Re: Why knowledge is NOT power

Regardless of whether James Harris made a worthwhile discovery about
prime numbers, your following criticism is off the mark by a wide
margin.

[EMAIL PROTECTED] (Thomas Bushnell, BSG) wrote in message news:<[EMAIL PROTECTED]>...
> 1) An explanation of why it is important--for example, does it enable
>    faster computation of primes? (no); does it make for faster
>    factorizations? (no).  Did you know there is a diophantine equation
>    whose roots are exactly the set of primes?  I could tweak that
>    equation in a million ways and produce a "previously unknown
>    formula" for primes, but that's hardly very interesting.

The existence of such a diophantine equation is an interesting
mathematical fact. The existence of an exponential diophantine
equation for any recursively enumerable set is a more interesting
fact.

Indeed, if these are not interesting mathematical facts, I can hardly
think of any mathematical fact worth deeming valuable.

Let us leave the value of a mathematical proposition to mathematicians
in proper and free them of philosophical obscurity about what is
interesting or valuable. Such arguments can achieve no better than
clouding their vision.

Encoding computation in diophantine equations will be enormously
interesting to a theoretical computer scientist and a number theorist,
and a proof of Poincare conjecture will be of interest to a
topologist. I believe the specialists have a much better idea of what
is of interest to them!

Sincerely,

--
Eray Ozkural