[FOM] Only one proof
William Tait
williamtait at mac.com
Mon Aug 31 12:46:15 EDT 2009
Two examples in set theory are Goedel's proof of the consistency of CH
relative to ZF using inner models and Cohen's proof of the consistency
of Not-CH using forcing.
There seems to be something different about these example in
comparison with yours. [Qua examples, they seem less interesting.]
What is it?
Bill Tait
On Aug 29, 2009, at 9:37 PM, joeshipman at aol.com wrote:
> Almost all the important theorems of mathematics, over time, acquire
> multiple proofs. There are many reasons for this; but I am interested
> in important theorems which, long after they are discovered, have
> "essentially" only one proof. (Only important theorems, because they
> are the ones which one would expect to be revisited enough that other
> proofs would be found.)
>
> The best candidates I have are Dirichlet's 1837 theorem that every
> arithmetic progression with no common factor contains infinitely many
> primes, and the 1960 Feit-Thompson theorem that every group with odd
> order is solvable.
>
> Can anyone think of other examples of comparable significance, or
> explain what is special about these theorems, or argue that one of
> these is not special because an essentially different proof than the
> original one has been found?
>
> -- JS
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