Mathematical Century The 30 Greatest Problems of the Last 100 Years

ISBN-10: 0691128057
ISBN-13: 9780691128054
Edition: 2004
List price: $28.95 Buy it from $7.15
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Description: Piergiorgio Odifreddi leads us through 'the mathematical century'. The past century has seen a phenomenal expansion of our understanding of mathematics, knowledge which laid the foundations for the modern age of technology. This text highlights the  More...

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Book details

List price: $28.95
Copyright year: 2004
Publisher: Princeton University Press
Publication date: 10/22/2006
Binding: Paperback
Pages: 224
Size: 5.50" wide x 8.50" long x 0.75" tall
Weight: 0.594
Language: English

Piergiorgio Odifreddi leads us through 'the mathematical century'. The past century has seen a phenomenal expansion of our understanding of mathematics, knowledge which laid the foundations for the modern age of technology. This text highlights the most significant achievements.

Arturo Sangalli is a freelance science journalist and writer. He has a PhD in mathematics from the University of Montreal. He is the author of "The Importance of Being Fuzzy: And Other Insights from the Border between Math and Computers" (Princeton) and has contributed many pieces to "New Scientist".

Foreword
Acknowledgments
Introduction
The Foundations
The 1920s: Sets
The 1940s: Structures
The 1960s: Categories
The 1980s: Functions
Pure Mathematics
Mathematical Analysis: Lebesgue Measure (1902)
Algebra: Steinitz Classification of Fields (1910)
Topology: Brouwer's Fixed-Point Theorem (1910)
Number Theory: Gelfand Transcendental Numbers (1929)
Logic: Gouml;del's Incompleteness Theorem (1931)
The Calculus of Variations: Douglas's Minimal Surfaces (1931)
Mathematical Analysis: Schwartz's Theory of Distributions (1945)
Differential Topology: Milnor's Exotic Structures (1956)
Model Theory: Robinson's Hyperreal Numbers (1961)
Set Theory: Cohen's Independence Theorem (1963)
Singularity Theory: Thom's Classification of Catastrophes (1964)
Algebra: Gorenstein's Classification of Finite Groups (1972)
Topology: Thurston's Classification of 3-Dimensional Surfaces (1982)
Number Theory: Wiles's Proof of Fermat's Last Theorem (1995)
Discrete Geometry: Hales's Solution of Kepler's Problem (1998)
Applied Mathematics
Crystallography: Bieberbach's Symmetry Groups (1910)
Tensor Calculus: Einstein's General Theory of Relativity (1915)
Game Theory: Von Neumann's Minimax Theorem (1928)
Functional Analysis: Von Neumann's Axiomatization of Quantum Mechanics (1932)
Probability Theory: Kolmogorov's Axiomatization (1933)
Optimization Theory: Dantzig's Simplex Method (1947)
General Equilibrium Theory: The Arrow-Debreu Existence Theorem (1954)
The Theory of Formal Languages: Chomsky's Classification (1957)
Dynamical Systems Theory: The KAM Theorem (1962)
Knot Theory: Jones Invariants (1984)
Mathematics and the Computer
The Theory of Algorithms: Turing's Characterization (1936)
Artificial Intelligence: Shannon's Analysis of the Game of Chess (1950)
Chaos Theory: Lorenz's Strange Attractor (1963)
Computer-Assisted Proofs: The Four-Color Theorem of Appel and Haken (1976)
Fractals: The Mandelbrot Set (1980)
Open Problems
Arithmetic: The Perfect Numbers Problem (300 BC)
Complex Analysis: The Riemann Hypothesis (1859)
Algebraic Topology: The Poincare Conjecture (1904)
Complexity Theory: The P=NP Problem (1972)
Conclusion
References and Further Reading
Index

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