A
fundamental problem of cognition is just where does mathematical
insight come from? We certainly adopt language and forms that allow
insights to arise. Here Ramanujan had a dream that spelled out a
particular insight. Been part of a deep spiritual tradition he would
have had specific tools available to facilitate this.
My
own insight which is key to fully expanding mathematics and is
central to my published paper, came about before I entered
University. Other insights flowed from that including a method to
absorb particles into geometry.
It is
difficult to not suspect that all knowledge is out there waiting for
us to learn the language and to accept it. Particularly when we are
dealing with a natural conjecture regarding the GOD machine as a
human prospective invention soon to arrive in our presence trough our
own efforts again having done so over thirty thousand years ago.
Mathematician's
Century-Old Secrets Unlocked
by LiveScience Staff
Date: 27 December 2012
While on his death
bed, the brilliant Indian mathematician Srinivasa Ramanujan
cryptically wrote down functions he said came to him in dreams,
with a hunch about how they behaved. Now 100 years later, researchers
say they've proved he was right.
"We've solved the
problems from his last mysterious letters. For people who work
in this area of math, the problem has been open for 90 years,"
Emory University mathematician Ken Ono said.
Ramanujan, a
self-taught mathematician born in a rural village in South India,
spent so much time thinking about math that he flunked out of college
in India twice, Ono said.
But he sent
mathematicians letters describing his work, and one of the most
preeminent ones, English mathematician G. H. Hardy, recognized the
Indian boy's genius and invited him to Cambridge University in
England to study. While there, Ramanujan published more than 30
papers and was inducted into the Royal Society. [Creative Genius:
The World's Greatest Minds]
"For a brief
window of time, five years, he lit the world of math on
fire," Ono told LiveScience.
But the cold weather
eventually weakened Ramanujan's health, and when he was dying, he
went home to India.
It was on his deathbed
in 1920 that he described mysterious functions that mimicked theta
functions, or modular forms, in a letter to Hardy. Like trigonometric
functions such as sine and cosine, theta functions have a repeating
pattern, but the pattern is much more complex and subtle than a
simple sine curve. Theta functions are also "super-symmetric,"
meaning that if a specific type of mathematical function called a
Moebius transformation is applied to the functions, they turn into
themselves. Because they are so symmetric these theta functions are
useful in many types of mathematics and physics, including string
theory.
Ramanujan believed
that 17 new functions he discovered were "mock modular forms"
that looked like theta functions when written out as an infinte sum
(their coefficients get large in the same way), but weren't
super-symmetric. Ramanujan, a devout Hindu, thought these
patterns were revealed to him by the goddess Namagiri.
Ramanujan died before
he could prove his hunch. But more than 90 years later, Ono and his
team proved that these functions indeed mimicked modular forms, but
don't share their defining characteristics, such as super-symmetry.
The expansion of mock
modular forms helps physicists compute the entropy, or level of
disorder, of black holes.
In developing mock
modular forms, Ramanujan was decades ahead of his time, Ono said;
mathematicians only figured out which branch of math these equations
belonged to in 2002.
"Ramanujan's
legacy, it turns out, is much more important than anything anyone
would have guessed when Ramanujan died," Ono said.
The findings were
presented last month at the Ramanujan 125 conference at the
University of Florida, ahead of the 125th anniversary of the
mathematician's birth on Dec. 22.
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