| RefNo | EC/1988/41 |
| Previous numbers | Cert XXII, 138 |
| Level | Item |
| Title | Arnold, Vladimir Igorevich: certificate of election to the Royal Society |
| Date | 1987 |
| Description | Certificate of Candidate for Election to Foreign Membership. Citation typed |
| Citation | V. I. Arnold has made outstanding contributions to both pure and applied mathematics. Most of his work has been motivated towards better understanding of the physical world; but in his studies of physical phenomena he has often discovered and incisively explored mathematical subtleties that have led to powerful new insights. These discoveries have prompted him to pioneer several areas of pure mathematics which are now studies extensively in their own right.
Arnold worked as a student with Kolmogorov, and his first important achievement, in 1961, was to extend Kolmogorov's theorem on the existence of invariant tori in dynamical systems so that he could apply it to questions of the stability of planetary motions. Although his findings did not fully explain the stability of the solar system, they profoundly illuminated the character of this problem, transforming our understanding of it.
Turning to dynamical systems with chaotic behaviour, he then proved several impressive theorems in ergodic theory. Again the novel viewpoint propounded by him has been even more influential than details of his particular results. In particular, he initiated the valuable idea that the turbulent motion of a fluid can be understood as the geodesic flow on an infinite-dimensional negatively curved manifold of its possible instantaneous states.
In the 1960s, expanding ideas that had primitive antecedents in the writings of Kelvin on vortex motions, Arnold published a series of remarkably inventive papers on the hydrodynamic stability of inviscid fluids. These papers hugely reinvigorated the subject and, in common with other contributions by him to applied mathematics, they have been widely influential. The identification of inviscid-fluid motions as a Hamiltonian system, the variational characterization of steady motions and the possibility of thereby proving stability are concepts developed by him that have since been used by many other researchers.
In addition to the practically oriented research already cited, Arnold has also successfully studied various topics at the purest end of mathematics. He solved one of Hilbert's classic problems, on the representability of algebraic functions, he revealed this problem to depend on the cohomology of Artin's braid groups; and in calculating the cohomology he opened up a long train of developments in algebraic topology. In recent years he has allied his pure and applied mathematical interests with particular effectiveness in studying singularities of smooth maps. He has become the leading authority on this subject, which has pivotal importance in nonlinear mathematics and has a vast range of scientific applications. Having come into the subject originally by analyses of caustics in geometrical optics, he soon found it well suited to extensions of his earlier studies of algebraic branching and braid groups.
Arnold is one of the world's best respected mathematicians, having the uncommon distinction of equally high esteem among both the pure and applied mathematical communities. The brilliance and diversity of his many achievements in research, his sustained creativity over nearly three decades and his exemplary text-books all contribute to his international repute. |
| AccessStatus | Closed |
Fellows associated with this archive
| Code | PersonName | Dates |
| NA4741 | Arnold; Vladimir Igorevich (1937 - 2010) | 1937 - 2010 |