Tribute to Vladimir Arnold (Q2883514)

This is the first of two articles planned in the same journal and constituting a collaborative effort to appreciate life and work of the outstanding Russian mathematician Vladimir Arnold (1927--2010). It starts with the English version of an unpublished interview with Arnold performed by the second author in 1990 for a Russian popular journal, reporting among other things on Arnold`s childhood and his opinions about educational problems of mathematics.NEWLINENEWLINEArnold's former student Alexander Givental then publishes his recommendation letter of 2005 for an unnamed prize committee on Arnold's mathematical achievements (381--386), the prize in the end not being awarded to Arnold. This is the longest and mathematically most detailed contribution of the article, going into Arnold's work on small denominators in Kolmogorov-Arnold-Moser (KAM) theory and on Arnold's diffusion (having now separate entries in the Mathematics Subject Classification), in symplectic geometry and symplectic topology, and in singularity theory. Arnold's affirmative solution of the 13th Hilbert problem and his results on the 16th Hilbert problem are then discussed as well as several notions invented and discussed by him such as Arnold's Strange Duality. The author remarks that Arnold, with the exception of KAM-theory and singularity theory, in most cases left to his followers the development of advanced machinery for the complete solution of problems originally attacked by himself.NEWLINENEWLINEIn the following contribution Arnold's friend Yakov Sinai remembers the early years of the mathematician going particularly into the role of A.N. Kolmogorov as Arnold's teacher. Steve Smale reports about his first meetings with Arnold in Moscow and Hong Kong and his influence on his own work. Mikhail Sevryuk goes again into the relationship between Arnold and Kolmogorov and stresses Arnold's `fight against Bourbakism'. Askold Khovanski and Alexander Varchenko recall the first years of Arnold's famous Moscow seminar from 1966 onwards. They report also on Arnold's strong physical presentation, particularly in skiing. Michael Berry's memories of Arnold stress his uncompromising, often ironic personality and his strong feelings about an underestimation of the Russian research contribution.NEWLINENEWLINEThe article includes several interesting photographs of Arnold and colleagues, as well as a list of his fifty or so doctoral students.