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From: Tonico on 1 Jul 2010 16:57
http://news.yahoo.com/s/ap/20100701/ap_on_sc/eu_sci_russia_math_genius

It's interesting to note that Perelman says his contribution to
Poincare's Conjecture's solution is no greater than that of Richard
Hamilton, and this rises some interesting questions: is Andrew Wiles'
contribution to solve FLT greater than R. Taylor's, P. Serre's,
Ribet's, Kolyvagin's, Flach's or Falting's? It seems obvious that FLT
theorem wouldn't have been possible without at least some of the above
people's results, so wouldn't it be "more fair" to acknowledge them as
"solvers"?
This is, apparently, what Perelman's words seem to be implying.

Tonio
From: OwlHoot on 2 Jul 2010 06:47
On Jul 1, 9:57 pm, Tonico <Tonic...(a)yahoo.com> wrote:
>
> http://news.yahoo.com/s/ap/20100701/ap_on_sc/eu_sci_russia_math_genius
>
> It's interesting to note that Perelman says his contribution to
> Poincare's Conjecture's solution is no greater than that of  Richard
> Hamilton, and this rises some interesting questions: is Andrew Wiles'
> contribution to solve FLT greater than R. Taylor's, P. Serre's,
> Ribet's, Kolyvagin's, Flach's or  Falting's? It seems obvious that FLT
> theorem wouldn't have been possible without at least some of the above
> people's results, so wouldn't it be "more fair" to acknowledge them as
> "solvers"?
> This is, apparently, what Perelman's words seem to be  implying.

One could say that about practically any similar result.
Most build on the work of others, whether isolated results
or whole theories and approaches.

For example, I bet whoever solves the Riemann Hypothesis
will do so by using the Baez-Duarte condition, and B-D
has been working on it for years (and probably still is,
although I couldn't find his web page, if any).

It looks tantalizingly simple, involving only zeta values
at positive even integers, and a graph of the condition
for large values looks as regular as clockwork. See:

http://www.man.poznan.pl/cmst/2008/v_14_1/cmst_47-54a.pdf

But that's prizes for you - In a running competition, only
one person usually comes in first even though others make
the same effort and are only fractions of a second behind.

As it happens, both Wiles and Perelman worked like Trojans
for years to develop their results. But even if they'd had
a flash of inspiration and obtained their results in a day,
they would still deserve their prize.


Regards

John Ramsden
From: Marko Amnell on 2 Jul 2010 07:42

"OwlHoot" <ravensdean(a)googlemail.com> wrote in message
e4e8dca9-298c-4a76-a8f5-247b96eba24f(a)18g2000vbi.googlegroups.com...

> On Jul 1, 9:57 pm, Tonico <Tonic...(a)yahoo.com> wrote:
>>
>> http://news.yahoo.com/s/ap/20100701/ap_on_sc/eu_sci_russia_math_genius
>>
>> It's interesting to note that Perelman says his contribution to
>> Poincare's Conjecture's solution is no greater than that of Richard
>> Hamilton, and this rises some interesting questions: is Andrew Wiles'
>> contribution to solve FLT greater than R. Taylor's, P. Serre's,
>> Ribet's, Kolyvagin's, Flach's or Falting's? It seems obvious that FLT
>> theorem wouldn't have been possible without at least some of the above
>> people's results, so wouldn't it be "more fair" to acknowledge them as
>> "solvers"?
>> This is, apparently, what Perelman's words seem to be implying.
>
> One could say that about practically any similar result.
> Most build on the work of others, whether isolated results
> or whole theories and approaches.
>
> For example, I bet whoever solves the Riemann Hypothesis
> will do so by using the Baez-Duarte condition, and B-D
> has been working on it for years (and probably still is,
> although I couldn't find his web page, if any).
>
> It looks tantalizingly simple, involving only zeta values
> at positive even integers, and a graph of the condition
> for large values looks as regular as clockwork.

The Baez-Duarte condition may look simple, but in reality
may bring us no closer to a proof of RH. The appearance
of simplicity may be deceptive. In fact, according to some
objective measures, we are no closer to a proof of RH
today than a century ago. The zero-free region of the
critical strip is very nearly the same now as it was in 1906.



From: OwlHoot on 2 Jul 2010 08:20
On Jul 2, 12:42 pm, "Marko Amnell" <marko.amn...(a)kolumbus.fi> wrote:
>
> [..]
>
> The Baez-Duarte condition may look simple, but in reality
> may bring us no closer to a proof of RH. The appearance
> of simplicity may be deceptive.

That's the trouble - most _look_ simple. For example
Robin's Theorem looks, if anything, even simpler:

http://groups.google.com/group/sci.math/browse_frm/thread/dce22c64ecd46fa1#

Seems like it's little more than a matter of minimizing
a function subject to the constraint of a product within
it being fixed.

(But obviously there's more to it than that, or else Robin
would have figured out the solution!)


Cheers

John Ramsden
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