Spare Time

[WikiGuru]

link

What a nightmare it would have been to solve! And the worst part is that it doesn't appear to have much use yet...

[IAmACalculator]

For more fun, Click here.
You can also attempt to reproduce Fermat's original proof in his last theorem.

[DigiTan]

Sounds useless to me. We're we trying to cure cancer at some point?

[Neekstar]

Sounds like they had fun.

[DarkerLine]

Ah, I remember my math teacher talking about Lie algebras...

TEACHER: "This has direct applications to quantum physics and string theory."
CLASS: *laughter*
TEACHER: "No, I'm actually serious."

[luby]

But 4 years to solve it... That is dedication. That is like highschool where all you do is try to solve it. I wonder how they did so.

[frenchcalc1]

Wow! To spend *years* solving problems that are, at this point, useless in modern-day society's dilemnas...now that's dedication!

[DarkerLine]

That article never actually states the problem. It talks about "the problem's proof" but it only makes sense to have a proof if there's a theorem - what's the theorem?

Also, I would hesitate to say the word "useless" - the way branches of mathematics and indeed many other sciences are coming together these days, this could have implications in the most unexpected places. Fermat's last theorem, for example, was proved by a result not in number theory, but in topology. This result could have a similar impact, and there are a number of unsolved problems out there which it would change our lives greatly to have a solution to.

[WikiGuru]

Here's what the theorem is:
The Lie group E₈
Click link for more info about the problem.
link

[DigiTan]

Fair enough. I'm mostly leery of the litany of useless multi-million dollar studies that pour out of these institutes. Though I never was crazy about academia in other aspects. I might help if the news article mentioned the nature of this math problem though.

[WikiGuru]

[quote name='"CNN"']The 18-member group of mathematicians and computer scientists was convened by the American Institute of Mathematics in Palo Alto to map a theoretical object known as the "Lie group E8."

Lie (pronounced Lee) groups were invented by 19th-century Norwegian mathematician Sophus Lie in his study of symmetrical objects, especially spheres, and differential calculus.

The E8 group, discovered in 1887, is the most complicated Lie group, with 248 dimensions, and was long considered impossible to solve.[/quote]

[DigiTan]

I kind of gathered when I followed the link. But they don't shed any light on what variation(s) of math were used, what tools/methods were applied, or what general form the solution had.

[DarkerLine]

Ti-Ho: "The Lie group E₈" is a mathematical object, not a theorem.

I gather from the slightly more informative wikipedia article that the "mapping" referred to in CNN was finding a representation of the group in a vector space (over the complex numbers? that part was unclear). Basically, it's a different way to look at the elements of the group: each element becomes a linear transformation in the vector space, and the product of two elements becomes the composition of two transformations.
That's really all I know about the subject, since my only knowledge of representation theory comes from a week-long class this summer (and my knowledge of Lie groups is even weaker)

But if I'm reading that article right, then the solution was actually a definition of the mapping from Lie group element to vector space transformation.