Fomenko, Anatoly Timofeevich

Chronicle of Moscow University · Encyclopaedic Dictionary

FOMENKO, ANATOLY TIMOFEEVICH (b. 13.03.1945, Stalino/Donetsk, Ukrainian SSR), mathematician.

Graduated from the Faculty of Mechanics and Mathematics of Moscow State University (1967). A student of V.V. Rumyantsev and P.K. Rashevsky.

Candidate of Physical and Mathematical Sciences (1970, “Totally Geodesic Models of Cycles”). Doctor of Physical and Mathematical Sciences (1972, “The Multidimensional Plateau Problem on Riemannian Manifolds”). Professor (1981).

Academician of the Division of Mathematics (Mathematics) of the USSR/Russian Academy of Sciences (1994; Corresponding Member since 1990).

Head of the Department of Differential Geometry and Applications (1992–present); Professor of the Department of Higher Geometry and Topology (1983–1992) of the Faculty of Mechanics and Mathematics. He has worked at Moscow State University since 1969.

Research and teaching activity. His research interests cover multidimensional variational calculus, differential geometry and topology, the theory of Lie groups and Lie algebras, applications to mathematical physics, symplectic and computer geometry, the theory of integrable Hamiltonian systems, and mathematical methods for the analysis of historical sources.

A.T. Fomenko’s first major results were connected with his development of variational methods in differential geometry and topology and with the theory of minimal surfaces. He solved the multidimensional Plateau problem on Riemannian manifolds in the class of spectral surfaces (spectral bordisms): he proved the existence of a “geometric” solution — a globally minimal stratified surface representable as a continuous image of the spectrum of manifolds with boundary (1969).

He made a major contribution to the study of integrable Hamiltonian systems of differential equations and integrable equations on Lie groups and Lie algebras, which have important applications in mechanics, physics and geometry. He developed algebraic constructions of integrable Hamiltonian systems and the theory of noncommutative integration, and constructively proved the existence of completely integrable systems on semisimple Lie algebras (jointly with A.S. Mishchenko). He created a new theory of the topological classification of integrable dynamical systems and developed methods for the topological analysis of the behaviour of such systems based on Fomenko invariants and Fomenko–Zieschang invariants. He discovered unexpected deep connections between well-known Hamiltonian systems of physics, mechanics and geometry.

Together with his students he created a new direction — the theory of integrable topological billiards — which makes it possible to construct new visual models of complex multidimensional integrable systems of mathematical physics and to describe their geometry and topology. It turned out that all typical singularities of integrable Hamiltonian systems with two degrees of freedom and all their coarse invariants are realized by means of such billiards.

He is one of the founders of the application of empirical-statistical methods to the study of historical texts; he created new statistical methods for dating events and recognizing dependent historical texts. On this basis he formulated and proved the main tenets of the “New Chronology”, which seeks to revise the traditional chronology of events in Russian and world history up to the 17th century. Together with colleagues he published a large series of scholarly and popular-science books, including “Studies in the History of the Ancient World and the Middle Ages. Mathematical Methods of Source Analysis” (1993), “The New Chronology and the Concept of the Ancient History of Rus, England and Rome. Facts. Statistics. Hypotheses”, in 2 vols. (1995), and “The New Chronology of Greece. Antiquity in the Middle Ages” (1996). The “New Chronology” concept has provoked lively debate in the scholarly community.

Laureate of the State Prize of the Russian Federation for the series of works “Study of Invariants of Smooth Manifolds and Hamiltonian Dynamical Systems” (1996, co-author).

Laureate of the M.V. Lomonosov Prize for the series of works “Integrability and Billiard Systems” (2025).

Laureate of the M.V. Lomonosov Prize for teaching activity (2024).

Honoured Professor of Moscow University (1999).

Artistic and exhibition activity. A.T. Fomenko is known as an original graphic artist. He is the author of the text and illustrations of the book “Mathematics and Myth through the Prism of Geometry” (2001), which reveals the distinctive world of modern mathematics; of the album of paintings “Mathematical Impressions” (1990, American Mathematical Society); and the illustrator of M.A. Bulgakov’s novel “The Master and Margarita” (2016, AST). The animated film “The Pass” (1988, directed by V. Tarasov), based on K. Bulychev’s science-fiction novella “The Settlement”, was based on A.T. Fomenko’s paintings.

More than 100 of his personal exhibitions have been organized in various cities of the USSR, Russia and abroad (1971–present). Permanent displays are mounted in the Regional Museum of Magadan and the Museum of Voronezh State University. He took part in the well-known international exhibitions “Time–Space–Man” (1980), “Scientists Draw” (1982), and “Hyperrealism. When Reality Becomes an Illusion” (2015).

“I am a professional mathematician and have no special artistic education (my mother, Valentina Polikarpovna, taught me to draw). However, there was a period in my life (a fairly long one, which ended in the late 1980s) when I illustrated certain mathematical books — both my own and those of my fellow mathematicians — with graphic works on mathematical themes... The point is that geometric imagination and intuition play an enormous role in modern mathematical research, especially in work connected with mathematical physics, geometry and topology. It sometimes happens that the proof of a rigorous mathematical fact can first be ‘made out’ only in informal geometric images, and only then be set out as careful logical reasoning. It also turned out that when giving lectures on mathematics it is often useful to illustrate a complex mathematical proof with informal images. This helps students grasp the essence of the problem more quickly. In this sense many of my graphic works have an applied character. Thus it was mathematics and teaching at Moscow State University that led me, in due course, to create graphic works. It was an attempt, as it were, to photograph from within the fascinating world of geometry and topology. Many of my graphic sheets are based on mathematical ideas and theorems, or depict real physical processes and important mathematical concepts.”

State awards: medal of the Order of Merit for the Fatherland (2nd degree, 2024).

Principal works: “Variational Principles in Topology” (1982), “Integrability and Nonintegrability in Geometry and Mechanics” (1988), “The Plateau Problem”, in 2 vols. (1990), “Statistical Chronology” (1990), “Algorithmic and Computer Methods in Three-Dimensional Topology” (co-author, 1991), “Elements of the Geometry and Topology of Minimal Surfaces” (co-author, 1991), “Visual Geometry and Topology. Mathematical Images in the Real World” (1992), “Algebra and Geometry of Integrable Hamiltonian Differential Equations” (co-author, 1995), “Introduction to the Topology of Integrable Hamiltonian Systems” (co-author, 1997), “Integrable Hamiltonian Systems. Geometry. Topology. Classification”, in 2 vols. (co-author, 1999), “Selected Problems in Differential Geometry and Topology” (co-author, 2012), “Modern Geometry. Methods and Applications”, in 3 vols. (co-author, 2013), “Homotopical Topology” (co-author, 2016), “Mathematics, Myth, ‘The Master and Margarita’ in 199 Paintings: Closing the Heights of Rational Thought with the Depths of the Archaic and the Unconscious” (2022); and the textbooks and teaching aids “Lectures on Differential Geometry” (co-author, 1974), “A Course in Differential Geometry and Topology” (co-author, 1980), “A Problem Book in Differential Geometry and Topology” (co-author, 1981), “Differential Geometry and Topology. Additional Chapters” (1983), “Topological Variational Problems” (1984), “Elements of Differential Geometry and Topology” (co-author, 1987), “Symplectic Geometry. Methods and Applications” (1988), “A Course in Homotopy Topology” (co-author, 1989), “A Short Course in Differential Geometry and Topology” (co-author, 2004), “Computer Geometry: A Practical Course” (co-author, 2010), “A Course in Visual Geometry and Topology” (co-author, 2014), “Elements of the Geometry and Topology of Minimal Surfaces” (co-author, 2019); “Rector of Moscow University. Academician Viktor Antonovich Sadovnichy” (co-author, 2019).

Fact. Organizer and leader of the student music club “VEAF–TOPAZ” (1963–1988).

“I had my own collection of classical music gramophone records in Moscow from the very beginning. We obtained a good powerful radiogram and held listening sessions in the large drawing rooms of the MSU dormitory. First in the second dormitory building on Lomonosovsky Prospekt, and later in the large drawing rooms of zone ‘B’ of the Main Building of MSU. I gave short lectures on the history of musical works and on performers, after which the recordings were played. Within the club we also organized the popular musical evenings of P.S. Alexandrov (the famous ‘Alexandrov Tuesdays’), A.N. Kolmogorov, Yu.M. Smirnov and G.E. Shilov.”

Literature: A.T. Fomenko. Personal website; Academician A.T. Fomenko is 75. RAS.