120 Year Old Math Puzzle Solved! Lie group E8
 

http://www.cnn.com/2007/TECH/science....ap/index.html

For you eggheads out here.

How did this puzzle go unsolved for 120 years????

Amazing!

It's like a fibinacci or something.

wow...thats amazing.

And to think i still use my fingers to do math.

more info needed...i dont know what problem they solved

so basically it was a giant was of time

Damn thats some awesome math.

"248 dimensions"

:)

That's the kinda stuff that even Stephen Hawking has a hard time getting his head around.

that's intense.. what's perhaps more intense is that they spent 4 years dedicated to solving the problem and they say there are no obvious practical applications for the resulting calculation..

lol gotta love it! :upsidedow

The E8 calculation
A group of mathematicians started to develop algorithms and software to do these calculations (for any Lie group) in 2002. Fokko du Cloux took on the monumental task of writing the software, and by the fall of 2005 this software was ready. After calculations on smaller groups, they were ready to tackle E8.

Specifically the goal was to compute Kazhdan-Lusztig-Vogan polynomials for the large block of the split real form of E8. This block as 453,060 irreducible representations. For more information here are even more details.

The enormous size and complexity of E8 meant that his program needed a very large computer to run - one with more than 200 gigabytes of RAM. Starting in the summer of 2006, du Cloux, David Vogan and Marc van Leeuwen worked to make the program run on a smaller computer. After some experiments on other computers, by Birne Binegar and Dan Barbasch, the computations were run on the supercomputer Sage, provided by William Stein at the University of Washington. Sage has 64 gigabytes of memory and 16 processors.
The size of the answer
The result of the E8 calculation is a matrix, or grid, with 453,060 rows and columns. There are 205,263,363,600 entries in the matrix, each of which is a polynomial. The largest entry in the matrix is:

152 q22 + 3,472 q21 + 38,791 q20 + 293,021 q19 + 1,370,892 q18 + 4,067,059 q17 + 7,964,012 q16 + 11,159,003 q15 + 11,808,808 q14 + 9,859,915 q13 + 6,778,956 q12 + 3,964,369 q11 + 2,015,441 q10 + 906,567 q9 + 363,611 q8 + 129,820 q7 + 41,239 q6 + 11,426 q5 + 2,677 q4 + 492 q3 + 61 q2 + 3 q

If each entry was written in a one inch square, then the entire matrix would measure more than 7 miles on each side.

Even with a supercomputer it required very sophisticated mathematics and computer science to carry out the calculation. The computation was completed on January 8, 2007. Ultimately the computation took 77 hours of computer time, and 60 gigabytes to store the answer in a highly compressed form.

This is a huge amount of data. By way of comparison, a human genome can be stored in less than one gigabyte. For a more down to earth comparison, 60 gigabytes is enough to store 45 days of continuous music in MP3-format.

Some other facts about the answer
Size of the matrix: 453,060

Number of distinct polynomials: 1,181,642,979

Number of coefficients in distinct polynomials: 13,721,641,221

Maximal coefficient: 11,808,808

Polynomial with the maximal coefficient: 152q22 + 3,472q21 + 38,791q20 + 293,021q19 + 1,370,892q18 + 4,067,059q17 + 7,964,012q16 + 11,159,003q15 + 11,808,808q14 + 9,859,915q13 + 6,778,956q12 + 3,964,369q11 + 2,015,441q10 + 906,567q9 + 363,611q8 + 129,820q7 + 41,239q6 + 11,426q5 + 2,677q4 + 492q3 + 61q2 + 3q
Value of this polynomial at q=1: 60,779,787

Polynomial with the largest value at 1 which we've found so far: 1,583q22 + 18,668q21 + 127,878q20 + 604,872q19 + 2,040,844q18 + 4,880,797q17 + 8,470,080q16 + 11,143,777q15 + 11,467,297q14 + 9,503,114q13 + 6,554,446q12 + 3,862,269q11 + 1,979,443q10 + 896,537q9 + 361,489q8 + 129,510q7 + 41,211q6 + 11,425q5 + 2,677q4 + 492q3 + 61q2 + 3q
Value of this polynomial at q=1: 62,098,473

source

tahts some jew shit right there

That's what I love about math. The most difficult subject you have to take and there are no practical applications at all.

Hah, it took mathematicians a while

No practical application yet.

Just remember George Boole who died in poverty in 1864. He invented some silly math using just 1 and 0 and his work gathered dust for almost 100 years until it was used to make the first digital computer.

That is crazy and cool

I need to get out more.

















NOT!

apparently it may have some application to string theory. Also, it wasnt a puzzle in the sense of Fermats Last Theorem or something like that, it was more that the computing power /programming wasnt in place to perform the calculations needed to solve the space until recently.

Here's the party animals of E8.

http://upperclassvideo.googlepages.com/partyanimals.jpg

Apparently sock and sandals are required for the Group photo.

E8-4Life

wow this is great!!!!!!!!!!

I was going to solve that for them, but my crayon broke.

:1orglaugh so it seems! What a brain Trust:thumbsup

Technically this and all you have ever done is a waste of time.

No practical application? WTF! All of that wasted time! Could've been baking cookies!!!

Impresive, as sad before it will find application one day. Many parts of math are discovered much before practical explanation. About sandals: maybe that is where all their ideas comes from. So friends, I am going to buy a pair. It looks that old belive that people with the glasses are smart is wrong. Sandals are the key.

amazing, but what is it good for?

thats amazing, i'm still working on the rubiks cube ..!

That computing power should have been used for a practical application, like internet porn.

same thing i was going to ask :1orglaugh

amazing ...

never said it wasn't ;)

lol same hahaha
i always use my fingers to count :thumbsup

damn that's badass...though what would they gain after solving this?