Monday, July 25, 2016

A Chinese Migrant With No College Education But With a Hayekian Kind of Mind Makes a Major Discovery

A Chinese migrant worker with no college degree has found a solution to a complex math problem.

CNN tells the story:
Yu Jianchun, who works for a parcel delivery company, said he'd always had a passion for numbers and has created an alternative method to verify Carmichael numbers.
His solution amazed academics, who said his proof was much more efficient than the traditional one. 
"It was a very imaginative solution," said Cai Tianxin, a math professor at Zhejiang University.
"He has never received any systematic training in number theory nor taken advanced math classes. All he has is an instinct and an extreme sensitivity to numbers."
Carmichael numbers are sometimes described as "pseudo primes" -- they complicate the task of determining true prime numbers, which are divisable only by 1 and itself. They play an important role in computer science and information security.
Yu worked on his proof during his free time while building a new home in his village last year.
"I was overwhelmed with joy, because my solution was completely different to the classic algorithm," said Yu.
William Banks, a mathematician at the University of Missouri, who works with Carmichael numbers said, if verified, an alternative proof would be an exciting discovery for his field.
He said that the only construction of an infinite family of Carmichael number was done by academics 20 years ago.
"There have been additional theoretical results in this area -- including several by myself and my co-authors -- but these are all variations on a theme," he said.
Yu presented his proof -- along with solutions to four other problems -- to the public on June 13 at a graduate student seminar on the invitation of Cai.
However, it took Yu more than eight years of writing letters to prominent Chinese mathematicians to get any recognition for his talent.
Cai, the professor, says he will include Yu's solution in an upcoming book.
But what really caught my eye in the CNN story is this: 
Yu, who describes himself as shy and introverted, said he would pore over numbers with a calculator while he studied animal breeding at a vocational school....
"I'm slow-witted," he says. "I need to spend far more time studying math problems than others. Although I am sensitive to numbers, I barely have any knowledge about calculus or geometry."
He has a damn Hayekian kind of mind.  F.A. Hayek once wrote an essay titled Two Types of Mind (Chapter 3). In the essay,  he discussed two types of scientific thinkers, the "master of his subject" versus the "puzzler."

WHAT PRESERVED ME from developing an acute
feeling of inferiority in the company of those
more efficient scholars was that I knew that I
owed whatever worth-while new ideas I ever had
to not possessing their capacity, i.e. to often not
being able to remember what every competent
specialist is supposed to have at his fingertips.
Whenever I saw a new light on something it was as
the result of a painful effort to reconstruct an
argument which most competent economists

would effortlessly and instantly reproduce..

I am inclined to call minds of this type the
"puzzlers." But I shall not mind if they are called
the muddlers, since they certainly will often give
this impression if they talk about a subject before
they have painfully worked through to some
degree of clarity.

Their constant difficulties, which in rare
instances may be rewarded by a new insight, are
due to the fact that they cannot avail themselves
of the established verbal formulae or arguments
which lead others smoothly and quickly to the
result. But being forced to find their own way of
expressing an accepted idea, they sometimes discover
that the conventional formula conceals
gaps or unjustified tacit presuppositions. They
will be forced explicitly to answer questions
which had been long effectively avoided by a
plausible but ambiguous turn of phrase or an
implicit but illegitimate assumption.


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