Books, Books, Books...

A Math Forum Project

Table of Contents:

Famous Problems Home

The Bridges of Konigsberg
· Euler's Solution
· Solution, problem 1
· Solution, problem 2
· Solution, problem 4
· Solution, problem 5

The Value of Pi
· A Chronological Table of Values
· Squaring the Circle

Prime Numbers
· Finding Prime Numbers

Famous Paradoxes
· Zeno's Paradox
· Cantor's Infinities
· Cantor's Infinities, Page 2

The Problem of Points
· Pascal's Generalization
· Summary and Problems
· Solution, Problem 1
· Solution, Problem 2

Proof of the Pythagorean Theorem

Proof that e is Irrational

Book Reviews



Bell, E.T. Men of Mathematics. New York: Simon and Schuster. 1967.

As Bell himself points out in his introduction, this book is not a history of mathematics. It is instead the story of the lives of a few of the thinkers who have contributed greatly to the development of modern mathematics. As such it is very useful. The stories Bell tells are always well researched and interesting, and are combined nicely with brief explanations of the mathematics that each of these men did. The mathematics is accessible to high school students. Unfortunately, the book contains only white men, but for those it does include it is an excellent resource, often going beyond the 'stock histories' to find out which anecdotes about these men are actually true. The biographies also contain a great deal of Bell's own opinions and ideas, and so to the true student of history present a very interesting source.

List of mathematicians whose biographies are contained in Men of Mathematics: Zeno, Exodus, Archimedes, Descartes, Fermat, Pascal, Newton, Leibniz, The Bernoullis, Euler, Lagrange, Laplace, Monge, Poncelet, Gauss, Cauchy, Lobatchewsky, Abel, Jacobi, Hamilton, Galois, Sylvester, Weierstrauss (Kowalewski), Boole, Hermite, Kronecker, Riemann, Kummer, Poincaré, Cantor.

Eves, Howard. Great Moments in Mathematics (Before 1650). Mathematical Association of America. 1980.
Great Moments in Mathematics (After 1650). Mathematical Association of America. 1981.

These two volumes, part of the Dolciani Mathematical Expositions Series, are a true joy to read and at the same time are very informative and very educational. Eves' style is impeccable, his explanations clear, his appreciation for mathematical beauty well expressed, and his sense of humor is pleasantly light. Okay. Now that I'm done raving about these books, I'll actually tell you about them. In all, they contain 39 'lectures' on various 'GREAT MOMENTS IN MATHEMATICS'. Taking inspiration from a pre-television-era NBC radio series called the "Music Appreciation Hour," Eves' work is not a comprehensive history of mathematics or a biographical account of mathematics. Instead it focuses on specific problems (either posed or solved) that represented great leaps forward in mathematical thought. Eves has a remarkable ability to make the most complex achievements and their relevance to the mathematical and scientific world accessible to the reader who has knowledge of some high school mathematics (some 'lectures' do not even require that). The 'moments' range from humans learning to count to the development of the abacus to Fourier series to Godel's Incompleteness Theorem. At the end of each lecture is a set of exercises that involve the mathematics learned in that lecture.

What's so great about these books is that you can just open them up to any section, start reading, and be assured that in 30 minutes you will know more mathematics, and more math history (in particular the historical significance of certain ideas and mathematical inventions). If you have a student, teacher, or friend who already has Mathematics: A Human Endeavor, (see the next page for a review), or for someone who you think would enjoy the historical slant taken here, give them these books.

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