03289nam a22002057a 450000500170000000800410001702000180005808200160007610000260009210000190011824501050013726000450024230000470028750522380033452004170257265000170298965500300300665500210303670000260305720181113122723.0181113b xxu||||| |||| 00| 0 eng d a9788173715426 a510.904 ODI aPiergiorgio Odifreddi a;Freeman Dyson aThe Mathematical Centuryb : the 30 greatest problems of the last 100 yearsc/ Piergiorgio Odifreddi aHyderabad b: Universities Pressc: 2011 axvi, 204 pages b: illustrations c; 22 cm aThe 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). aThe 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 aMathematics  aMathematics -- History -- aMathématiques  aPiergiorgio Odifreddi