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
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