THE 



POPULAR SCIENCE 



MONTHLY. 



MARCH, 1913 



HENRI POINCARE AS AN INVESTIGATOR 1 



By Professor JAMES BYRNIE SHAW 



UNIVERSITY OF ILLINOIS 



IT has not seemed to me appropriate, nor would there be time, nor 

 should I be able, to enter into an exhaustive study of the life-work 

 of a master-mind like Jules Henri Poincare. Indeed, to analyze his con- 

 tributions to astronomy needs a Darwin ; to report on his investigations 

 in mathematical physics needs a Planck; to expound his philosophy of 

 science needs a Royce; to exhibit his mathematical creations in all their 

 fullness needs Poincare. Let it suffice that he was the pride of France, 

 not only of the aristocracy of scholars, but of the nation. He was in- 

 spired by the genius of France, with its keen discernment, its eternal 

 search for exact truth, its haunting love of beauty. The mathematical 

 world has lost its incomparable leader, and its admiration for the mag- 

 nitude of his achievements will be tempered only by the vain desire tc 

 know what visions he had not yet given expression to. Investigators of 

 brilliant power for years to come will fill out the outlines of what he had 

 time only to sketch. His vision penetrated the universe from the elec- 

 tron to the galaxy, from instants of time to the sweep of space, from the 

 fundamentals of thought to its most delicate propositions. 



In his funeral oration, Painleve, speaking for the Academie des 

 Sciences, said : 2 



He was only twenty-four years of age, when after four years of silent and 

 sustained reflection, he began the series of mathematical publications which 

 leaves us in doubt whether to admire most its surprising profundity or its sur- 

 prising fecundity. 



Whether he attacked the ascension, step by step, of the truths of arithmetic 

 discontinuity, or unloosed the tangle of geometric form, or followed the subtlest 



1 For a biographical sketch of Poincare^ see Revue des deux Mondes, 1912, 

 September 15. Also the second edition of Lebon's book on Poincare has appeared. 



2 Revue du Mois, Vol. 7 (1912), p. 133. 



VOL. LXXXII. — 15. 



