MATHEAIATICAL CONGRESS.

Dominion, Volume 6, Issue 1583, 29 October 1912, Page 3

MATHEAIATICAL CONGRESS.

CAMBRIDGE AND THE APPLIED SCIENCE. The first sitting of the International Congress of . Mathematicians, .which recently hold its fifth meeting nt Cambridge, look place on August 11 in the large .Examination Hull, when Professor Sir George Darwin, president of the Cambridge Philosophical Society, which four years ago, at the Congress at Rome, invited the members to meet at Cambridge, delivered the presidential address. The science of mathematics,* he said, was now so wide and was already so much specialised, that, it might bo doubled whether there existed to-day any man fully . com-, petent to understand mathematical restarch' in all its many diverse branches, and he told them frankly that when ( ho gazed.on some of the papers written , by .men in that room he folt himself iniicli in (ho same- position as if (he,r wore written in Sanscrit. There had been in the past at Cambridge great, pure mathematicians, such as Caylcy and Sylvester, but they might claim without undue boasting that Cambridge University had played a conspicuous part in the advance of applied mathematics. Newton was a glory to all mankind, yet Cambridge* men were proud that he should have, been Lurasoan Professor there. But as regarded the part played by Cambridge, he referred rather to the men of the last hundred years, such as Airy, Adams, Maxwell, Stokes, Kelvin; and other lesser lights, who had marked out the lines of research in applied mathematics as studied at Cambridge University. Up to a few weeks ago there was one man who alone of all mathematicians might "have occupied the place which he (Sir George) held, without misgivings as to his fitness. He meant Henri Poincare. The loss of Franco in his death affected tho whole world.

It afforded an interesting study to ■ attempt to anajyse the difference in (lie lexturo of the minds of pure and applied mathematicians. Sir Francis , Gnlton had pointed out that the pure geometrician must bo endowed with great powers of visualisation. That view was confirmed by Sir George's recollection of«the difficulty of attaining to clear conceptions of the geometry of space until practice in ths art of visualisation had enabled him .to picture clearly the relationship of lines and surfaces to one another. The pureanalyst probably relied far less on visual images, or at least his pictures were not of a geometrical character, He suspected that the mathematician would drift naturally to one branch or another of their scienoe, according to the texture of his mind and the nature of the, mechanism by which he worked. Both tho pure and applied mathematician wro in. search "of truth, biit tho former sought truth in itself and the latter truths about tho universe in which we lived. Tn both fields there, was room for indefinite advance, but it seemed to Sir George that it was easier to find a field for advantageous research in pure than in applied mathematics. Tho appropriate formulation nf the problem !o lie'solved was one of the greatest difficulties which beset tho applied mathematician, and when he had attained to a true insight but too often there remained tho fact that his problem ■ was beyond the reach of mathematical solution.