The Mathematical Century: The 30 Greatest Problems of the Last 100 Years

The Mathematical Century: The 30 Greatest Problems of the Last 100 Years

by Piergiorgio Odifreddi
     
 

ISBN-10: 069109294X

ISBN-13: 9780691092942

Pub. Date: 03/08/2004

Publisher: Princeton University Press

"The twentieth century was a time of unprecedented development in mathematics, as well as in all sciences: more theorems were proved and results found in a hundred years than in all of previous history. In The Mathematical Century, Piergiorgio Odifreddi distills this unwieldy mass of knowledge into a fascinating and authoritative overview of the subject. He…  See more details below

Overview

"The twentieth century was a time of unprecedented development in mathematics, as well as in all sciences: more theorems were proved and results found in a hundred years than in all of previous history. In The Mathematical Century, Piergiorgio Odifreddi distills this unwieldy mass of knowledge into a fascinating and authoritative overview of the subject. He concentrates on thirty highlights of pure and applied mathematics. Each tells the story of an exciting problem, from its historical origins to its modern solution, in lively prose free of technical details." This book will be treasured not only by students and their teachers but also by all those who seek to make sense of the elusive macrocosm of twentieth-century mathematics.

Product Details

ISBN-13:
9780691092942
Publisher:
Princeton University Press
Publication date:
03/08/2004
Pages:
224
Product dimensions:
5.80(w) x 8.75(h) x 0.77(d)

Related Subjects

Table of Contents

Foreword
Acknowledgments
Introduction1
Ch. 1The Foundations8
1.1The 1920s: Sets10
1.2The 1940s: Structures14
1.3The 1960s: Categories17
1.4The 1980s: Functions21
Ch. 2Pure Mathematics25
2.1Mathematical Analysis: Lebesgue Measure (1902)29
2.2Algebra: Steinitz Classification of Fields (1910)33
2.3Topology: Brouwer's Fixed-Point Theorem (1910)37
2.4Number Theory: Gelfand Transcendental Numbers (1929)39
2.5Logic: Godel's Incompleteness Theorem (1931)43
2.6The Calculus of Variations: Douglas's Minimal Surfaces (1931)47
2.7Mathematical Analysis: Schwartz's Theory of Distributions (1945)52
2.8Differential Topology: Milnor's Exotic Structures (1956)56
2.9Model Theory: Robinson's Hyperreal Numbers (1961)59
2.10Set Theory: Cohen's Independence Theorem (1963)63
2.11Singularity Theory: Thom's Classification of Catastrophes (1964)66
2.12Algebra: Gorenstein's Classification of Finite Groups (1972)71
2.13Topology: Thurston's Classification of 3-Dimensional Surfaces (1982)78
2.14Number Theory: Wiles's Proof of Fermat's Last Theorem (1995)82
2.15Discrete Geometry: Hales's Solution of Kepler's Problem (1998)87
Ch. 3Applied Mathematics92
3.1Crystallography: Bieberbach's Symmetry Groups (1910)98
3.2Tensor Calculus: Einstein's General Theory of Relativity (1915)104
3.3Game Theory: Von Neumann's Minimas Theorem (1928)108
3.4Functional Analysis: Von Neumann's Axiomatization of Quantum Mechanics (1932)112
3.5Probability Theory: Kolmogorov's Axiomatization (1933)116
3.6Optimization Theory: Dantzig's Simplex Method (1947)120
3.7General Equilibrium Theory: The Arrow-Debreu Existence Theorem (1954)122
3.8The Theory of Formal Languages: Chomsky's Classification (1957)125
3.9Dynamical Systems Theory: The KAM Theorem (1962)128
3.10Knot Theory: Jones Invariants (1984)132
Ch. 4Mathematics and the Computer139
4.1The Theory of Algorithms: Turing's Characterization (1936)145
4.2Artificial Intelligence: Shannon's Analysis of the Game of Chess (1950)148
4.3Chaos Theory: Lorenz's Strange Attractor (1963)151
4.4Computer-Assisted Proofs: The Four-Color Theorem of Appel and Haken (1976)154
4.5Fractals: The Mandelbrot Set (1980)159
Ch. 5Open Problems165
5.1Arithmetic: The Perfect Numbers Problem (300 B.C.)166
5.2Complex Analysis: The Riemann Hypothesis (1859)168
5.3Algebraic Topology: The Poincare Conjecture (1904)172
5.4Complexity Theory: The P = NP Problem (1972)176
Conclusion181
References and Further Reading187
Index189

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