100 THE SQUARING OF THE CIRCLE. 



tial person, has offered a great prize to be given to the one that first 

 solves the problem. As a matter of fact we find the hope of obtaining 

 this large prize of money the principal incitement to action with many 

 circle-squarers. And the author of the book above referred to begs h>s 

 readers to lend him their assistance in obtaining the prizes offered. 



The problem among mathematicians. — Although the opinion is widely 

 current in the unprofessional world that professional mathematicians 

 are still busied with the solution of the problem, this is by no means 

 the case. On the contrary, for some two hundred years, the endeavors 

 of many considerable mathematicians have been solely directed towards 

 demonstrating with exactness that the problem is insolvable. It is, as 

 a rule — and naturally — more difficult to prove that something is impos- 

 sible than to prove that it is possible. And thus it has happened, that 

 up to within a few years ago, despite the employment of the most varied 

 and the most comprehensive methods of modern mathematics, no one 

 succeeded in supplying the wished-for demonstration of the problem's 

 impossibility. At last, Professor Lindemann, of Konigsberg, in June, 

 1882, succeeded in furnishing a demonstration — and the first demonstra- 

 tion — that it is impossible by the exclusive employment of ruler and 

 compasses to construct a square that is mathematically exactly equal 

 in area to a given circle. The demonstration, naturally, was not effected 

 with the help of the old elementary methods; for if it were, it would 

 surely have been accomplished centuries ago; but methods were requis- 

 ite that were first furnished by the theory of definite integrals and de- 

 partments of higher algebra developed in the last decades ; in other 

 words, it required the direct and indirect preparatory labor of many 

 centuries to make finally possible a demonstration of the insolvability 

 of this historic problem. 



Of course, this demonstration will have no more effect than the reso- 

 lution of the Paris Academy of 1775 in causing the fecund race of 

 circle squarers to vanish from the face of the earth. In the future as 

 in the past, there will be people who know nothing and will not want 

 to know anything of this demonstration, and who believe that they 

 can not help but succeed in a matter in which others have failed, and 

 that just they have been appointed by Providence to solve the famous 

 puzzle. But unfortunately the ineradicable passion of wanting to 

 solve the quadrature of the circle has also its serious side. Circle- 

 squarers are not always so self-contented as the author of the book we 

 have mentioned. They often see or at least divine the insuperable 

 difficulties that tower up before them, and the conflict between their 

 aspirations and their performances, the consciousness that they want 

 to solve the problem but are unable to solve it, darkens their soul and, 

 lost to the world, they become interesting subjects for the science of 

 psychiatry. 



