DEVELOPMENT OF MATHEMATICAL THOUGHT. 629 



calculating and measuring, that there is really nothing 

 new in mathematics, that two and two always make 

 four, that the sum of the angles in a triangle always 

 make two right angles, and that all progress in mathe- 

 matics is merely a question of intricacy, a never-ending 

 process of increased complication by which you can 

 puzzle even the cleverest calculator. To them the his- 

 tory of mathematics would be something analogous to 

 the history of games like whist or chess, the resources and 

 complications of which seem to be inexhaustible. So they 

 think 1 that the intricacies and refinements of elementary 

 and higher mathematics will supply endless material for 

 training the minds of schoolboys or trying the ingenuity 



1 " Some people have been found 

 to regard all mathematics, after the 

 47th proposition of Euclid, as a 

 sort of morbid secretion, to be 

 compared only with the pearl said 

 to be generated in the diseased 

 oyster, or, as I have heard it de- 

 scribed, ' une excroissance inaladive 

 de 1'esprit humain.' Others find 

 its justification, its raison d'etre, in 

 its being either the torch-bearer 

 leading the way, or the handmaiden 

 holding up the train of Physical 

 Science ; and a very clever writer 

 in a recent magazine article ex- 

 presses his doubts whether it is, in 

 itself, a more serious pursuit, or 

 more worthy of interesting an in- 

 tellectual human being, than the 

 study of chess problems or Chinese 

 puzzles. What is it to us, they 

 say, if the three angles of a triangle 

 are equal to two right angles, or if 

 every even number is, or may be, 

 the sum of two primes, or if every 

 equation of an odd degree must 

 have a real root ? How dull, stale, 

 flat, and unprofitable are such and 

 such like announcements ! Much 

 more interesting to read an account 



of a marriage in high life, or the 

 details of an international boat- 

 race. But this is like judging of 

 architecture from being shown some 

 bricks and mortar, or even a quar- 

 ried stone of a public building, or of 

 painting from the colours mixed on 

 the palette, or of music by listening 

 to the thin and screech sounds pro- 

 duced by a bow passed haphazard 

 over the strings of a violin. The 

 world of ideas which it discloses or 

 illuminates, the contemplation of 

 divine beauty and order which it 

 induces, the harmonious connexion 

 of its parts, the infinite hierarchy 

 and absolute evidence of the truths 

 with which it is concerned, these, 

 and suchlike, are the surest grounds 

 of the title of mathematics to 

 human regard, and would remain 

 unimpeached and unimpaired were 

 the plan of the universe unrolled 

 like a map at our feet, and the 

 mind of man qualified to take in 

 the whole scheme of creation at a 

 glance" (Prof. J. J. Sylvester, 

 Address before Brit. Assoc., see 

 'Report,' 1869, p. 7). 



