niranjan

Here is an article on the Indian mathematician Ramanujan, considered to be one of the greatest mathematicians of all time....



Computing the Mathematical Face of God: S. Ramanujan

He died on his bed after scribbling down
revolutionary mathematical formulas that bloomed
in his mind like ethereal flowers -- gifts, he
said, from a Hindu Goddess.

He was 32 the same age that the advaitan advocate
Adi Shankara died. Shankara, born in 788, left
earth in 820. Srinivasa Ramanujan was born in
1887. He died in 1920 -- an anonymous Vaishnavite
brahmin who became the first Indian mathematics
Fellow at Cambridge University. Both Shankara and
Ramanujan possessed supernatural intelligence, a
well of genius that leaves even brilliant men
dumb-founded. Ramanujan was a meteor in the
mathematics world of the World War I era. Quiet,
with dharmic sensibilities, yet his mind blazed
with such intuitive improvisation that British
colleagues at Cambridge -- the best math brains in
England -- could not even guess where his ideas
originated. It irked them a bit that Ramanujan
told friends the Hindu Goddess Namagiri whispered
equations into his ear. Today's mathematicians --
armed with supercomputers -- are still
star-struck, and unable to solve many theorems the
young man from India proved quickly by pencil and
paper.

Ramanujan spawned a zoo of mathematical creatures
that delight, confound and humble his peers. They
call them "beautiful," "humble," "transcendent,"
and marvel how he reduced very complex terrain to
simple shapes.

In his day these equations were mainly pure
mathematics, abstract computations that math sages
often feel describe God's precise design for the
cosmos. While much of Ramanujan's work remains
abstract, many of his theorems are now the
mathematical power behind several 1990's
disciplines in astrophysics, artificial
intelligence and gas physics. According to his
wife -- Janaki, who still lives outside Madras --
her husband predicted "his mathematics would be
useful to mathematicians for more than a
century." Yet, before sailing to England,
Ramanujan was largely ignorant of the prevailing
highest-level math. He flunked out of college in
India. Like Albert Einstein, who toiled as a
clerk in a Swiss patent office while evolving his
Special Theory of Relativity at odd hours,
Ramanujan worked as a clerk at a port authority in
Madras, spending every spare moment contemplating
the mathematical face of God. It was here in
these sea-smelling, paper-pushing offices that he
was gently pushed into destiny -- a plan that has
all the earmarks of divine design.

Ramanujan was born in Erode, a small, rustic town
in Tamil Nadu, India. His father worked as a
clerk in a cloth merchant's shop. his namesake is
that of another medieval philosophical giant --
Ramanuja -- a Vaishnavite who postulated the
Vedanta system known as "qualified monism." the
math prodigy grew up in the overlapping
atmospheres of religious observances and ambitious
academics. He wasn't spiritually preoccupied, but
he was steeped in the reality and beneficence of
the Deities, especially the Goddess Namagiri.
Math, of course, was his intellectual and
spiritual touchstone. No one really knows how
early in life ramanujan awakened to the psychic
visitations of Namagiri, much less how the
interpenetration of his mind and the Goddess'
worked. By age twelve he had mastered
trigonometry so completely that he was inventing
sophisticated theorems that astonished teachers.
In fact his first theorems unwittingly duplicated
those of a great mathematician of a hundred years
earlier. This feat came after sifting once
through a trigonometry book. he was disappointed
that his "discovery" has already been found. then
for four years there was numerical silence. At
sixteen a copy of an out-of-date math book from
Cambridge University came into his hands. It
listed 5,000 theorems with sparse, short-cut
proofs. Even initiates in the arcane language of
mathematics could get lost in this work.
Ramanujan entered it with the giddy ambition and
verve of an astronaut leaping onto the moon. It
subconsciously triggered a love of numbers that
completely saturated his mind. He could envision
strange mathematical concepts like ordinary people
see the waves of an ocean.

Ironically, his focus on math became his academic
undoing. he outpaced his teachers in numbers
theory, but neglected all other subjects. He
could speak adequate English, but failed in it and
history and other science courses. He lost a
scholarship, dropped out, attempted a return but
fell ill and quit a second time. By this time he
was married to Janaki, a young teenager, and was
supporting his mother. Often all night he
continued his personal excursions into the math
universe - being fed rice balls by his wife as he
wrote lying belly-down on a cot. During the day
he factored relatively mundane accounts at the
post office for 20 pounds a year. He managed to
publish one math paper.

As mathematicians would say, one branch of
potential reality could have gone with Ramanujan
squandering his life at the port. But with one
nudge from the invisible universe, Namagiri sent
him Westward. A manager at the office admire the
young man's work and sensed significance. He
talked him into writing to British mathematicians
who might sponsor him. Ramanujan wrote a simple
letter to the renowned G. W. Hardy at Cambridge,
hinting humbly at his breakthroughs and describing
his vegetarian diet and spartan needs if he should
come to the university. He enclosed one hundred
of his theorem equations.

Hardy was the brightest mathematician in England.
Yet, as he knew and would write later at the
conclusion of his life, he had done no original,
mind-bending work. At Cambridge he collaborated
with an odd man named Littlewood, who was so
publicly retiring that people joked Hardy made him
up. The two, though living within a hundred yards
of each other, communicated by exchange of terse,
math-laden letters. Ramanujan's letter and
equations fell to them like a broadcast from alien
worlds. AT first they dismissed it as a
curiosity. Then, they suddenly became intrigued
by the Indian's musings. Hardy later wrote: "A
single look at them is enough to show that they
could only be written down by a mathematician of
the highest class. They must be true, for if they
were not true, no one would have the imagination
to invent them."

Hardy sensed an extremely rare opportunity, a
"discovery," and quickly arranged a scholarship
for the then 26-year-old Ramanujan. The
invitation came to India and landed like a bomb in
Ramanujan's family and community circle. His
mother was horrified that he would lose caste by
traveling to foreign shores. She refused to let
him go unless it was sanctioned by the Goddess.
According to one version of the story, the aged
mother then dreamt of the blessing from Namagiri.
But Janaki says her husband himself went to the
namagiri temple for guidance and was told to make
the voyage. Ramanujan consulted the astrological
data for his journey. He sent is mother and wife
to another town so they wouldn't see him with his
long brahmin's hair and bun trimmed to British
short style and his Indian shirt and wrapcloth
swapped for European fashion. He left India as a
slightly plump man with apple-round cheeks and
eyes like bright zeroes.

(continued in the next post)