Sergey P. Novikov (1938–2024)

A great Soviet and Russian mathematician, Sergey Petrovich Novikov, passed away a year ago, on June 6, 2024, in Moscow.He was born in a family of outstanding mathematicians on March 20, 1938, in Nizhnii Novgorod, called at that time Gorky, the city to which his parents moved for a short period from Moscow.His father, Pyotr Sergeyevich Novikov is well known for his proof of the existence of a finitely presented group for which the word problem is undecidable, and for the negative solution (jointly with his former student S. Adian) of the Burnside problem, which in turn follows from the proof that the free Burnside groups B(m, n) are infinite for sufficiently large odd exponents n.In 1960 P. Novikov was elected full member of the Academy of Sciences of the Soviet Union.His mother, Lyudmila Keldysh worked in the Steklov Mathematical Institute and authored outstanding papers on set theory and set-theoretical topology.In 1955, Sergey Novikov entered the Moscow State University.After a couple of years, Sergey chose as scientific advisor Mikhail Postnikov, whose impressive course on Galois theory he attended as a second-year student.This is how Sergey Novikov became a student in the Department of Higher Algebra.At the beginning, Postnikov gave Novikov a preprint of the article "On the structure and applications of the Steenrod algebra" by J. F. Adams, and left for a year to teach in China.Novikov always told that unlike other branches of mathematics, algebraic and differential topology have to be studied not from textbooks, but from the original articles, whose expositional level is hardly achieved by graduate texts.In the 2000s, when he together with the author of this text organised the publication of the three-volume set of such articles, titled "Topological Library," we included Adams' article in which the Adams spectral sequence was introduced.In 1959, Novikov published his first paper, "Cohomology of the Steenrod algebra," Dokl.Akad.Nauk SSSR 128, 893-895, in which he generalized certain results from Adams' article and, in particular, showed that there are arbitrarily long compositions of maps that realize nontrivial elements of stable homotopy groups of spheres: