Well this is cool

September 11, 2012

Brit Trogen


Of all the allegedly cool things I will never understand (the Higgs, string theory, 30 Rock) this may be the allegedly coolest. A Japanese mathematician named Shinichi Mochizuki claims to have written one of the most important previously-unsolved proofs in number theory.


From LiveScience:


If Shinichi Mochizuki's 500-page proof stands up to scrutiny, mathematicians say it will represent one of the most astounding achievements of mathematics of the twenty-first century. The proof will also have ramifications all over mathematics, and even in the real-world field of data encryption...


The ABC conjecture makes a statement about pairs of numbers that have no prime factors in common... If A and B are two such numbers and C is their sum, the ABC conjecture holds that the square-free part of the product A x B x C, denoted by sqp(ABC), divided by C is always greater than 0. Meanwhile, sqp(ABC) raised to any power greater than 1 and divided by C is always greater than 1.


Hear that? That was the sound of every mathematician squeeing with geek-love. And while I may be incapable of grasping the full awesomeness of the ABC conjecture, it does have one important thing in common with many of the cool things I do understand (genetics, evolution, Maru): simplicity.


"The ABC conjecture is amazingly simple compared to the deep questions in number theory," Andrew Granville of the University of Georgia in Athens was quoted as saying in the MAA article... "It's at the center of everything that's been going on."

The conjecture has also been described as a sort of grand unified theory of whole numbers, in that the proofs of many other important theorems follow immediately from it... [The ABC conjecture] is more than utilitarian; to mathematicians it is also a thing of beauty.


While it's impossible to know whether any idea will stand the test of time, one of the most fascinating things about science is that many of our most enduring concepts also share both incredible elegance and simplicity. It will still take an enormous amount of time before other mathematicians can verify this proof, but it certainly sounds like a prime candidate for this rule if it works out.


(Get it, Shinichi? Prime candidate! That one was for you.)



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