MODERN MATHEMATICS

mathematics in the 20th and 21st century

introduction

in 20th century, mathematics became a major profession

hundreds of specialized areas

development of computers enabled mathematics to expand

mathematics progressed more than ever

Hilbert and 23 problems

David Hilbert (1862-1943) – German mathematician

“The Problems of Mathematics” – introduced in 1900

interest in physics

worked on general relativity

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

four colour theorem

problem proposed in 1852 by Francis Guthrie

Haken and Appel

proved the four colour theorem in 1976

Wolfgang Haken –born in 1928, Berlin

Kenneth Ira Appel – born in 1932, New York

game theory and two John’s

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

John Forbes Nash, Jr. – born in 1928, West Virginia

interest: game theory, differential geometry, partial equations

games: Hex in 1947 and So Long Sucker in 1950

“Nash equilibrium” Nobel Prize in Economics in 1994 A Beautiful Mind – Oscar winning

movie

game theory

attempts to mathematicly capture behavior in strategic situations

Theory of Games and Economic

Behavior in 1944

awards in mathematics 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