In addition to this blog, I have started a series of "softer" mathematical essays on hubpages.com.
You can see my first posting in the series here. It is on Abel's proof.
Friday, July 18, 2008
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The purpose of this blog is to present the story behind Fermat's Last Theorem and Wiles' proof in a way accessible to the mathematical amateur.
Topic Index
Completed Proofs
- x2 + y2 = z2 (rational integers)
- x2 - dy2 = 1 (periodic continued fractions)
- x2 - dy2 = 4 (reduced quadratic equations)
- x3 + y3 = z3 (rational integers)
- x3 + y3 = z3 (eisenstein integers)
- x4 + y4 = z4 (rational integers)
- x4 + y4 = z4 (gaussian integers)
- x4 - y4 = z2 (Fermat's proof)
- x5 + y5 = z5 (Dirichlet's proof)
- x7 + y7 = z7 (rational integers)
- Quadratic Reciprocity (rational integers)
- eiπ + 1 = 0
- eix = cos(x) + isin(x)
- Fundamental Theorem of Algebra (complex numbers)
- xn + yn = zn (regular primes)
- ∑n-s = ∏ (1 - p-s)-1
- Abel's proof on the quintic
Recommended Books
- Yearning for the Impossible(A K Peters, 2006)
- Fermat's Enigma (Anchor, 1998)
- 100 Great Problems of Elementary Mathematics (Dover, 1965)
- An Introduction to Number Theory (MIT Press, 1978)
- Elements of Number Theory (Springer, 2002)
- Problems in Algebraic Number Theory (Springer, 2004)
- Elementary Number Theory (Springer, 1998)
- Contemporary Abstract Algebra (Houghton Mifflin Company, 2001)
- Abel's Proof (MIT Press, 2003)
- Galois' Theory of Algebraic Equations (World Scientific, 2001)
Required Reading for Experts
- Fermat's Last Theorem for Amateurs (Springer, 2000)
- 13 Lectures on Fermat's Last Theorem (Springer, 1979)
- Fermat's Last Theorem: A Genetic Introduction (Springer, 2000)
- The Mathematical Career of Pierre de Fermat 1601-1665 (Princeton University Press, 1994)
- Fearless Symmetry: Exposing the Hidden Patterns of Numbers (Princeton University Press, 2006)
About Me
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