1. mathematics in the 20th and 21st century

2.  in 20th century, mathematics became a major profession  hundreds of specialized areas  development of computers enabled mathematics to expand  mathematics progressed more than ever

3.  David Hilbert (1862-1943) – German mathematician  “The Problems of Mathematics” – introduced in 1900  interest in physics  worked on general relativity

4. Who among us would not be happy to lift the veil behind which is hidden the future; to gaze at the coming developments of our science and at the secrets of its development in the centuries to come? What will be the ends toward which the spirit of future generations of mathematicians will tend? What methods, what new facts will the new century reveal in the vast and rich field of mathematical thought? David Hilbert, 1900, Paris

5.  problem proposed in 1852 by Francis Guthrie

6.  proved the four colour theorem in 1976  Wolfgang Haken –born in 1928, Berlin  Kenneth Ira Appel – born in 1932, New York

7.  John von Neumann (1903-1957) – American mathematician  interests: set theory, game theory, computer science, hydrodynamics of explosions  minimax theorem in 1928  member of Manhattan project

8.  John Forbes Nash, Jr. – born in 1928, West Virginia  interest: game theory, differential geometry, partial equations

9.  games: Hex in 1947 and So Long Sucker in 1950  “Nash equilibrium”  Nobel Prize in Economics in 1994  A Beautiful Mind – Oscar winning movie

10.  attempts to mathematicly capture behavior in strategic situations Theory of Games and Economic Behavior in 1944

11.  why is there no Nobel Prize in Mathematics?  Millenium Prize Problems - presented in 2000  Fields Medal - awarded since 1936  Abel Prize – first awarded in 2003