The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world.

He studied at the Imperial and Royal Military Academy (TherMilAk) in Vienna from 1818 to 1822, and Bolyai received his commission as sub-lieutenant.

Carl Friedrich Gauss, on reading the Appendix, wrote in a letter, "I regard this young geometer Bolyai as a genius of the first order.

For the entire content of the work...coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years.

"[9][6][8][7] Indeed, Gauss had disclosed his discovery of a consistent non-Euclidean geometry in a letter in 1827, and in 1829 wrote that he feared backlash if he published about it.

[12] In 1848 Bolyai learned that Nikolai Ivanovich Lobachevsky had published a piece of work similar to his appendix in 1829.

[13] He was an accomplished linguist, speaking several foreign languages beside his native Hungarian, these being German, Latin, French, Italian and Romanian.

Bolyai is a minor character in the 1969 science-fiction/fantasy story "Operation Changeling", where his unique abilities allow the protagonists to navigate the non-Euclidean geometry of Hell.