Most of Srinivasa Ramanujan’s knowledge came from a single mathematics book.
He spent all of his time thinking about math and little else.
It's no wonder he flunked out of college - twice…
Yet somehow, he found his way to the University of Cambridge
where he performed ground-breaking research on mathematical problems.
Ramanujan was born on December 22, 1887,
in the town of Erode, south of Madras (present-day Chennai) in South India.
Ramanujan was born on December 22, 1887 in Erode, a town south of Madras,
what's now called Chennai in South India.
He was considered a miracle child…the only one of his
mother’s first four children to survive infancy.
He also survived an outbreak of smallpox. Poor
health would afflict him his whole life yet it never slowed down his passion.
Math equations danced in his head as if they appeared from thin air.
He believed his gifts came from the Hindu goddess Namagiri.
He used to go to the nearby Sarangapani "Temple as
a boy to sketch complex mathematical equations in chalk on stone slabs.
As a teen, he got his hands on a copy of a book of math theorems written by
British mathematician George Carr which was intended as a teaching aid for students.
However, many students found it tough to read because it listed
answers without showing the steps to get there.
But for Ramanujan, this book awakened the genius in him.
Carr’s book was “like a crossword puzzle, with its empty grids begging to be filled in”,
as Robert Kanigel describes in his biography on Ramanujan.
He had a natural intuition for math which can be illustrated by this problem he solved.
Imagine you're on a street with 50 to 500 houses. You're looking for a special house
where the sum of all house numbers to its left equals the sum to its right.
Can you find it?
This actually happened on a street with 288 houses. The special house was number 204,
with both sides totaling 20,706.
When the Indian statistician, P. C. Mahalanobis asked Ramanujan about
this problem that he read in a magazine, Ramanujan thought for a moment and gave a
formula that works for any number of houses, not just between 50 and 500.
On a street with just 8 houses, house 6 is special because 1+2+3+4+5 equals 7+8.
Ramanujan said he knew the answer was a continued fraction,
showing his unique ability to see patterns that others would miss.
He received a scholarship to study at the reputable Government Arts College
in his hometown. of Kumbakonam.
However, his obsession with math got in the way.
He flunked his English composition paper, lost his scholarship, and dropped out because his
family couldn’t afford the 32 rupee tuition per term, a substantial amount of money at the time.
His father worked as a clerk in a sari shop and never made more than 20 rupees a month.
Ramanujan felt humiliated and ran away from home.
He gave university another shot,
but failed the entrance exams administered by the University of Madras again and again.
He scored less than 10% on the physiology exam.
A former student whom he tutored in math recalled his state of remind,
“...he used to bemoan his wretched conditions in life…he would reply that many a great man
like Galileo died in inquisition and his lot would be to die in poverty. But
I continued to encourage him that God, who is great, would surely help him…”
His failures turned out to be a blessing in
disguise because now he could focus on his one true passion.
He educated himself with that outdated math book and began feverishly stuffing
his notebooks with new formulas of his own, totaling nearly 4,000 in his lifetime.
He started to build a reputation after publishing his work in the first academic
journal dedicated to mathematics in India, the Indian Mathematical Society.
But it wasn’t long before he had to find a job.
At the age of 21, Ramanujan's parents arranged his
marriage to nine-year-old Janaki a distant relative. Such customs were common then.
He began working as an accounting clerk at the Port of Madras,
a big shipping hub known today as the Port of Chennai.
As luck would have it, his direct supervisor happened to be a mathematician,
and the head of the port was a British engineer.
They encouraged him to write to English mathematicians about his discoveries.
But two esteemed Cambridge mathematicians rejected him.
However, a third was intrigued.
In January 1913, G.H. Hardy, a fellow of Trinity College at the
University of Cambridge, received a letter from Ramanujan that read:
Dear Sir,
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office
at Madras on a salary of only £20 per annum. I am now about 23 years of age. I have had no
University education…After leaving school I have been employing the spare time at my
disposal to work at Mathematics. I have made a special investigation of divergent series
in general and the results I get are termed by the local mathematicians as "startling".
The ‘startling’ claim is that adding up all positive integers, 1, 2, 3,
4, and so on, to infinity added up to -1/12.
Bear in mind, this isn't your typical addition.
Divergent series emerge from a complex mathematical process.
Ramanujan’s letter was ten pages long,
consisting mostly of technical results from a wide range of mathematics.
He claimed to have a technique for counting prime
numbers - numbers greater than 1 that can only be divided by 1 and by itself.
Prime numbers are notoriously unpredictable.
It’s like trying to understand if there's a pattern that would somehow help you
know exactly when your favorite song will be played on the radio.
Although Ramanujan failed to find a perfect formula for predicting primes,
his work provided fresh insights into their distribution.
He also included theorems related to integral calculus.
Integral calculus can be likened to slicing a sausage and then
reassembling it, making it whole or “integral”.
It's a mathematical tool with real-world applications,
like determining the drag on a plane's wing.
As a plane flies, the air hits the wing in tiny "slices" over time, each contributing
to drag. Integral calculus adds up these small effects to calculate the total drag.
Ramanjuan’s letter to Hardy ended this way:
“Being poor, if you are convinced that there is anything of value I would like to have my theorems
published. Being inexperienced I would very highly value any advice you give me. Requesting
to be excused for the trouble I give you. I remain, Dear Sir, Yours truly, S. Ramanujan.”
Hardy didn’t know what to make of this unusual letter from a young man 5,000 miles away.
Was this a practical joke? Or, had he stumbled upon a second Sir Isaac Newton?
Hardy showed the letter to his colleague, J. E. Littlewood, who was equally amazed.
Some of the formulas were familiar, others Hardy remarked “seemed scarcely possible to believe…”
He concluded that the letter “...was certainly the most remarkable that I have ever received…”
Hardy responded to Ramanujan:
“I was exceedingly interested by your letter and by the theorems which you state. You will
however understand that, before I can judge properly of the value of what you have done,
it is essential that I should see proofs of some of your assertions.”
Such proof was required if others were to be convinced of the results.
Ramanujan didn’t bother explaining how he arrived at his conclusions;
he just lept from insight to insight.
Perhaps he took a page out of the book that so inspired him.
In his response to Hardy’s request to see proof, Ramanujan mentioned his divergent series result,
writing: “If I tell you this you will at once point out to me the lunatic asylum as my goal.”
Ramanujan wanted someone of stature like Hardy to recognize the worth in his work so that he could
get a scholarship, since, “I am already a half starving man. To preserve my brains I want food…”
Hardy wanted to arrange a scholarship for him to study at Cambridge.
But crossing the ocean was considered a serious violation of Ramanujan’s devout
orthodox Hindu faith that could lead to losing his caste status.
Hardy’s colleague E.H. Neville who was lecturing in Madras had the
task of convincing Ramanujan to go to Cambridge.
He assured him his strict vegetarian diet would be respected in England.
Any concerns Ramanujan had disappeared after his mother had a vivid dream in which
the Hindu goddess Namagiri instructed her not to hinder her son's destiny.
On March 17, 1914, Ramanujan set sail for the journey of his life.
He prepared for European life by learning to eat
with a knife and fork and learning how to tie a tie.
After a three-day journey, he arrived at Trinity College,
Cambridge, to start an extraordinary collaboration.
He and Hardy couldn’t have been any more different.
Ramanujan was a self-taught savant who believed equations expressed the thoughts of God.
Hardy was a Cambridge professor and
an avowed atheist who refused to believe what he could not prove.
Yet their partnership flourished.
Ramanujan and Hardy contributed substantially to number theory, a branch of mathematics that
deals with the fascinating properties and patterns found within ordinary numbers.
One of their most notable works calculated the 'partitions' of a number.
4 can be partitioned (or broken down) in five ways.
While this may sound straightforward, figuring out how many ways a number can be partitioned
becomes increasingly complex with larger numbers.
The number of partitions of 50 is 204,226.
This has practical implications that aren’t immediately obvious.
Partitions can help computers operate more efficiently; by dividing tasks or
data into smaller parts, devices can process information quicker.
Ramanujan pressed on with his work despite being
in poor health for much of his five years in England.
The colder weather didn’t help.
He was one found shivering in his Cambridge room,
sleeping atop the blankets, unaware he should be under them.
Maintaining a nutritious vegetarian diet was also difficult in light of
the rationing imposed during World War One.
He also skipped meals and ate at random hours of the day, with no mother or wife to care for him.
Ramanujan was eventually diagnosed with tuberculosis and a severe vitamin deficiency.
Being ill and far away from his family also affected his mental well-being.
In 1918, he threw himself onto the tracks
of the London Underground in front of an approaching train.
Luckily, a guard spotted him and pulled a switch,
bringing the train to a stop a few feet before hitting him.
His spirits improved considerably later that year when Britain’s elite body of scientists,
the Royal Society, named him a Fellow, the second Indian at the time to be so honored.
He was elected partly for his work on elliptic functions,
which are used to explain complex shapes and patterns.
Elliptic functions can accurately describe the movement of planets around the sun,
which is neither a perfect circle nor an exact oval.
It’s like having a super-detailed map of the movement of planets.
Becoming a fellow of the Royal Society is believed
to have stimulated the discovery of some of his most beautiful theorems,
which he continued to develop upon returning to India in 1919…to a hero’s welcome.
His life inspired the movie The Man Who Knew Infinity,
reflecting his profound insights into the nature of infinity.
An example is Pi, which starts with 3.14 and has an infinite number of decimal places. We
can never write down every single digit of pi, because there's no end to them!
Ramanujan got us closer and closer to this mysterious number in a faster way.
Back home in India, Ramanujan kept in touch with Professor Hardy,
and, in a letter that turned out to be his last, he hinted at an incredible discovery:
Dear Hardy,
I am extremely sorry for not writing you a single letter up to now. I discovered
very interesting functions recently which I call “Mock” ϑ-functions.
Mock theta functions are a highly abstract concept,
like a secret code mathematicians are still trying to understand.
In 2012, mathematician Ken Ono relied on Ramanujan’s mock theta functions
to devise a new math formula to better understand black holes.
This approach helps calculate the entropy of black holes,
a measure of how information gets scrambled or mixed up inside.
Ramanujan's cryptic work still conceals many mathematical treasures waiting to be discovered.
As Ono put it: “It’s like he was writing down a bible for us, but it was incomplete. He gave
us glimpses of what the future would be, and our job is to figure it out.”
Ramanujan left behind three notebooks packed
with his formulas and loose pages that were only discovered in 1976.
He was still scribbling away four days before he died on April 26, 1920.
Ramanujan was only 32 years old.
Most of his orthodox relatives stayed away from his funeral because they considered him
tainted for having crossed the waters to England, and he had been too ill to
make it to the purification ceremonies his mother had arranged at the seaside.
When Hardy was invited to receive an honorary degree at Harvard, he mentioned in his speech
that the most significant achievement of his life was discovering Ramanujan.
“I did not invent him — like other great men, he invented himself - but I was the
first really competent person who had the chance to see some of his work, and I can still remember
with satisfaction that I could recognize at once what a treasure I had found.” (page 207)
“...my association with him is the one romantic incident in my life.”
We are left to wonder how many Ramanujans are in
India or elsewhere today, waiting to be discovered.
This isn’t just a story about a brilliant mathematician.
It’s a story about how educational institutions can nurture talent and hinder it.
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Thanks for watching. I’m Cindy Pom.