This volume 6 of the Collected Works comprises 27 papers by V.I.Arnold, one of the most outstanding mathematicians of all times, written in 1991 to 1995. During this period Arnold's interests covered Vassilievs theory of invariants and knots, invariants and bifurcations of plane curves, combinatorics of Bernoulli, Euler and Springer numbers, geometry of wave fronts, the Berry phase and quantum Hall effect.
The articles include a list of problems in dynamical systems, a discussion of the problem of (in)solvability of equations, papers on symplectic geometry of caustics and contact geometry of wave fronts, comments on problems of A.D.Sakharov, as well as a rather unusual paper on projective topology. The interested reader will certainly enjoy Arnolds 1994 paper on mathematical problems in physics with the opening by-now famous phrase Mathematics is the name for those domains of theoretical physics that are temporarily unfashionable.
The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science. The volume also includes translations of two interviews given by Arnold to the French and Spanish media. One can see how worried he was about the fate of Russian and world mathematics and science in general.
1 BernoulliEuler updown numbers associated with function singularities,
their combinatorics and arithmetics.- 2 Congruences for Euler, Bernoulli and
Springer numbers of Coxeter groups.- 3 The calculus of snakes and the
combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups.- 4
Springer numbers and Morsification spaces.- 5 Polyintegrable flows.- 6 Bounds
for Milnor numbers of intersections in holomorphic dynamical systems.- 7 Some
remarks on symplectic monodromy of Milnor fibrations.- 8 Topological
properties of Legendre projections in contact geometry of wave fronts [ On
topological properties of Legendre projections in contact geometry of wave
fronts].- 9 Sur les propriétés topologiques des projections lagrangiennes en
géométrie symplectique des caustiques [ On topological properties of
Lagrangian projections in symplectic geometry of caustics].- 10 Plane curves,
their invariants, perestroikas and classifications (with an appendix by F.
Aicardi).- 11 Invariants and perestroikas of plane fronts.- 12 The Vassiliev
theory of discriminants and knots.- 13 The geometry of spherical curves and
the algebra of quaternions.- 14 Remarks on eigenvalues and eigenvectors of
Hermitian matrices, Berry phase, adiabatic connections and quantum Hall
effect.- 15 Problems on singularities and dynamical systems.- 16 Sur quelques
problčmes de la théorie des systčmes dynamiques [ On some problems in the
theory of dynamical systems].- 17 Mathematical problems in classical
physics.- 18 Problčmes résolubles et problčmes irrésolubles analytiques et
géométriques [ Solvable and unsolvable analytic and geometric problems].- 19
Projective topology.- 20 Questions ą V.I. Arnold (an interview with M. Audin
and P. Iglésias) [ Questions to V.I. Arnold].- 21 En todo matemįtico hay un
įngel y un demonio (an interview with Marimar Jiménez) [ In every
mathematician, there is an angel and a devil].- 22 Will Russian mathematics
survive?.- 23 Will mathematics survive? Report on the Zurich Congress.- 24
Why study mathematics? What mathematicians think about it.- 25 Preface to the
Russian translation of the book by M.F. Atiyah The Geometry and Physics of
Knots.- 26 A comment on one of A.D. Sakharovs Amateur Problems.- 27
Comments on two of A.D. Sakharovs Amateur Problems.- Acknowledgements.
Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors.
