Some apparently simple math problems still with...

Originally posted by agryson
Because the original "Nobel" who started the prize was a little miffed at his wife running off with a mathematician... apparently.

Apparently... according to myth. < http://www.snopes.com/science/nobel.asp >. You might as well ask why he left it to his successors, almost seventy years later, to institute a prize for economics. Did an economist perhaps run over his dog? No, he simply didn't think it necessary.

Richard

Originally posted by Shallow Blue
Apparently... according to myth. < http://www.snopes.com/science/nobel.asp >. You might as well ask why he left it to his successors, almost seventy years later, to institute a prize for economics. Did an economist perhaps run over his dog? No, he simply didn't think it necessary.

Richard

That article seems to make sence. Even if they were to award a Nobel to mathematicians, who would understand the reason for the award beside MAYBE other mathematicians? In a way it no reward is the reward......

Originally posted by joe shmo
That article seems to make sence. Even if they were to award a Nobel to mathematicians, who would understand the reason for the award beside MAYBE other mathematicians? In a way it no reward is the reward......

Who understood what einstein was talking about, besides mathematicians and physicists?

Originally posted by TheMaster37
Who understood what einstein was talking about, besides mathematicians and physicists?

Touche....I'm not saying mathematicians dont deserve to be included in the award....but even with einstien the idea of general realitivity is somewhat tangible: gravity, time ,light, speed, direction,mass..ect are all things we experience on a day to day basis. The mathematics behind the natural phenomena, however inescapably important, are to abstract and are unrelatable to the physical world without intense inquisition and study. The Nobel is nothing more than a popularity contest. How can a person or group determine the importance of there contribution without being factored out.....If i were better at math, I would do some factorization problem that would explicitly prove my point....lol

perhaps (a + b + c) represents every contribution of man fro the betterment of man before the addition of z

how can Z determine his numerical weight without bieng factored out of the group (a + b + c + Z)

something like that............

Originally posted by Shallow Blue
Apparently... according to myth. < http://www.snopes.com/science/nobel.asp >. You might as well ask why he left it to his successors, almost seventy years later, to institute a prize for economics. Did an economist perhaps run over his dog? No, he simply didn't think it necessary.

Richard

Hmm... lesson to be learned here is that journalists should check out snopes before writing articles. As should those reading such articles (like me). But who snopes the snopers?

Originally posted by joe shmo
Touche....I'm not saying mathematicians dont deserve to be included in the award....but even with einstien the idea of general realitivity is somewhat tangible: gravity, time ,light, speed, direction,mass..ect are all things we experience on a day to day basis. The mathematics behind the natural phenomena, however inescapably important, are to abstract and ...[text shortened]... ight without bieng factored out of the group (a + b + c + Z)

something like that............

As posted before, there is a the "Nobel" math which is the Fields Medal. However- and this is very strange- the winner must be no older than 30!

Can the square occupy some space not covered in the closed curve?

Originally posted by twilight2007
Can the square occupy some space not covered in the closed curve?

Yes, it can, and the curve does not need to be "smooth".
The square can even be totally outside the curve.

Originally posted by smaia
Yes, it can, and the curve does not need to be "smooth".
The square can even be totally outside the curve.

have you done anywork on the problem? I won't pretend like i have the slightest inkling of an idea of how to solve it,but i'm interest in mathematics...compared to you I would most likely considered to be pre-novice in mathematics. However, i would still like to hear where the plroblem arises in the proof, and i bet some of the others wouldn't mind either, so they could cut to the chase.

Originally posted by joe shmo
have you done anywork on the problem? I won't pretend like i have the slightest inkling of an idea of how to solve it,but i'm interest in mathematics...compared to you I would most likely considered to be pre-novice in mathematics. However, i would still like to hear where the plroblem arises in the proof, and i bet some of the others wouldn't mind either, so they could cut to the chase.

No, not at all.
I know there is some literature about the problem describing attempts to solve it.
Of course it is trivial to proof it for very special cases, such as if the curve has 2 axis of symmetry.
In a more general case, I think some researchers were close to proof the case where the curve is "smooth", but am not sure.

How do we know it's even provable if no one's proved it?

Originally posted by Jirakon
How do we know it's even provable if no one's proved it?

We don't, thus is the way of mathematics. You find a problem and then hypothesise whether it is true or false. If you believe it to be false, find a counter example or try and prove it so, otherwise you should try and prove it is true.

However, there is exception(s) to this rule. In ZFC - that is, the fundamental (although oft disputed) axioms of set theory - the continuum hypothesis about infinite sets is said exception. This states that there are sets of size (cardinality) less than the size of the real numbers but greater than the size of the natural numbers.

It has been shown that you cannot prove it. However, it has also been proven that you cannot disprove it. Thus is it seen as being "independent of ZFC".

Originally posted by Swlabr
This states that there are sets of size (cardinality) less than the size of the real numbers but greater than the size of the natural numbers.

It has been shown that you cannot prove it. However, it has also been proven that you cannot disprove it. Thus is it seen as being "independent of ZFC".

That's interesting. I understand the idea of unprovable statements - but proving them unprovable is where it gets tricky.

Presumably if you could find such a set, you've proved the theorem (as stated). So to prove it unprovable, you have to prove you can't find such a set. But haven't you then proved it false?

Or...does it mean that you can find a set where the cardinality cannot be determined, so that it might satisfy those conditions, but it might not.

Or is the explanation something else again?