Sergei Novikov

Native spelling: Сергей Новиков

1938–2024, Gorky (now Nizhny Novgorod), Soviet Union, Moscow, Russia

TopologyMathematical physicsFields Medal 1970Wolf Prize in Mathematics 2005

Russian mathematician who proved the topological invariance of Pontryagin classes and reshaped manifold topology and soliton theory; Fields Medal 1970, Wolf Prize 2005.

Sergei Petrovich Novikov was born in Gorky (now Nizhny Novgorod) into a family of prominent mathematicians — his father Petr Novikov was a leading logician. He studied at Moscow State University, where his research career began spectacularly: while still a student he solved problems on the cohomology of the Steenrod algebra, work that led to the Adams–Novikov spectral sequence, a central tool of stable homotopy theory.

In the mid-1960s Novikov proved his celebrated theorem on the topological invariance of rational Pontryagin classes, developed surgery theory for classifying high-dimensional manifolds, and posed the Novikov conjecture relating higher signatures to homotopy invariants — a conjecture that links topology to the Novikov–type index theory and noncommutative geometry. For this body of work he was awarded the Fields Medal in 1970, though Soviet authorities prevented him from attending the Nice congress; he received the medal a year later in Moscow.

From the early 1970s Novikov turned to mathematical physics, working at the Landau Institute on the inverse scattering method for the Korteweg–de Vries equation and on integrable systems, periodic soliton theory and the Novikov–Veselov equation. He headed the geometry and topology department at the Steklov Institute for decades and later also held a professorship at the University of Maryland. He received the Wolf Prize in 2005 and died in Moscow in 2024.

Workplaces: Steklov Institute of Mathematics, Moscow, L.D. Landau Institute for Theoretical Physics, University of Maryland

Russia

Award-winning work

Fields Medal 1970Awarded for his work in algebraic and differential topology. Novikov proved that the rational Pontryagin classes of a differentiable manifold are topological invariants — not merely invariants of the smooth structure — settling a problem posed by Hirzebruch, and he created surgery-theoretic methods for classifying simply connected manifolds in high dimensions. His calculation of the unitary cobordism ring and the Adams–Novikov spectral sequence transformed stable homotopy theory. He also formulated the Novikov conjecture on the higher signatures of manifolds, still a driving problem in topology and noncommutative geometry.

Contributions, linked to the library

Library topicSmooth manifoldsDeveloped surgery theory for classifying smooth manifolds and proved Pontryagin classes are topological invariants.Library topicDifferential geometryHis higher-signature conjecture links the differential geometry and topology of manifolds to index theory.