Arnold's Problems [Paperback]

Vladimir Arnold is one of the most outstanding mathematicians of our time

Many of these problems are at the front line of current research

Arnold's Problems contains mathematical problems brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books.

The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (especially of physics), i.e. an experimental science. Many of these problems are still at the frontier of research today and are still open, and even those that are mainly solved keep stimulating new research, appearing every year in journals all over the world.

The second part of the book is a collection of commentaries, mostly by Arnold's former students, on the current progress in the problems' solutions (featuring a bibliography inspired by them).

This book will be of great interest to researchers and graduate students in mathematics and mathematical physics.

From the reviews:

For a working mathematician, it is much more important to know what questions are not answered so far and failed to be solved by the methods already available, than all lists of numbers already multiplied, and than the erudition in the ocean of literature that has been created by previous generations of researchers over twenty thousand years , V.I.Arnold states in the preface of this impressive compilation. And indeed, the list of problems collected in this volume, posed by him over a period of more than 40 years in his seminar on the theory of singularities of differentiable mappings, continues to provide invaluable impetus for a variety of mathematical fields (e.g., symplectic topology, dynamical systems, Kl��