Okay, math lovers, this is the one you've been waiting for: Shinichi Mochizuki of Kyoto University in Japan is claiming to have found proof (divided into four separate studies with 500+ pages) of the so-called abc conjecture, a longstanding problem in number theory which predicts that a relationship exists between prime numbers. The tricky part? Now other mathematicians need to dig into his extensive work, and confirm that he's right.

Now, because I failed grade 9 math, I'm going to let Philip Ball of Nature News explain this one to you:

Like Fermat's theorem, the abc conjecture refers to equations of the form a+b=c. It involves the concept of a square-free number: one that cannot be divided by the square of any number. Fifteen and 17 are square free-numbers, but 16 and 18 - being divisible by 42 and 32, respectively - are not.

The 'square-free' part of a number n, sqp(n), is the largest square-free number that can be formed by multiplying the factors of n that are prime numbers. For instance, sqp(18)=2×3=6.

If you've got that, then you should get the abc conjecture. It concerns a property of the product of the three integers axbxc, or abc - or more specifically, of the square-free part of this product, which involves their distinct prime factors. It states that for integers a+b=c, the ratio of sqp(abc)r/c always has some minimum value greater than zero for any value of r greater than 1. For example, if a=3 and b=125, so that c=128, then sqp(abc)=30 and sqp(abc)2/c = 900/128. In this case, in which r=2, sqp(abc)r/c is nearly always greater than 1, and always greater than zero.

If you don't get any of that or what Mochizuki has done, don't worry — many mathematicians don't either. And in fact, Mochizuki is considered somewhat of a genius and a guy who's in a league of his own. He thinks in terms of mathematical 'objects' — abstract entities like geometric objects, sets, permutations, topologies, and matricies. Ball quotes mathematician Dorian Goldfeld as saying, "At this point, he is probably the only one that knows it all."