For almost 200 years, Euler's conjecture reigned in mathematics unchecked. Then, a paper came out that turned the whole thing on its head... and it did it all in just two sentences.


In 1769, mathematician Leonhard Euler took Fermat's famous last theorem — that there is no positive integer n value greater than 2 for which an + bn = cn — and extrapolated it a little further: Fermat's theorem could also be true for the sum of any set of integers n-1, raised to the nth power. Or, to put it another way, you couldn't for instance take the sum of (a4 + b4 + c4) and expect it to add up tidily to d4.

It was called Euler's sum of powers conjecture and, for approximately the next two centuries, it was believed to be true. Then, as more powerful computers became available in the 1960s, two mathematicians decided to run a quick program to test it out.


That led to the writing and publishing of what Cliff Pickover recently pointed out was the "shortest-known paper in a serious math journal," essentially just a short note on the kind of computer than ran the search on and the example they found that disproved the theory. You can see it in full in the picture above. It was published in The Bulletin Of The American Mathematical Society in 1966, and so, rather undramatically, ended Euler's conjecture.

Of course, when you can be both concise and mathematically accurate, what is there really left to say?



[Via OpenCulture]