Great Currents of Mathematical Thought: Mathematics: Concepts and DevelopmentYears in the making, this feast of mathematical ideas comprises works by 50 eminent French scholars. The first book of the two-volume set embraces "Mathematics: Concepts and Development," with several essays each under the categories of "Structures," Disciplines," "Space," "Function," "Group," "Probability," and "The Mathematical Epic." The second volume, "Mathematics in the Arts and Sciences," comprises essays on "Mathematics and the Human Intellect," "Mathematics and Technology," and "Mathematics and Civilization." 1962 edition. |
Contents
BOOK ONE STRUCTURES page | 9 |
The Architecture of Mathematics by Nicolas Bourbaki | 23 |
Analogy in Mathematics by Robert Deltheil | 37 |
Symmetry and Dissymmetry in Mathematics and Physics | 44 |
Intuitive Approaches Toward some Vital Organs of Mathematics | 57 |
BOOK TWO DISCIPLINES page | 67 |
Fermats Last Theorem | 81 |
The History of the Mysterious Numbers by Paul Dubreil | 92 |
The Innateness of the Transfinite by Arnoud Denjoy | 191 |
GROUP | 201 |
E PROBABILITY | 209 |
Chance and Mathematics by Pius Servien | 221 |
BOOK ONE THE PAST page | 229 |
Views on Newtons Mathematical Thought by Pierre Brunet | 249 |
Sophus Lie by Élie Cartan | 262 |
Women Mathematicians by Mme MarieLouise Dubreil | 268 |
Transfinite Numbers and Alephs | 109 |
From ThreeDimensional Space to the Abstract Spaces | 115 |
A Journey into the Fourth Dimension by André SainteLagüe | 125 |
On the Curvature of Space and the Possibility of Forming | 143 |
FUNCTION | 153 |
The Role of Families of Functions in Mathematical Analysis | 174 |
From Cauchy to Riemann or the Birth of the Theory of Real | 181 |
BOOK TWO THE PRESENT page | 281 |
Renewer of Modern Analysis by Louis Perrin | 298 |
David Hilbert 18621943 by Jean Dieudonné | 304 |
The International Congresses of Mathematicians by Rolin | 312 |
BOOK THREE THE FUTURE page | 319 |
Modern Methods and the Future of Applied Mathematics | 337 |
Common terms and phrases
abstract algebraic curve algebraic integers algebraic numbers analogous analysis analytic functions applied arithmetic axiomatic axioms calculus called Cauchy century circle complex numbers complex variable conception consider constructed continuous continuous functions convergent corresponding curve defined definition Descartes differential equations discovery domain elements Elie Cartan Émile Borel Emmy Noether equal Euclidean Euclidean geometry Euler example existence expression Felix Klein Fermat finite number fourth dimension geometry given Greek Henri Lebesgue Henri Poincaré Hilbert idea ideal infinite infinity integral intuition irrational numbers later Lebesgue Leibniz logical mathe mathematicians mathematics matical method modern natural numbers Newton non-Euclidean geometry notion obtained operations physics plane Poincaré polynomial possible problem properties propositions question rational numbers real numbers relations Riemann role sequence solution Sophus Lie space structure surface symmetry tangent theorem theory of probability tion topological transfinite transformation Unabridged republication universe Weierstrass zero