Veniamin Fedorovich Kagan (Russian: Вениами́н Фёдорович Ка́ган; 10 March 1869 – 8 May 1953) was a Russian and Soviet mathematician and expert in geometry. He is the maternal grandfather of mathematicians Yakov Sinai and Grigory Barenblatt.
Kagan was born in Shavli, Russian Empire (now Šiauliai, Lithuania) in 1869, to a poor Ashkenazi Jewish family. In 1871 his family moved to Yekaterinoslav (now Dnipropetrovsk), where he grew up. Kagan entered the Imperial Novorossiya University in Odessa in 1887, but was expelled for revolutionary activities in 1889. He was put on probation and sent back to Yekaterinoslav. He studied mathematics on his own and in 1892 passed the state exam at Kiev University.
In 1894 Kagan moved to St Petersburg where he continued his studies with Andrey Markov and Konstantin Posse. They tried to help him to obtain an academic position, but Kagan's Jewish background was an obstacle. Only in 1897 was he allowed to become a dozent at the Imperial Novorossiya University, where he continued to work until 1923. His students in the theory of relativity class he taught in 1921-22 included Nikolaj Papaleksi, Alexander Frumkin and Igor Tamm. Kagan worked at Moscow State University where he held the Geometry Chair from 1923 till 1952.
In 1924 he joined Otto Schmidt in drawing up plans for the Great Soviet Encyclopedia.
Aging and disillusioned with anti-Semitic practices, he resigned from the university and died in Moscow soon afterwards.
He published over 100 mathematical papers in different parts of geometry, particularly on hyperbolic geometry and on Riemannian geometry. He received the USSR State Prize in 1943. He founded the science publisher Mathesis in Odessa. He was a director of the mathematics and natural sciences department of the Great Soviet Encyclopaedia. He wrote a definitive biography of Nikolai Lobachevsky and edited his collected works (5 volumes, 1946–1951).
Kagan's doctoral students include Pyotr Rashevsky, Viktor Wagner and Isaak Yaglom.
- Mathematician Veniamin Fedorovich Kagan from Odessa is a minor character in The Fourth Prose (1930) by Osip Mandelstam.