408 



SCIENCE. 



[N. S. Vol. XIX. No. 480. 



c£ the continuum, and the discovery of 

 non-Euclidean geometry. ' ' 



The importance of the advance they had 

 made was fully realized by John Bolyai 

 and Lobachevski, who claimed at once, un- 

 flinchingly, that their discovery or creation 

 marked an epoch in human thought so mo- 

 mentous as to be unsurpassed by anything 

 recorded in the history of philosophy or 

 science, demonstrating, as had never been 

 proved before, the supremacy of pure 

 reason, at the very moment of overthrow- 

 ing what had forever seemed its surest 

 possession, the axioms of geometry. 



15. THE YOUTH LOBACHEVSKI. 



Young Lobachevski at the University of 

 Kazan, though a charity student, and, as 

 seeking a learned career, utterly dependent 

 on the authorities, yet plunged into all 

 sorts of insubordination and wildness. 

 Among other outbursts, one night at eleven 

 o 'clock he scandalized the despotic Russian 

 authorities of the Tartar town by shooting 

 off a great skyrocket, which prank put him 

 promptly in prison. However, he con- 

 tinued to take part in all practical jokes 

 and horse-play of the more daring stu- 

 dents, and the reports of the commandant 

 and inspector are never free from bitter 

 complaints against the outrageous Loba- 

 chevski. His place as 'Kammerstudent' 

 he lost for too great indulgence toward the 

 misbehavior of the younger students at a 

 Christmas festivity. In spite of all, he 

 ventured to attend a strictly forbidden 

 masked ball, and what was worse, in dis- 

 cussing the supposed interference of God 

 to make rain, etc., he used expressions 

 which subjected him to the suspicion of 

 atheism. From the continual accusing re- 

 ports of the commandant to the Eektor, 

 the latter took a grudge against the 

 troublesome Lobachevski, and reported his 

 badness to the curator, who, in turn, with 

 expressions of intense regret that Loba- 



chevski shoiild so tarnish his brilliant 

 qualities, said he would be forced to in- 

 form the minister of education. Loba- 

 chevski seemed about to pay dear for his 

 youthful wantonness. He was to come up 

 as a candidate for the master's degree, but 

 was refused by the senate, explicitly be- 

 cause of his bad behavior. But his friend, 

 the foreign professor of mathematics, now 

 rallied the three other foreign professors 

 to save him, if he would appear before the 

 senate, declare that he rued his evil be- 

 havior, and solemnly promise complete 

 betterment. 



This was the mettle of the youth, the 

 dare-devil, the irrepressible, who startled 

 the scientific sleep of two thousand years, 

 who contemptuously overthrew the great 

 Legendre, and stood up beside Euclid, the 

 god of geometers ; this the Lobachevski who 

 knew he was right against a scornful world, 

 who has given us a new freedom to explain 

 and understand our universe and ourselves. 



16. THE BOY BOLYAI. 



Of the boy Bolyai, joint claimant of the 

 new world, we have a brief picture by his 

 father. "My (13 + |-) year old son, when 

 he reached his ninth year, could do nothing 

 more than speak and write German and 

 Magyar, and tolerably play the violin by 

 note. He knew not even to add. I began 

 at first with Euclid; then he became fa- 

 miliar with Euler; now he not only knows 

 of Vega (which is my manual in the col- 

 lege) the first two volumes completely, but 

 has also become conversant with the third 

 and fourth volumes. He loves differential 

 and integral calculus, and works in them 

 with extraordinary readiness and ease. 

 Just so he lightly carries the bow through 

 the hardest runs in violin concerts. Now 

 he will soon finish my lectures on physics 

 and chemistry. On these once he also 

 passed with my grown pupils a public ex- 

 amination given in the Latin language, an 



