Mathematics-- The Music Of Reason Pour L'honneur De L'esprit Humain. English

Mathematics: The New Golden Age offers a glimpse of the extraordinary vistas and bizarre universes opened up by contemporary mathematicians: Hilbert's tenth problem and the four-color theorem, Gaussian integers, chaotic dynamics and the Mandelbrot set, infinite numbers, and strange number systems. Why a "new golden age"? According to Keith Devlin, we are currently witnessing an astronomical amount of mathematical research. Charting the most significant developments that have taken place in mathematics since 1960, Devlin expertly describes these advances for the interested layperson and adroitly summarizes their significance as he leads the reader into the heart of the most interesting mathematical perplexities -- from the biggest known prime number to the Shimura-Taniyama conjecture for Fermat's Last Theorem.Revised and updated to take into account dramatic developments of the 1980s and 1990s, Mathematics: The New Golden Age includes, in addition to Fermat's Last Theorem, major new sections on knots and topology, and the mathematics of the physical universe.Devlin portrays mathematics not as a collection of procedures for solving problems, but as a unified part of human culture, as part of mankind's eternal quest to understand ourselves and the world in which we live. Though a genuine science, mathematics has strong artistic elements as well; this creativity is in evidence here as Devlin shows what mathematicians do -- and reveals that it has little to do with numbers and arithmetic. This book brilliantly captures the fascinating new age of mathematics I. Mathematics And Mathematicians. 1. The Concept Of Mathematics. 2. A Mathematician's Life. 3. The Work Of Mathematicians And The Mathematical Community. 4. Masters And Schools -- Ii. The Nature Of Mathematical Problems. 1. Pure Mathematics And Applied Mathematics. 2. Theoretical Physics And Mathematics. 3. Applications Of Mathematics In The Classical Era. 4. The Utilitarian Attacks. 5. Fashionable Dogmas. 6. Conclusions -- Iii. Objects And Methods In Classical Mathematics. 1. The Birth Of Pre-mathematical Ideas. 2. The Idea Of Proof. 3. Axioms And Definitions. 4. Geometry, From Euclid To Hilbert. 5. Numbers And Magnitudes. 6. The Idea Of Approximation. 7. The Evolution Of Algebra. 8. The Method Of Coordinates. 9. The Concept Of Limit And The Infinitesimal Calculus -- App. 1. Calculation Of Ratios In Euclid's Book V -- App. 2. The Axiomatic Theory Of Real Numbers -- App. 3. Approximation Of The Real Roots Of A Polynomial -- App. 4. Arguments By Exhaustion -- App. 5. Applications Of Elementary Algorithms Of The Integral Calculus -- Iv. Some Problems Of Classical Mathematics. 1. Intractable Problems And Sterile Problems. 2. Prolific Problems -- App. 1. Prime Numbers Of The Form 4k-1 Or 6k-1. App. 2. The Decomposition Of [actual Symbol Not Reproducible](s) As A Eulerian Product -- App. 3. Lagrange's Method For The Solution Of Ax[superscript 2] + Bxy + Cy[superscript 2] = N In Integers -- App. 4. Bernoulli Numbers And The Zeta Function -- V. New Objects And New Methods. 1. New Calculations. 2. The First Structures. 3. The Language Of Sets And General Structures. 4. Isomorphisms And Classifications. 5. Mathematics Of Our Day. 6. Intuition And Structures -- App. 1 The Resolution Of Quartic Equations -- App. 2 Additional Remarks On Groups And On The Resolution Of Algebraic Equations -- App. 3 Additional Remarks On Rings And Fields -- App. 4. Examples Of Distances -- App. 5. Fourier Series -- Vi. Problems And Pseudo-problems About Foundations 1. Non-eueclidean Geometries. 2. The Deepening Of The Concept Of Number. 3. Infinite Sets. 4. Paradoxes And Their Consequences. 5. The Rise Of Mathematical Logic. 6. The Concept Of Rigorous Proof -- App. 1. Geometry On A Surface -- App. 2. Models Of The Real Numbers -- App. 3. Theorems Of Cantor And Of His School. Jean Dieudonné ; Translated By H.g. And Hc. Dales. Includes Bibliographical References And Indexes. This book is of interest for students of mathematics or of neighboring subjects like physics, engineering, computer science, and also for people who have at least school level mathematics and have kept some interest in it. Also good for younger readers just reaching their final school year of mathematics.