Am I a crank?
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From: Han de Bruijn on 30 Aug 2006 07:07 John Schutkeker wrote: > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote in > news:20b9$44f53d00$82a1e228$14726(a)news1.tudelft.nl: >> >>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 There are people all over the place specializing in fluid simulation, who do *not* appreciate such work. The problem is that, in areas of applied mathematics, such questions are not considered as important. The reason being that there exist other generally accepted solutions. The situation would be different if people were prepared to view upon numerical analysis as a discipline of pure mathematics which is quite interesting in itself, apart from any "Demanding Applications". As for myself, I *do* consider "purified applied mathematics" as an important and interesting way of doing mathematics. With plenty of new subjects. Han de Bruijn
From: schoenfeld.one on 30 Aug 2006 08:01 Han de Bruijn wrote: > 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? Falsifiability does not _need_ to apply in mathematics. In math, statements can be true without their being a proof of it being true. Likewise, they can be false. In physics, a hypothesis is never true only verified xor false. > > Han de Bruijn
From: Jesse F. Hughes on 30 Aug 2006 08:30 Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > Jesse F. Hughes wrote: > >> *Fortunately* mathematics is not an experimental science. > > Not true. Part of 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? Er, to be painfully honest, I don't really have an opinion on the experimental status of mathematics. I was just joshing and reacting to John's disagreement over the statement "Unfortunately mathematics is not an experimental science." Though I wouldn't call computing a large prime is an experiment. What hypothesis is being tested? As far as "structural (numerical) analysis" goes, I don't know the subject. At least not if it's different than numerical analysis (which is clearly a deductive, analytic branch, and not experimental). Okay, I guess I do have an opinion after all. Mathematics does not seem to have experiments in the same sense that physics, biology, sociology, etc., have experiments. > Welcome to the 21th century! Thanks! -- I don't want to wine and dine and date you once or twice. I want to hold you now. I just want to spend the night. You tell me a better plan. Baby, I'm not a patient man. -- Jimmy Lafave, the romantic troubadour.
From: Jesse F. Hughes on 30 Aug 2006 08:36 Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > 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? I wouldn't call that application of the principle of falsifiability. It's just a fact that some conjectures (but not all) are of the form "for all x, there exists y,z < x such that..." and these can be refuted by finding a counterexample. But this is a special case of deductive reasoning and is not the same as a "crucial experiment" in empirical science (even though it seems similar). -- Jesse F. Hughes "Hey look, Captain, next time someone wants to tie us up, let's put up a fight." --Adventures by Morse
From: Jesse F. Hughes on 30 Aug 2006 09:09
There's nothing at all wrong with playing around and learning what you can learn, whether with Goldbach's conjecture or something more pedestrian. But as others have said, the probability of finding a new, promising path to a proof are very slim. Nonetheless, if you enjoy it, have at it. Crankery comes when you think you have the proof and refuse to accept that others doubt this. Especially if you begin grand conspiracy theories about how the mathematical cabal is trying to suppress your work. The mathematical cabal *hates* criticism and you'll be a crank ever after for that. (Note: The last sentence is a joke--not a very good one--but the rest isn't.) -- Jesse F. Hughes "The people who made up the words could have said 'newspaper' is 'trees'." -- Quincy P. Hughes, five-year-old Wittgensteinian (This comment came out of the blue at breakfast.) |