Vladimir Arnold is one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work.
His first mathematical work, which he did being a third-year student, was the solution of the 13th Hilbert problem about superpositions of continuous functions. His early work on KAM (Kolmogorov, Arnold, Moser) theory solved some of the outstanding problems of mechanics that grew out of fundamental questions raised by Poincare and Birkhoff based on the discovery of complex motions in celestial mechanics. In particular, the discovery of invariant tori, their dynamical implications, and attendant resonance phenomena is regarded today as one of the deepest and most significant achievements in the mathematical sciences.
Arnold has been the advisor to more than 60 PhD students, and is famous for his seminar which thrived on his ability to discover new and beautiful problems. He is known all over the world for his textbooks which include the classics Mathematical Methods of Classical Mechanics, and Ordinary Differential Equations, as well as the more recent Topological Methods m Hydrodynamics written together with Boris Khesin, and Lectures on Partial Differential Equations.

Huygens and Barrow, Newton and Hooke.- 1. The law of universal gravitation.- § 1. Newton and Hooke.- § 2. The problem of falling bodies.- § 3. The inverse square law.- § 4. The Principia.- § 5. Attraction of spheres.- § 6. Did Newton prove that orbits are elliptic?.- 2. Mathematical analysis.- § 7. Analysis by means of power series.- § 8. The Newton polygon.- § 9. Barrow.- §10. Taylor series.- §11. Leibniz.- §12. Discussion on the invention of analysis.- 3. From evolvents to quasicrystals.- §13. The evolvents of Huygens.- §14. The wave fronts of Huygens.- §15. Evolvents and the icosahedron.- §16. The icosahedron and quasicrystals.- 4. Celestial mechanics.- §17. Newton after the Principia.- §18. The natural philosophy of Newton.- §19. The triumphs of celestial mechanics.- §20. Laplace's theorem on stability.- §21. Will the Moon fall to Earth?.- §22. The three body problem.- §23. The Titius-Bode law and the minor planets.- §24. Gaps and resonances.- 5. Kepler's second law and the topology of Abelian integrals.- §25. Newton's theorem on the transcendence of integrals.- §26. Local and global algebraicity.- §27. Newton's theorem on local non-algebraicity.- §28. Analyticity of smooth algebraic curves.- §29. Algebraicity of locally algebraically integrable ovals.- §30. Algebraically non-integrable curves with singularities.- §31. Newton's proof and modern mathematics.- Appendix 1. Proof that orbits are elliptic.- Appendix 2. Lemma XXVIII of Newton's Principia.- Notes.