His father, Mikhail Ivanovich Vinogradov, was a hydraulics scientist; his mother, Ilza Alexandrovna Firer, was a medical doctor.

He obtained his habilitation degree (doktorskaya dissertatsiya) in 1984 at the Institute of Mathematics of the Siberian Branch of the USSR Academy of Science in Novosibirsk in Russia.

[3] Between the sixties and the seventies, inspired by the ideas of Sophus Lie, Vinogradov changed once more research interests and began to investigate the foundations of the geometric theory of partial differential equations.

Having become familiar with the work of Spencer, Goldschmidt and Quillen on formal integrability, he turned his attention to the algebraic (in particular, cohomological) component of that theory.

[4] Vinogradov’s approach to nonlinear differential equations as geometric objects, with their general theory and applications, is developed in details in some monographs[5][6][7] as well as in some articles.

[15][16][17] The first term of this spectral sequence gives a unified cohomological approach to various notions and statements, including the Lagrangian formalism with constraints, conservation laws, cosymmetries, the Noether theorem, and the Helmholtz criterion in the inverse problem of the calculus of variations (for arbitrary nonlinear differential operators).

Vinogradov’s construction is a precursor of the general concept of a derived bracket on a differential Leibniz algebra introduced by Kosmann-Schwarzbach in 1996.

[21][22] Together with Peter Michor [de], Vinogradov was concerned with the analysis and comparison of various generalizations of Lie (super) algebras, including

[30][31][10] Considerable attention to the mathematical understanding of the fundamental physical notion of observable is given in a book written by Vinogradov jointly with several participants of his seminar, under the pen name of Jet Nestruev.

In 1985, he created a laboratory that studied various aspects of the geometry of differential equations at the Institute of Programming Systems in Pereslavl-Zalessky and was its scientific supervisor until his departure for Italy.