Ivan Ivanovich Zhegalkin (Russian Ива́н Ива́нович Жега́лкин; alternative romanizations: Žegalkin, Gégalkine, Shegalkin) (3 August 1869, Mtsensk – 28 March 1947, Moscow) was a Russian mathematician. He is best known for his formulation of Boolean algebra as the theory of the ring of integers mod 2, via what are now called Zhegalkin polynomials.
Zhegalkin was professor of mathematics at Moscow State University. He helped found the thriving mathematical logic group there, which became the Department of Mathematical Logic established by Sofia Janovskaja in 1959. Reminiscing on his student days, Nikolai Nikolaevich Luzin recalls Zhegalkin as the only professor he was not afraid of.