Posted by: jai@aloha.com (Dr. Jai Maharaj)

HINDUISM TODAY                     February 1990
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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 
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.
Arriving in 1914 on the eve of World War I, 
Ramanujan experienced severe culture shock at 
Cambridge.  he had to cook for himself and 
insisted on going bare foot Hindu style on the 
cold floors.  But Hardy, a man without airs or 
inflated ego, made him feel comfortable amidst the 
stuffy Cambridge tradition.  Hardy and Littlewood 
both served as his mentors for it took two 
teachers to keep pace with his advances.  Soon, as 
Hardy recounts, it was Ramanujan who was teaching 
them, in fact leaving them in the wake of 
incandescent genius.
Within a few months war broke out.  Cambridge 
became a military college.  vegetable and fruit 
shortages plagued Ramanujan's already slim diet.  
The war took away Littlewood to artillery 
research, and Ramanujan and Hardy were left to 
retreat into some of the most recondite math 
possible.  One of the stunning examples of this 
endeavor is a process called partitioning, 
figuring out how many different ways a whole 
number can be expressed as the sum of other whole 
numbers.  Example: 4 is partitioned 5 ways (4 
itself, 3+1, 2+2, 2+1+1, 1+1+1+1), expressed as 
p(4)=5.  The higher the number, the more the 
partitions.  Thus p(7)=15.  Deceptively though, 
even a marginally larger number creates 
astronomical partitions.  p(200)=397,999,029,388.  
Ramanujan -- with Hardy offering technical checks 
-- invented a tight, twisting formula that 
computes the partitions exactly.  To check the 
theorem a fellow Cambridge mathematician tallied 
by hand the partitions for 200.  It took one 
month.  Ramanujan's equation was precisely 
correct.  U.S. mathematician George Andrews, who 
in the late 1960's rediscovered a "lost notebook" 
of Ramanujan's and became a lifetime devotee, 
describes his accuracy as unthinkable to even 
attempt.  Ramanujan's partition equation helped 
later physicists determine the number of electron 
orbit jumps in the "shell" model of atoms.
ANother anecdote demonstrates his mental 
landscape.  By 1917, Ramanujan had fallen 
seriously ill and was convalescing in a country 
house.  Hardy took a taxi to visit him.  As math 
masters like to do he noted the taxi's number -- 
1729 -- to see if it yielded any interesting 
permutations.  To him it didn't and he thought to 
himself as he went up the steps to the door that 
it was a rather dull number and hoped it was not 
an inauspicious sign.  He mentioned 1729 to 
Ramanujan who immediately countered, "Actually, it 
is a very interesting number.  It is the smallest 
number expressible as the sum of two cubes in two 
different ways."
Ramanujan deteriorated so quickly that he was 
forced to return to India -- emaciated -- leaving 
his math notebooks at Cambridge.  He spent his 
final year face down on a cot furiously writing 
out pages and pages of theorems as if a storm of 
number concepts swept through his brain.  Many 
remain beyond today's best math minds.
Debate still lingers as to the origins of 
Ramanujan's edifice of unique ideas.  
Mathematicians eagerly acknowledge surprise states 
of intuition as the real breakthroughs, not 
logical deduction.  There is reticence to accept 
mystical overtones, though, like Andrews, many can 
appreciate intuition *in the guise* of a Goddess.  
But we have Ramanujan's own testimony of feminine 
whisperings from a Devi and there is the sheer 
power of his achievements.  Hindus cognize this 
reality.  As an epilogue to this story, a seance 
held in 1934 claimed to have contacted Ramanujan 
in the astral planes.  Asked if he was continuing 
his work, he replied, "No, all interest in 
mathematics dropped out after crossing over."
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HINDUISM TODAY                     February 1990
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