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Wednesday, July 20, 2016

"an extreme sensitivity to numbers"

Am largely taking vacation from blogging for a couple of weeks (’til political conventions are over), and will again skip Friday potpourri over at MathTango, but put up an occasional post here (and still be on Twitter) -- between the two blogs I've averaged over 5 posts per week for the last 6 years so won’t feel too guilty taking a vacation ;-)
Anyway, passing along this interesting recent piece from the Christian Science Monitor on a supposed real life “Good Will Hunting” Chinese migrant (Yu Jianchun) using a creative/imaginative approach to solve a long-standing problem involving “Carmichael numbers” :
…alternatively, this coverage from the Washington Post:
With all the reporting on Ramanujan in recent months (including in these articles), Yu's story sounds a bit familiar. According to one professor, “All he has is an instinct and an extreme sensitivity to numbers.” And Yu himself says, “I made my discoveries through intuition.”

I love this almost inexplicable notion of math prodigies and savants possessing a “sensitivity to numbers,” whatever that means, and connecting to mathematics more through intuition than pure deduction. In some way it harks back to the Platonist/non-Platonist divide in mathematics. Are such gifted individuals intuitively in touch with some Platonic realm of math that exists apart from humans, and that most of us lack direct access to, or are they merely in touch with some special corner of their own working brains? Are they discovering math or creating it? And what is it like to be “sensitive” to something as abstract and ethereal as numbers?

It all makes me think a bit of physicist Max Tegmark's controversial view that all there is in the Universe is mathematics (or mathematical structure), and ultimately nothing more. But then how would such mathematical structure evolve into human brains capable of looking back on itself with objective analysis? And are the philosophers and cognitive scientists who tackle such questions simply caught in some sort of infinite regress or word loop... explaining an explanation by an explanation of an explanation of... (that really explains nothing!).
Anyway, go read about the "package delivery worker" Jianchun who, after 8 years of emailing prominent mathematicians "to no avail," finally got someone to take note.

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