France/Russia

Mikhael Gromov

1999 Balzan Prize for Mathematics

For his numerous, most original and profound contributions to geometry in its various forms, and for the way in which he has applied them to many other domains of mathematics and of theoretical physics.

Mikhael Gromov was born in 1943 in Boksitogorsk (USSR); he has been a French citizen since 1992.
He is a professor at the Institute of Advanced Scientific Studies (Hautes Etudes Scientifiques) at Bures-sur-Yvette, near Paris.
Professor Gromov can be considered a true giant in his field for the originality and impact of his ideas.

The experts will recall his contribution to Geometry, and his succinct methods regarding Differential Geometry. Those even more specialised give due recognition to his theory on Pseudo-Holomorphic Curves.

Mikhael L. Gromov is, without any doubt, one of the greatest geometers of this century. His work is unique through the abundance and the force of the concepts he has created, as well as through the new techniques he has devised and applied to solve problems, often simple to state and to understand, and which seem, at first sight, inaccessible. Some of those problems were long standing, and their unexpected solutions caused wonder and surprise due to the originality and elegance of the method conceived by Gromov: famous instances are his proof of the old conjecture according to which a finitely generated group of polynomial growth has a nilpotent subgroup of finite index, or the beautiful construction (together with I. Pyatetski-Shapiro) of non-arithmetic discrete groups of hyperbolic transformations in arbitrary dimension.

On the other hand, new techniques developed by Gromov for different purposes led to completely new kinds of problems: one can imagine the great variety of questions arising from the introduction of a natural geometric structure on the set of all (isomorphism classes) of Riemannian manifolds, or from the discovery of many new and remarkable invariants of manifolds (e.g., the K-area, the simplicial volume, the minimal volume, etc.), not to forget important new notions, such as that of hyperbolic groups, which is at the origin of major recent developments in differential geometry.

To summarise, Gromov has brought about not only solutions to famous and time-old problems, but also the bases of new fields of study for many scholars. It has been emphasised above that he tends to look at all questions from the geometric side: he translates them in ad hoc geometric terms, and uses his extraordinary geometric intuition to investigate them thoroughly; it should be added that he is also able to treat, in the same way, questions coming from the most diverse branches of mathematics: algebra, analysis, differential equations, probability theory, theoretical physics, etc.
Due to the large number of his disciples and the wide repercussions aroused by his important discoveries, Mikhael Gromov has had, and will continue to have, a considerable influence on contemporary mathematics.