INNATE MATHEMATICAL GENIUS. 



< The same faculty, improved by cultivation, appears to 

 have been possessed by the illustrious Euler, who had not 

 only a most extraordinary memory for numbers to the 

 extent, it is said, of being able to recall the first six 

 powers of any number under 100 but also a kind of 

 divining povjer, by which he perceived, almost at a 

 glance, the factors of which his formulae were composed ; 

 the particular system of factors belonging to the question 

 under consideration ; the various artifices by which that 

 system might be simplified and reduced ; and the relation 

 of the several factors to the conditions of the hypothesis. 

 This power of divining truths in advance of existing 

 knowledge is the special attribute of those mathematicians 

 who have done most for the development of their science. 

 A notable instance of it is furnished by the celebrated 

 formula devised by Newton for the solution of equations ; 

 for although its correctness was proved experimentally by 

 the results of its application in every -conceivable variety 

 of case, its rationale seems to have been unknown to 

 Newton himself, and remained a puzzle to succeeding 

 mathematicians until discovered by the persevering labours 

 of Professor Sylvester, who is himself specially distin- 

 guished for the possession of this highest form of mathe- 

 matical genius. That such a power as Zerah Colburn's 

 should exist in a child who had never been taught even 

 the rudiments of arithmetic, seems to point (as Mr. Baily 

 remarks) to the existence of properties of numbers as yet 

 undiscovered, somewhat analogous to those on which the 

 system of logarithms is based. And if, as he grew older, 

 he had become able to make known to others the methods 

 by which his results were obtained, a real advance in 

 knowledge might have been looked for. But it seems to 

 have been the case with him, as with George Bidder and 

 other " calculating boys," that with the general culture of 



