Am I a crank?
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From: John Schutkeker on 30 Aug 2006 04:59 Jeremy Boden <jeremy(a)jboden.demon.co.uk> wrote in news:1156925658.5449.8.camel(a)localhost.localdomain: > On Wed, 2006-08-30 at 09:15 +0200, Han de Bruijn wrote: >> Jesse F. Hughes wrote: >> >> Modern mathematics _is_ an experimental science. >> In very much the same way as physics is: theory as well as >> experiment. Or would you like to say that structural (numerical) >> analysis is not a form of mathematics? And how about computing a >> large prime number? >> >> Welcome to the 21th century! > > Do you mean that there are theories of numerical analysis which are > accepted until found to be wrong due to practical experiments? > > Actually, I don't think anyone has discovered a practical method of > *computing* a large prime number - although there are methods of > performing primality checking on a given number. The faster methods > are only probabilistic - but slower methods will give a definite > answer. All of which is just quibbling over details. You are describing numerical experiments.
From: John Schutkeker on 30 Aug 2006 05:06 Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote in news:20b9$44f53d00$82a1e228$14726(a)news1.tudelft.nl: > Gerry Myerson wrote: > >> Somewhere along the way you should check to see whether what you have >> done (or what you are planning to do) has already been done. [ ... ] > > Precisely! And there are a lot of things out there which have NOT been > done. To mention an example. Take a couple of (3-D) bricks and find > out how to make a discretization of the equations describing > incompressible and irrotational 3-D flow with the least squares finite > element method. > > But ah .. nobody will appreciate (or even comprehend) if you have done > such an uncommon thing. There are people all over the place specializing in fluid simulation, who would appreciate such work. If you feel that such a simulation would answer an important question (and you have the talent to write it) it is unsconscionable not to do so, even if you have to write a fresh grant application first. :P
From: schoenfeld.one on 30 Aug 2006 05:43 Proginoskes wrote: > schoenfeld.one(a)gmail.com wrote: > > Han de Bruijn wrote: > > [...] > > > Or is it just mathematics? In the latter case, computing a large prime > > > is also mathematics, because it could be done - in principle - by hand. > > > (What else does computer science add except more speed and more space.) > > > > Then there is no experiementation. Mathematics is not an experimental > > science, it is not even a science. The principle of falsifiability does > > not apply. > > Written by someone who has not done any math research. > > One of many examples: Try dividing 2^n by n and keeping track of the > remainders. You won't get 1; you get 2 a lot, but you never seem to get > a 3. So you conjecture: > > CONJECTURE: The remainder of 2^n divided by n is never 3. > > However, this conjecture is false; in particular, the remainder of 2^n > divided by n is 3 if n = 4,700,063,497 (but for no smaller n's). Hello Crackpot. > --- Christopher Heckman
From: Han de Bruijn on 30 Aug 2006 06:51 schoenfeld.one(a)gmail.com wrote: > Then there is no experiementation. Mathematics is not an experimental > science, it is not even a science. The principle of falsifiability does > not apply. Any even number > 2 is the sum of two prime numbers. Now suppose that I find just _one_ huge number for which this (well-known) conjecture does _not_ hold. By mere number crunching. Isn't that an application of the "principle of falsifiability" to mathematics? Han de Bruijn
From: Han de Bruijn on 30 Aug 2006 06:57
schoenfeld.one(a)gmail.com wrote: > Proginoskes wrote: >> >>CONJECTURE: The remainder of 2^n divided by n is never 3. >> >>However, this conjecture is false; in particular, the remainder of 2^n >>divided by n is 3 if n = 4,700,063,497 (but for no smaller n's). > > Hello Crackpot. Hey, hey! Wash your mouth! If *that* is crackpottery, I'll eat my hat! Han de Bruijn |