On the Verification of Inter-Universal Teichmuller Theory

The story of fighter pilots encountering a UFO reminds me of the incident in Solaris—a practical man encountering the supernatural—

The subject of the novel is the limitations of human knowledge, a boundary which Lem predicted but which, I think, we are encountering in our lifetime. A few years ago, the mathematician Shinichi Mochizuki proved one of the [….] which would be a tremendous achievement, if any other mathematician could understand enough of the theory to verify it, which they can’t. Like the hero of Borges’ “The Secret Miracle,”—the Jewish playwright who completes his masterpiece in his head in a divinely-protracted instant of time, just before the Nazi bullet kills him— Mochizuki has achieved something marvelous but it was for himself alone, almost in secret, and may also vanish with him.

Read Shinichi Mochizuki’s reports “ON THE VERIFICATION OF INTER-UNIVERSAL TEICHMULLER THEORY” and you will find a tragicomical history of failure

“In particular, Hoshi’s case is of substantial interest in that it demonstrates that, even if one starts from such a level of mathematical maturity, it is quite possible to achieve a rigorous understanding of IUTeich within 10 years.”

There exists a threshold we have passed in certain areas of expertise where stretching the boundary of human knowledge even slightly requires such a tremendous expenditure of time and ability that it exceeds the limits of our short lifetimes. The few working on this level are so few indeed that…

When we discuss modern global inequality, we should remember that it is not limited to capital; it also now applies to human ability. A few of us have pioneered alien branches of mathematics; the rest of us struggle to read a brunch receipt, arguing over one should tip on the tax.

We are reduced to the F-18 pilot who still scratches his head, saying, “I have no idea what that was…but I’d like to fly it.”