Pyotr Sergeyevich Novikov (Russian: Пётр Сергеевич Новиков; 15 August 1901, Moscow, Russian Empire – 9 January 1975, Moscow, USSR) was a Soviet mathematician.

Novikov is known for his work on combinatorial problems in group theory: the word problem for groups, and Burnside's problem. For proving the undecidability of the word problem in groups he was awarded the Lenin Prize in 1957.

In 1953 he became a corresponding member of the USSR Academy of Sciences and in 1960 he was elected a full member.

He was married to the mathematician Lyudmila Keldysh (1904 – 1976). The mathematician Sergei Novikov is his son. Sergei Adian and Albert Muchnik were among his students.