Vladimir Arnold

Vladimir Igorevich Arnold was nineteen when he solved Hilbert's thirteenth problem, a question that had stood for over fifty years. He was the most brilliant student of Andrey Kolmogorov at Moscow State University, and for the rest of his life he carried the Moscow mathematical tradition — geometric, intuitive, fearless — to the rest of the world.

In 1963 he published the full proof of what Kolmogorov had sketched in 1954: that most invariant tori of an integrable Hamiltonian system survive small perturbations. The resulting theorem, completed independently by Jürgen Moser in the smooth case, is the KAM theorem, and it is the reason the solar system has not flown apart. Arnold's 1978 textbook Mathematical Methods of Classical Mechanics rewrote the subject from the ground up, treating phase space as a symplectic manifold and making geometry the native language of dynamics.

He worked across singularity theory, hydrodynamics, algebraic geometry, and dynamical systems with equal fluency. He was loud, opinionated, relentlessly generous to students, and famous for his dictum that 'mathematics is the part of physics where experiments are cheap.' His later years were spent in Paris and Moscow, lecturing to packed halls and writing a stream of essays on the state of mathematical education. He died in Paris in 2010; he is remembered as the most influential Russian mathematician of the second half of the twentieth century.