1829 – Non-Euclidean geometry

Lobachevsky becomes the first to publish a theory of non-Euclidean geometry even though Gauss had worked on the same ideas earlier and Bolyai was working on it concurrently although independently of Lobachevsky. Bolyai published in 1832. Riemann and Klein advanced the work later.

Euclid’s “The Elements” contained postulates and axioms of geometry that set the standard for a thousand years. The fifth postulate described parallel lines that never intersect as long as the space involved is considered to be a flat plane. When the space becomes curved, parallel lines can either converge, as around a sphere in elliptic geometry, or diverge, as on a saddle shaped plane in hyperbolic geometry.

Alhazen, Omar Khayyam, al-Tusi and Saccheri worked on various issues related to the parallel postulate of Euclid. Lambert was the first to introduce hyperbolic functions and then Lobachevsky, Bolyai and Gauss developed what was later called hyperbolic geometry by Felix Klein.

-0300 – Euclid
0965 – Alhazen
1048 – Khayyam
1667 – Saccheri
1728 – Lambert
1752 – Legendre
1777 – Gauss
1792 – Lobachevsky
1802 – Bolyai
1809 – Grassman
1826 – Riemann
1849 – Klein
1864 – Minkowski

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