Computing the Mathematical Face of God: S. Ramanujan

[kabbadi_singh]

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.

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."