of assistants ; the 

 university library contains an ample store of mathe- 

 matical books, and all other necessary equipment is 

 supplied. Every seventh year the professor is relieved 

 of his official duties ; and the use which he generally 

 makes of his respite may be illustrated by the " History 

 of the Theory of Numbers " (now in course of publica- 

 tion), by Prof. L. E. Dickson. His special subject is 

 the highly abstract one of group-theory : but he spent 

 his sabbatical year in ransacking the libraries of 

 Europe, as well as of the United States, for works on 

 the higher arithmetic. The result is an extraordinary 

 display of laborious and accurate research : the first 

 volume alone contains summaries, almost all of them 

 based upon the author's personal examination, of 

 thousands of papers. The value of the work, when 

 complete, can scarcely be overestimated. 



Finally, it is dangerous to neglect mathematics in 

 schemes for a course of general education. From a 

 school teacher's point of view the subject naturally 

 falls into two divisions : (a) computation, drawing 

 (including graphs), mensuration, and surveying ; and 

 (p) the theoretical treatment of the elementary parts of 

 the subject. No attempt should be made at premature 

 specialisation ; the needs of the exceptionally gifted 

 pupils may be met by giving them free access (with 

 occasional advice as to choice) to the school library, 

 which should contain books beyond the scope of the 

 school course, and also biographies of mathematicians 

 and works on the history of the subject. The main 

 results to be desired, in the case of an average student, 

 are these, among others : at the end of his course 

 he should have a correct idea of the importance of 

 mathematics and some acquaintance with its aims 

 and methods, whatever his actual acquirements 

 may be. Above all, he should have acquired the 

 habit of intellectual honesty. A mistake in a mathe- 

 matical exercise cannot be concealed by fudge, or 

 argued about, as in the case of a historical essay or 

 the hke. 



It is most disheartening to find that an organised 

 attempt is being made to restore the study of Greek 

 and Latin to its old position of prestige ; fortun- 

 ately, a number of eminent classical scholars have 

 taken up a reasonable attitude, so that the danger 

 may not be so great as it seems. Moreover, the 

 report already alluded to should convince everyone 

 that even with regard to the humanities it is not 

 Latin-Greek but English that should be made the 

 principal subject in English schools. The great Greek 

 writers had not been condemned, in their school days, 

 to wearisome lessons in Arabic or Hieroglyphics, 

 although everything now argued in favour of Latin- 

 Greek might have been urged equally well in favour 

 of such preposterous procedure. G. B. M. 



