12 
Journal of the Mitchell Society. 
[May 
matician, that in 1779 Gauss was still hopelessly attempting 
to prove that Euclid’s was the only non-self-contradictory 
system of geometry, and also the system of our space. Bol- 
yai, the elder, submitted to Gauss, in 1804, a pseudo-proof of 
the parallel-postulate, but Gauss immediately detected the 
fallacy. When Bolyai, the elder, submitted a second pseudo- 
proof to Gauss, in 1808, he never replied. Bolyai’s words, 
accompanying one of these pseudo-proofs, are pathetic in 
their earnestness and yearning: “Oft have I thought, gladly 
would I, as Jacob for Rachel, serve in order to know the par- 
allels founded even if by another. Now just as I thought it out 
on Christmas night, while the Christians were celebrating the 
birth of the Saviour in the neighboring church, I wrote it 
down yesterday, and I send it to you enclosed herewith.” 
On November 23, 1823, Bolyai the son, called Janos, wrote 
a letter to his father, professor of mathematics at Maros- 
Vasarhely, in which he announces his discovery of the non- 
Euclidian geometry — a letter full of youthful fire and enthus- 
iasm, from which I quote: 
“I intend to write, as soon as I have put it into order, and when 
possible to publish, a work on parallels. At this moment it is not 
yet finished, but the way which I have hit upon promises me with 
certainty the attainment of the goal, if it in general is attainable. 
It is not yet attained, butl have discovered such magnificent things 
that I myself am astounded at them. 
“It would be damage eternal if they were lost. When you see 
them, father, you yourself will acknowledge it. Now I cannot say 
more of them, only so much: that from nothing I have created another 
wholly new world. All that I have hitherto sent you compares to 
this only as a house of cards to a castle.”* 
His results were printed as an Appendix to his father’s 
work, entitled Tentamen Juventutem Studiosam in Elementa 
Matheseos Purae , Elementaris ac Sublimioris , Methodo In - 
tuitiva , Evidentia — que huic Propria Introducendi. The two 
dozen pages contributed by the younger Bolyai have been some- 
*The Science Absolute of Space, by John Bolyai, translated by G. B. 
Halsted; Introduction, pp. XXVII, XXVIII. 
