Nikolai Lobachevsky

23 February 1826: a faculty meeting in Kazan

At a meeting of Kazan University's Faculty of Physics and Mathematics on 23 February 1826, Nikolai Lobachevsky presented a paper setting out the principal foundations of what became non-Euclidean geometry. In the Julian calendar then used in Russia, the date read 11 February.

The title was in French: Exposition succincte des principes de la géométrie avec une démonstration rigoureuse du théorème des parallèles — a concise exposition of the principles of geometry, with a rigorous demonstration of the theorem of parallels.

What he put in front of his colleagues

The presentation challenged attempts to derive Euclid's parallel postulate, treating a geometry with different parallel behaviour as something that could be developed mathematically in its own right.

What the surviving evidence supports is a report of foundations, not a completed modern axiomatic theory. Nor was Lobachevsky the first to press on the postulate: Saccheri, Lambert, Schweikart and Gauss had already investigated alternatives or the consequences of denying it.

The paper that was never printed

The manuscript entered the university's review process, was not printed, and is lost. Lobachevsky first published his non-Euclidean geometry in Kazanskii Vestnik in 1829–1830.

Because the manuscript is gone, historians cannot establish how much of that later published system was already present in the lecture.

János Bolyai developed a related geometry independently; his account appeared in print in 1832, as an appendix to his father Farkas Bolyai's Tentamen.