Mathematical proofs can be simple or extremely
difficult. But they’ve got one thing in common; they are at least a little
elegant. Or just consist of 200 terabytes of data.
 |
| The computer that did the calculations |
Two hundred
terabytes look like a ridiculous amount of data, and it is. It is enough to
fill the hard drives of 441 laptops and the compressed version of the data only
takes already 30.000 hours to download, that’s about three and a half years. The
supercomputer that ran the calculations needed 2 days, with eight hundred
processors running at the same time. Nobody is, of course, going to read the
proof, since that is impossible. This gigantic thing also has the world record.
The proof took it from another mathematical proof that was ‘just’ thirteen
gigabytes big.
 |
| The first 7824 numbers with their valid colourings, the white squares can be either colour |
But for
what could you possibly need so much data? Well, the problem is called the Boolean
Pythagorean triples problem. It asks the question if it’s possible to give each
number a colour; red or blue, in such a way that there aren’t three numbers
that fit into Pythagoras’ equation; a2+b2=c2.
So when 3 and 5 are blue, 4 has to be red, because 32+42=52=9+16=25.
As it turns out, to the number 7824, numbers can be coloured in a ‘valid’ way,
but after 7824, not anymore. Up to 7824, there are 102,300 possible colour combinations, that's a 1 with 2300
zeroes. Fortunately, Oliver Kullmann and Victor Marek, the mathematician who
found the proof, could slim the amount of combinations the supercomputer had to
check to just under a trillion.
Where does maths end?
After this
proof, a new question arose. Is this really still maths? A lot of
mathematicians think otherwise. Because nobody knows why it’s possible to
create double-coloured triplets under 7824, but not above. Nor does anyone know
what’s special about the number 7825 that it ruins everything. Terence Tao
proved the former world record problem, which needed thirteen gigabytes of data
to proof, in the ‘old-fashioned’ way, so by reasoning and thinking logically, a
year after the computer proved it. Many mathematicians consider that a much
more satisfying way and thus the search for the proof of the Boolean
Pythagorean triples problem isn’t over yet.
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