Born in Gzhatsk, he studied at the Moscow State University where he received a Ph.D. in 1927 under the direction of Pavel Sergeevich Alexandrov.

He made important contributions to topology, functional analysis, mathematical physics, and certain classes of ill-posed problems.

Tikhonov regularization, one of the most widely used methods to solve ill-posed inverse problems, is named in his honor.

[3] Tikhonov played the leading role in founding the Faculty of Computational Mathematics and Cybernetics of Moscow State University and served as its first dean during the period of 1970–1990.

Tikhonov received numerous honors and awards for his work, including the Lenin Prize (1966) and the Hero of Socialist Labor (1954, 1986).