Turning Points in the History of Mathematics

• Main Authors: Grant, Hardy (Author), Kleiner, Israel (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Birkhäuser, 2015.
• Edition: 1st ed. 2015.
• Series: Compact Textbooks in Mathematics,
• Subjects: Mathematics.; Algebra.; Geometry.; History.; Social sciences.; Mathematics > Study and teaching.; History of Mathematical Sciences.; Mathematics Education.; Mathematics in the Humanities and Social Sciences.

This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, c...

Table of Contents:

• Axiomatics - Euclid's and Hilbert's: From Material to Formal
• Solution by Radicals of the Cubic: From Equations to Groups and from Real to Complex Numbers
• Analytic Geometry: From the Marriage of Two Fields to the Birth of a Third
• Probability: From Games of Chance to an Abstract Theory
• Calculus: From Tangents and Areas to Derivatives and Integrals
• Gaussian Integers: From Arithmetic to Arithmetics
• Non-Euclidean Geometry: From One Geometry to Many
• Hypercomplex Numbers: From Algebra to Algebras
• The Infinite: From Potential to Actual
• Philosophy of Mathematics: From Hilbert to Gödel
• Some Further Turning Points
• Index.