That may seem like an insignificant detail in an abstract theory without any real-world application. But physicists and mathematicians are flocking to visit the zoo, even though they probably don’t understand it all. Because it turns out the discovery has astonishing consequences for their own disciplines.
Imagine aliens landed on Earth and handed us certifiably correct answers to our most pressing questions: Does God exist? Is the Riemann hypothesis true? Did Oswald act alone?
We’d appreciate the info, but it wouldn’t be really useful if we didn’t know how they got their answers.
This is the situation in which mathematics now finds itself. In January, a team of computer scientists posted a sweeping proof that has been hailed as one of the top results in its field this century. Yet the proof went far beyond computer science. Through a long chain of implications, it also solved a major open problem in mathematics.
Mathematicians — in the field of operator algebra, where the problem occurs — are now like those earthlings, graced with knowledge from afar. Computer science has told them that a conjecture they care about is false. But to do anything useful with the information, they need to find a way to translate the proof into a language they can understand.
“If I see a paper that says MIP* = RE, I don’t think it has anything to do with my work,” said Navascués, who co-authored previous work tying Tsirelson’s problem and the Connes embedding conjecture together. “For me it was a complete surprise.”
He and his co-authors anticipate that mathematicians will translate this new result into the language of their own field. In a blog post announcing the proof, Vidick wrote, “I don’t doubt that eventually complexity theory will not be needed to obtain the purely mathematical consequences.”
Yet as other researchers run with the proof, the line of inquiry that prompted it is coming to a halt. For more than three decades, computer scientists have been trying to figure out just how far interactive verification will take them. They are now confronted with the answer, in the form of a long paper with a simple title and echoes of Turing.
Have you come across this in your departments @physicists?