Summary: Polymathematics :
is mathematics a single science or a set of arts?
Steklov Mathematics Institute, Moscow
CEREMADE, Universit'e ParisDauphine \Lambday
The shaft becomes too deep : : : and if new
veins would not be discovered, places for geom
etry in the Academy will become what already
are the Arabic chairs at the Universities.
Lagrange to D'Alembert, 1781
All mathematics is divided into three parts: cryptography (paid for by CIA, KGB
and the like), hydrodynamics (supported by manufacturers of atomic submarines)
and celestial mechanics (financed by military and by other institutions dealing with
missiles, such as NASA.).
Cryptography has generated number theory, algebraic geometry over finite fields,
algebra 1 , combinatorics and computers.
Hydrodynamics procreated complex analysis, partial derivative equations, Lie
groups and algebra theory, cohomology theory and scientific computing.
Celestial mechanics is the origin of dynamical systems, linear algebra, topology,
variational calculus and symplectic geometry.