686 



SCIENTIFIC THOUGHT. 



42. 

 Principle of 

 substitu- 

 tion. 



counterpart in the transformation of algebraical forms 

 by the processes of substitution, these latter had 

 already been extensively studied for their own sakes in 

 the theory of algebraical equations, which in the first 

 quarter of the century had undergone a great develop- 

 ment under the hands of two brilliant mathematical 

 talents both lost to science at an early age — the 

 Norwegian Abel and the Frenchman I^variste Galois.^ 

 Like all algebraical expressions, those termed equa- 

 tions were originally invented and commanded attention 



^ Evariste Galois is held to have 

 been one of the greatest mathema- 

 tical geniuses of modern times, who, 

 if he had lived, might have been a 

 rival of Abel: he was born in 1811, 

 and died before he was twenty-one, 

 in consequence of a duel. For a 

 long time his writings remained un- 

 published and unknown, till Liou- 

 ville published them in the 11th vol. 

 of his 'Journal' (1846). Liouville 

 was also the first to recognise the 

 importance and absolute correctness 

 of Galois's method, which, when sub- 

 mitted to the Academy in the year 

 1831, and reported on bj' Lacroix 

 and Poisson, had appeared almost 

 unintelligible. On the eve of his 

 death Galois addressed a letter to 

 his friend Auguste Chevalier, which 

 is a unique document in mathema- 

 tical literature, forming a kind of 

 mathematical testament. He de- 

 sires this letter to be published 

 in the 'Revue Encyclop^dique,' 

 referring publicly the "import- 

 ance," not the " correctness," of his 

 discoveries to the judgment of 

 Jacobi and Gauss, and expressing 

 the hope that some persons would 

 be found who would take the 

 trouble to unravel his hieroglyphics. 

 The first attempt to make Galois's 

 ideas generally accessible is to be 

 found in Serret's ' Algebre Superi- 

 eure' (3rd ed., 1866), but it was 



not till after the publication of i 

 Camille Jordan's ' Theorie des 

 Substitutions' (1870) that the 

 short papers of Galois were recog- 

 nised as containing the germs and i 

 beginnings of an entirely novel and 

 comprehensive mathematical theory, 

 — viz., the " Theory of Groups." 

 The relation between the writings, 

 of Abel and Galois is exhaustively', 

 treated in Prof. Sylow's Paper on^ 

 Abel's work, contained in the ' Me- 

 morial Volume,' 1892, p. 24. Hei 

 there .says: " Le merite de Galois 

 ne consiste pas essentiellement dans 

 ses propositions, mais dans la gener- 

 alite de la methode qu'il appliquaj 

 C'est son admirable theoreme fondan 

 mental qui a donne a la theorie 

 des Equations sa forme definitive, 

 et d'oii est sortie, en outre, la theorie 

 des groupes generalisee, qui est 

 d'une si grande importance, on peut 

 le dire, pour toutes les branches dee 

 mathematiques, et qui deja, entre 

 les mains de Jordan, de Klein, de 

 Lie, de Poincaro et d'autres, a eun 

 richi la science d'une longue suitt 

 de decouvertes importantes." Th( 

 memoirs of Abel and Galois reP 

 ferring to the Theory of Equations 

 have been conveniently edited, iu if 

 German translation, by H. Maserl 

 1889. See also Cayley's article oil 

 " Equation " in the ' Ency. Brit., I 

 § 32. 



