Re: Which one result in maths has surprised you the most?

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On 08 Jul 2013, at 23:22, Johnathan Corgan wrote:```
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```On 07/08/2013 02:16 PM, Jason Resch wrote:

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This one is very interesting, but the fact that Pi was a poor choice for
```the constant makes the equation considerably more ugly than it should
be.  There is a growing movement to usurp the number Pi with the much
more important constant "2*Pi"
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(see: http://www.math.utah.edu/~palais/pi.html ). If we call that new
```number tau (t).  Then Euler's identity becomes:

e^(t * i) = 1
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I think part of the appeal of the original formulation is realizing that
```the result of an exponentiation of a positive number can be a negative
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number. While this is unremarkable with complex exponents, many people
```are only used to seeing real (or even just integer) exponents.
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I like and often give the following exercise: compute i^i. Is it real or imaginary?
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Since sometimes my most amazing result in math is the Turing universality of the diophantine polynomials.
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My favorite simple result is the irrationality of sqr(2). A good exercise, using the fundamental theorem of arithmetic (existence and uniqueness of decomposition of numbers in prime factors) generalizes this for sqr(n) for any n not being a square. A result often attributed to Theaetetus.
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Of course the existence of universal numbers is also an amazing, stunning results, especially if you know how weak are the pretense of "universality" for mathematical notions. This needs Church thesis, which I consider as the most amazing thesis in cognitive science.
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Bruno

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```
Johnathan

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