A website, filled with mathematical equations that are simply insoluble, to frustrate and irritate those goody-two-shoes, mathematically adept types who pride themselves upon their clean-living, logical, parsimonious approach to life.
Drive them crazy with a website dedicated to modern equivalents of Fermat's Theorem, which stumped mathematicians for 358 years, until Wiles resolved the conundrum.-- UnaBubba, Apr 24 2012 If you'll take the merely unsolved in lieu of the unsolvable... http://en.wikipedia...lems_in_mathematics [jutta, Apr 25 2012] An Engineer, a Physisict and a Mathematician walk into a bar... http://jcdverha.hom...l/scijokes/6_2.html [zen_tom, Apr 26 2012] Math, physics engineering jokes http://www.cs.north...ck/mathphyseng.html [AusCan531, Apr 26 2012] This is a great idea apart from the fundamentals and the implementation.
What you're proposing, I infer, is a site full of mathematical conjectures, yes?
So, the first thing that any mathematician will do is to look at the conjectures to see if they are plausible and interesting. If they are, he or she will very quickly test the conjecture over a wide range to see if it holds true.
If it doesn't hold true in these numerical tests, then all you have done is make a prat of yourself. If it does hold true, of course, then you have an interesting mathematical conjecture which will keep one or more mathematicians usefully employed.
However, formulating conjectures which are (a) interesting (b) cannot be disproved numerically and (c) are difficult or impossible to prove comprehensively, is not trivial. That is why Fermat and Goldbach are better known than, say, de la Pavoire or [ubie].-- MaxwellBuchanan, Apr 24 2012 Quite a lot of this stuff would be (as Pauli said) "not even wrong".-- hippo, Apr 24 2012 That may be, [hippo] but it doesn't change the fact many maths problems are still unsolved, probably due to lack of accessibility by otherwise interested persons.
When it became technologically possible for the general public to search for undiscovered nebulae, distant planets and galaxies and other astronomical phenomena then the discovery of greater numbers of all of those than previously imagined likely became reality.-- UnaBubba, Apr 25 2012 [+] Desired.-- Inyuki, Apr 25 2012 Bring out the GIMPS (Great Internet Mersenne Prime Search).-- 4whom, Apr 25 2012 // many maths problems are still unsolved, probably due to lack of accessibility by otherwise interested persons.//
I'm not sure that's true. Interesting problems in maths generally have people trying to solve them. Important problems in maths generally have people trying to solve them. Useful problems in maths generally have people trying to solve them.
You're therefore left with a bunch of dull, unimportant and useless problems being tackled by mathematicians who aren't capable of tackling the interesting, important or useful problems.
The astronomy analogy is also a bit dodgy. Astronomy is always touted (mainly by amateur astronomers) as the only field where amateurs can and do make an important contribution.
[jutta]'s link, incidentally, shows that a lot of interesting, important and useful problems are already known, and are accessible to anyone. If I were an amateur (or professional) mathematician with any talent, I'd be tackling one of these problems already.-- MaxwellBuchanan, Apr 25 2012 Amateur astronomers work in the discovery space, so to speak. Not many in the solution space. Fermat, as an amateur, also worked in the discovery space. He did manage to resolve a few of his discoveries and became quite famous outside of his day job. A better analogy would be the gamers that are beating computer generated models of molecules. They operate in the solution space. Perhaps this website can provide tools, in the way of games, that are aligned to solve specific problems or parts of problems.
Having said that, widening a net always catches more fish. A lot of it may not be what you want, but sometimes you catch a Ramanujan.-- 4whom, Apr 25 2012 //Perhaps this website can provide tools, in the way of games, that are aligned to solve specific problems or parts of problems.//
I am no mathematician, but I don't think that approach works for most problems. Yes, you can numerically bash away at a conjecture to strengthen it or (possibly) disprove it by counterexample. And yes computation is now considered a respectable tool in mathematics. However, I don't think you can solve many problems by brute force distributed computing.
Also, [Ubie]'s idea as posted has nothing much to do with stimulating the masses to solve mathematical problems. As posted, it's a website designed to irritate mathematicians.-- MaxwellBuchanan, Apr 25 2012 Francis Guthrie's Four Colour problem was solved by brute force. Admittedly some serious thought had to go into reducing the problem into a space that could be attacked with brute force. Out of this methodology came "Proof Assistant" software. It is this software that can be turned into a game (of some sort). Not applicable to all problems, naturally.-- 4whom, Apr 26 2012 But no one really likes those brute force proofs (like the four-colour proof). They tell you whether the original proposition is proven or not, but, unlike a 'real' proof, don't give you any other insight into the way mathematics works.-- hippo, Apr 26 2012 Yes, I remember the mixed reactions to the 4-colour proof. As was mentioned, the real brainpower went into reducing the problem to a finite set that could be searched computationally.
I'm sure there's room for a distributed community of number-crunchers, but that's not the same thing. And again, as posted, the idea seems to be for a site to annoy mathematicians rather than to recruit new ones.-- MaxwellBuchanan, Apr 26 2012 An engineer, a mathematician, and a physicist are staying for the night in a hotel. A small fire breaks out in each of their rooms.
The physicist awakes, sees the fire, makes some careful observations, and on the back of the hotel's wine list does some quick calculations. Grabbing the fire extinguisher, he puts out the fire with one, short, well placed burst, and then crawls back into bed and goes back to sleep.
The engineer awakes, sees the fire, makes some careful observations, and cross references them against a series of industry-specific tables. He grabs the fire extinguisher (and after having factored in a safety threshold into his calculations), he puts out the fire by hosing down the entire room several times over, and then crawls into his soggy bed and goes back to sleep.
The mathematician awakes, sees the fire, makes some careful observations, and on a blackboard installed in the room, does some quick calculations. Jubliant, he exclaims "A solution exists!", and crawls into his dry bed and goes back to sleep.-- zen_tom, Apr 26 2012 An engineer, a physicist and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard.
After some observations and rough calculations the engineer realizes the situation and starts laughing.
A few minutes later the physicist understands too and chuckles to himself happily as he now has enough experimental evidence to publish a paper.
This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humour from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny. [link]-- AusCan531, Apr 26 2012 Wow, a whole world of humor I missed out on by learning a trade instead. I never knew. Welding jokes often involve fire, but are probably better classified as 'pranks'.-- Alterother, Apr 26 2012 Yes, [MB], I set it up as a prank to annoy mathematicians. Mathematicians are like accountants without a purpose, nowadays. This idea was proposed in honour of one particularly odious shit who wears a bright pink fedora everywhere he goes.-- UnaBubba, Apr 27 2012 //Mathematicians are like accountants without a purpose// You mean more like Mozarts than jingle- writers? Many true mathematicians would be horrified if they were found to be "useful", but the idea of pursuing a subject with no utility is, admittedly, not easy for everyone to grasp.
So, in which particular way did a mathematician embarrass you?-- MaxwellBuchanan, Apr 27 2012 A mathematician, a physicist and an historian are trying to divide the bill after a particularly extravagant meal. The historian says "...
(I have a truly remarkable punchline which this text box is too small to contain.)-- MaxwellBuchanan, Apr 27 2012 I have a truly remarkable punch for [MB] for which the distance is too great to deliver.-- AusCan531, Apr 28 2012 //But no one really likes those brute force proofs (like the four-colour proof).// I beg to differ.-- 4whom, Apr 28 2012 I am pretty sure that mathematicians for the most part don't like brute-force proofs. Such proofs leave the impression - right or wrong - that there's a more elegant "real" proof waiting to be found.-- MaxwellBuchanan, Apr 28 2012 Even Wile's proof has left some thinking that. There certainly are some aesthetically pleasing proofs that nobody dares try and better. But most are deemed "ugly" until they can be written in "The Book".-- 4whom, Apr 28 2012 The fact that brute force manipulations are deemed ugly, in no way detracts from the fact that they are proofs-- 4whom, Apr 28 2012 //in no way detracts from the fact that they are proofs//
They're proofs, but they don't contribute to mathematics in quite the same way as more elegant proofs.
A brute-force proof is still very useful, since it then proves all the conjectures which have been derived on the assumption that it was true. So, in that sense it has served its purpose.
However, brute-force proofs are still undesirable because:
(a) they may not produce as many interesting lemmas as a more elegant and "human" proof.
(b) the problem of proof has been bypassed rather than addressed. If the point of mathematics is to understand, then a "human" proof is still needed.
(c) I suspect (but don't know) that a brute force proof may be more likely to contain an error than a "human" proof.
I am sure there are still mathematicians working on Fermat, the four-colour theorem and other things which were solved computationally, in the hopes of finding a more elegant proof.
I think that if you accept brute force proofs, then you are not so far away philosophically from accepting things like statistical proofs (for things like Goldbach).-- MaxwellBuchanan, Apr 28 2012 a) absolutely
b) Not at all. Understanding something is suited to brute force (and why, and how) is enough.
c) This happens to be true, and fits with your last statement. Completely negating point b) above, but only philosophically. :-)-- 4whom, Apr 28 2012 random, halfbakery