His father was Pyotr Sergeyevich Novikov, who gave a negative solution to the word problem for groups.
[2] In 1971, he became head of the Mathematics Division of the Landau Institute for Theoretical Physics of the USSR Academy of Sciences.
[2] In 1983, Novikov was also appointed the head of the Department of Higher Geometry and Topology at Moscow State University.
[5][6] Novikov also carried out important research in geometric topology, being one of the pioneers with William Browder, Dennis Sullivan, and C. T. C. Wall of the surgery theory method for classifying high-dimensional manifolds.
Novikov's conjecture about the Riemann–Schottky problem (characterizing principally polarized abelian varieties that are the Jacobian of some algebraic curve) stated, essentially, that this was the case if and only if the corresponding theta function provided a solution to the Kadomtsev–Petviashvili equation of soliton theory.
This was proved by Takahiro Shiota (1986),[7] following earlier work by Enrico Arbarello and Corrado de Concini (1984),[8] and by Motohico Mulase (1984).