Sunday, 23 September 2012

S4.111 - Know Your ABCs

(Relatively) Prime Time News

"Big news in Mathematics!" Para announced as the cameras started rolling. "The ABC conjecture may have been proven by a Japanese mathematics professor named Shinichi Mochizuki! This leads to a few obvious questions..."

"Hey, first of all, what the heck is that?" Cubi chimed in. "Hey, answer, the ABC Conjecture is a statement involving square-free numbers (ie- not divisible by squares), and relatively prime numbers. Hey, related to the equation a + b = c, it's described as a game in this blog post by Brian Hayes."

"Second question, why do we care?" Circe said dryly.

"Answer, a proof of said conjecture would actually include many other Diophantine problems," Expona responded. "Diophantine meaning requiring integer solutions. For instance, this would include Fermat's Last Theorem (which John D. Cook contrasts here), along with other math problems that are still open."

"Well, yes, I was aware of that," Circe countered in annoyance. "But MY answer was going to be that Mochizuki uses an entirely new mathematical theory to do it! It's barely understood, leading some to wonder if the celebration is premature."

"Indeed, the science journal 'Nature' notes that the only resemblance of this proof to that of Andrew Wiles' proof of FLT is in the theory of elliptic curves," Hyper mused, tugging on the lapels of her lab coat. "And here we're talking four papers totaling 512 pages, so even if it were immediately understandable, it would take a while to verify."

"A third point of interest is the historical context," Quinn remarked. "This problem was posed less than 30 years ago, in 1985, independently by two mathematicians. There's a lot of older problems out there that mathematicians continue to work on."

Tangent smiled as she stepped into the frame. "For instance, many still regard the Riemann hypothesis to be the most significant unsolved problem in mathematics. Dating back to 1859, it's been verified for the first hundred billion cases, but not yet proven."

"To conclude, the ABC conjecture has wide reaching implications," Para stated. "We could draw a parallel to the Grand Unified Theory of Physics. For further reading, the Polymath site has a number of links."

There was a brief moment of silence, as Reci shut down the recording equipment. He then turned to look at Para. "So where'd Maud go in all this anyway?"

The quadratic sighed. "He's off trying to fix our video microphones to see if I can sound less like a chipmunk."


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