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The Mathematical Century : the 30 greatest problems of the last 100 years / Piergiorgio Odifreddi

By: Contributor(s): Material type: TextTextPublication details: Hyderabad : Universities Press : 2011Description: xvi, 204 pages : illustrations ; 22 cmISBN:
  • 9788173715426
Subject(s): Genre/Form: DDC classification:
  • 510.904 ODI
Contents:
The foundations. The 1920s : Sets -- The 1940s : Structures -- The 1960s : Categories -- The 1980s : Functions -- 2. Pure mathematics. Mathematical analysis : Lebesgue measure (1902) -- Algebra : classification of fields (1910) -- Topology : Brouwer's fixed-point theorem (1910) -- Number theory : Gelfand transcendental numbers (1929) -- Logic : Gödel's incompleteness theorem (1931) -- The calculus of variations : Douglas's minimal surfaces (1931) -- Mathematical analysis : Schwartz's theory of distribution (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 proof of Fermat's last theorem (1995) -- Discrete geometry : Hales's solution of Kepler's problem (1998). 3. 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) -- 4. 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) -- 5. Open problems. Arithmetic : the perfect numbers problem (300 B.C.) -- Complex analysis : the Riemann hypothesis (1859) -- Algebraic topology : the Poincaré conjecture (1904) -- Complexity theory : the P = NP problem (1972).
Summary: 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
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Item type Current library Call number Status Barcode
Mathematics Departmental Library Mathematics Departmental Library Mathematics Departmental Library 510.904 ODI (Browse shelf(Opens below)) Available M006
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The foundations. The 1920s : Sets --
The 1940s : Structures --
The 1960s : Categories --
The 1980s : Functions --
2. Pure mathematics. Mathematical analysis : Lebesgue measure (1902) --
Algebra : classification of fields (1910) --
Topology : Brouwer's fixed-point theorem (1910) --
Number theory : Gelfand transcendental numbers (1929) --
Logic : Gödel's incompleteness theorem (1931) --
The calculus of variations : Douglas's minimal surfaces (1931) --
Mathematical analysis : Schwartz's theory of distribution (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 proof of Fermat's last theorem (1995) --
Discrete geometry : Hales's solution of Kepler's problem (1998). 3. 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) --
4. 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) --
5. Open problems. Arithmetic : the perfect numbers problem (300 B.C.) --
Complex analysis : the Riemann hypothesis (1859) --
Algebraic topology : the Poincaré conjecture (1904) --
Complexity theory : the P = NP problem (1972).

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

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