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Beautiful proofs

 

"Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I knownumbers are beautiful. If they aren't beautiful, nothing is." - Paul Erdos.

"Mathematics is not about grammar, it's about the big stories… We tell those stories because they have the same effect on us as a piece of Shakespeare." - Marcus du Sautoy, on the assertion that literature is more moving than math

The proofs, techniques, and questions of mathematics can have a transcendental beauty. Come join a lively discussion about what makes mathematical proofs beautiful. We will cover some of the most beautiful proofs in mathematics including, but not limited to:

  • Cantor's Diagonalization Proof
  • Illustrative proof of Pythagorean theorem
  • Proof of Euler's identity thate^{i \pi} + 1 = 0
  • Proof that the hypotenuse of a triangle with two sides of 1 is not rational
  • Proof of the infinity of the Primes
  • Archimedes quadrature of the parabola and the second fundamental theorem of calculus

This should be fun. If you have a beautiful proof, please feel free to bring it and share it.

 

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  • Sister E.

    I have a (hopefully fairly succinct) variation on Cantor's theorem taken from FW Lawvere that states it as a theorem about the existence of fixed points of certain functions. It's one of my favorites!

    March 2, 2013

    • Nile

      Great! Please bring it.

      March 2, 2013

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