The "Extreme Ordinariness" of Prodigies

Of genius and childhood:

https://www.futilitycloset.com/2021/10/01/youth-and-genius/

"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” :

http://www.csmonitor.com/Science/2016/0719/In-China-a-real-life-Good-Will-Hunting

…alternatively, this coverage from the Washington Post:

https://www.washingtonpost.com/news/morning-mix/wp/2016/07/19/parcel-delivery-man-says-hes-solved-tough-number-problem-heralded-as-chinas-good-will-hunting/

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.

There's Something About Sitan...

A VERY interesting/enjoyable (transcribed) interview with 20-year-old Harvard student Sitan Chen, a young STEM whiz who combines prodigious talents in math, music, and computer science:
http://tinyurl.com/lhzg7wv

He lists his current interests as  "pseudorandomness, algebraic topology, and algebraic geometry." And when he's not working on complex math and computer science problems, he's playing classical piano at Carnegie Hall.

He has his own blog here (but not for the average math doodler):
https://formalreasons.wordpress.com/

And a previous short Khan Academy interview with Chen here:
http://life.khanacademy.org/post/55172352451/a-khanversation-with-super-humble-super

It's good to know that someone like Sitan is coming along, because, approaching his 40th birthday, Terry Tao is of course almost over-the-math-hill. ;-)

Below, Chen is in action a couple years back in a 19-minute video from the first article:

Jacob's Genius

Over a year ago I put up a brief post about the phenomenal math/science autistic prodigy Jacob (Jake) Barnett (I.Q. 170) after he'd appeared on a "60 Minutes" segment:

http://math-frolic.blogspot.com/2012/01/autistic-prodigy-1-in-10-million.html

I hadn't really followed his story since then (he's 14 years-old now, studying astrophysics at college), but noticed this week in the bookstore that his mother has authored a new book about raising him, entitled "The Spark."
From briefly flipping through pages and early reviews, looks to be a very interesting volume (though don't know when I'll have a chance to read all the way through). Anyway, passing it along for any, who like me, have a fascination with the linkages between math, language, music, and cognition/savantism. So hard to comprehend where this kind of genius or brain-wiring derives from, or alternatively, since it does exist, why it is so rare.

Many YouTube clips of young Jacob in action here:

http://www.youtube.com/user/mathboysmom

An older newspaper piece about him here:

http://tinyurl.com/4oa599v  

And a more recent piece here:

http://www.usatoday.com/story/news/nation/2013/04/08/indiana-boy-genius-book/2064921/

The Brain Is a Wondrous Mystery

via Wikimedia

Yet another fascinating story of a math prodigy of sorts… a young man whose math prowess only came about following a severe bodily attack:

http://tinyurl.com/866msww

From the article:

"Jason Padgett, 41, sees complex mathematical formulas everywhere he looks and turns them into stunning, intricate diagrams he can draw by hand. He’s the only person in the world known to have this incredible skill, which he obtained by sheer accident just a decade ago.
“I’m obsessed with numbers, geometry specifically,” Padgett said. “I literally dream about it. There’s not a moment that I can’t see it, and it just doesn’t turn off.”

"Padgett doesn’t have a PhD, a college degree or even a background in math. His talent was born out of a true medical mystery that scientists around the world are still trying to unravel.
"...One night he was walking out of a karaoke club in Tacoma when he was brutally attacked by muggers who beat and kicked him in the head repeatedly….

“All I saw was a bright flash of light and the next thing I knew I was on my knees on the ground and I thought, ‘I’m gonna get killed,’” he said.

"At the time, doctors said he had a concussion, but within a day or two, Padgett began to notice something remarkable. This college dropout who couldn’t draw became obsessed with drawing intricate diagrams, but didn’t know what they were.

“I see bits and pieces of the Pythagorean theorem everywhere,” he said. “Every single little curve, every single spiral, every tree is part of that equation.”

"The diagrams he draws are called fractals…."

Autistic Prodigy ('1 in 10 million')

In case you missed it, last night CBS's "60 Minutes" profiled autistic (math & science) prodigy Jake Barnett. Fascinating!:

Thinking vs. Rote Knowing

Assessing a 14-yr.-old math whiz for entrance to Cambridge (...and a nice thought puzzle):

http://www.bbc.co.uk/news/magazine-15574889

Incredible Kid!

WOW! 12-year-old autistic math/physics prodigy reworking Einstein here:

http://tinyurl.com/4oa599v

'nuther Oldie but Goodie

This is an old puzzle that comes in a variety of forms. I've adapted it here from a Martin Gardner version in his "Aha! Gotcha" volume:

6 students make reservations for a dinner at a popular pizza place. But at the last minute a 7th student decides to join them.
When the kids arrive the hostess immediately sees that there are 7 diners for her table set-up of 6. But she is a clever one. Thinking on her feet, she decides to seat the first student in chair #1 and then have his girlfriend (the second student) sit on his lap temporarily. Then the hostess can sit student #3 in the 2nd chair, student #4 in the 3rd chair, student #5 in the 4th chair, and finally student #6 goes into chair #5. Chair #6 is thus still leftover, and so of course the hostess can now move the original girlfriend to that seat. Waaah-laaaaah!!
Hope she gets a big tip... or, maybe not!?

Do you see the flaw in her method?
(For any who don't see through the flaw I'll wait 24 hrs. and explain the simple answer in the comments below... and then you can go "DOH!")

I'm sure the young lass (another child prodigy) reported on in this nice article can spot the catch in the math:

http://tinyurl.com/34arukx
 

Math: A Young Man's Game?

Another interesting post from Alex Bellos, this time on "maths' cult of youth" (the common notion that great mathematicians invariably do their best work in youth, and are past their prime by age 40).

http://alexbellos.com/?p=1354

Starts off focusing on now 15-year-old child prodigy Arran Fernandez, before addressing the issue more broadly.

(...Hopefully, we'll get a few more productive years out of 35-year-old Terence Tao , who some consider the world's greatest living mathematician, before he commences his downward slide. ;-))