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.

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].

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.

// 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.

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.

//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.

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.

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.

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.

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.

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]

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'.

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.

//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?

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.

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".

//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).