Hellman H. Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever

Hoboken, NJ: Wiley, 2006. — 256 p. — ISBN10: 1681620103; ISBN13: 978-1681620107.The prose is clear and engaging and, despite the title, there are very few equations such that those who are equation-phobic have little to fear. However, many of the disputes center on nineteenth to twentieth century front-line research in pure mathematics - areas such as set theory, concepts of infinity, etc. These early ideas were prone to heated discussion and, in many cases, led to feuds. In order to allow the reader to understand the basis for these feuds, the author has included the essence of some of the key contentious mathematical arguments, often directly quoting members of each camp. I found that carefully following these arguments in detail could be difficult at times, but I certainly agree that pondering them is important if one is to clearly understand the position of each side. The final chapter poses the fascinating question: Are mathematical advances discoveries or inventions?" And here again, there are avid supporters of each side. I gave the book five stars because of the interesting subject matter and because I feel that the author has done a truly excellent job in presenting such a potentially difficult subject to as broad an audience as possible. Nevertheless, I still believe that I would benefit from reading some chapters a second time. Although anyone reading this book could learn much from it, I believe that it would be most enjoyed by serious math buffs. [George Pourier @Amazon]Tartaglia versus Cardano. Solving Cubic Equations
Descartes versus Fermat. Analytic Geometry and Optics
Newton versus Leibniz. Credit for the Calculus
Bernoulli versus Bernoulli. Sibling Rivalry of the Highest Order
Sylvester versus Huxley. Mathematics: Ivory Tower or Real World?
Kronecker versus Cantor. Mathematical Humbug
Borel versus Zermelo. The "Notorious Axiom"
Poincare versus Russell. The Logical Foundations of Mathematics
Hilbert versus Brouwer. Formalism versus IntuitionismAbsolutists/Platonists versus Fallibilists/Constructlvlsts. Are Mathematical Advances Discoveries or Inventions?