Bolyai, Janos - Geometrical Examinations and Theorem 35
Type of Spiritual Experience
The same spiritual input going to two people. Almost as if the spirit world was hedging its bets.
A description of the experience
In 1848 Bolyai discovered that Lobachevsky had published a similar piece of work in 1829. Kagan writes :-
János studied Lobachevsky's work carefully and analysed it line by line, not to say word by word, with just as much care as he administered in working out the Appendix. The work stirred a real storm in his soul and he gave outlet to his tribulations in the comments added to the 'Geometrical Examinations'.
The 'Comments' to the 'Geometrical Examinations' are more than a critical analysis of the work. They express the thoughts and anxieties of János provoked by the perusal of the book. They include his complaint that he was wronged, his suspicion that Lobachevsky did not exist at all, and that everything was the spiteful machinations of Gauss: it is the tragic lament of an ingenious geometrician who was aware of the significance of his discovery but failed to get support from the only person who could have appreciated his merits.
In spite of his mental agitation amidst which János put observations to paper, he preserved enough objectivity to highly appreciate the work of his rival. In his comment to Theorem 35 he remarks that the proofs of Lobachevsky concerning spherical trigonometry bear the impress of genius and his work should be esteemed as a masterly achievement.
... He gave up working on mathematics in his last years and instead tried to construct a theory of all knowledge. There are interesting ideas contained in the sections on linguistics and sociology.