Hardy Gave Himself a score of 25, Littlewood 30, Hilbert 80 and the Indian Hindu Mathematical Genius a 100 on a 0-100 Scale

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Hardy Gave Himself a score of 25, Littlewood 30, Hilbert 80 and the
Indian Hindu Mathematical Genius a 100 on a 0-100 Scale.

But how many westerners know about this Indian Hindu Mathematical Genius
Srinivas Ramanujan outside the mathematics community in the west?

Zilch.

Because western white christians continuously establish their supremacy
in the minds of Non-Whites so Whites can literally commit any crime
against non-whites and get away with it.


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https://www.famousscientists.org/srinivasa-ramanujan/

Srinivasa Ramanujan

Lived 1887 – 1920.

Srinivasa Ramanujan was a largely self-taught pure mathematician.
Hindered by poverty and ill-health, his highly original work has
considerably enriched number theory. More recently his discoveries have
been applied to physics, where his theta function lies at the heart of
string theory.


Beginnings

Srinivasa Ramanujan was born on December 22, 1887 in the town of Erode,
in Tamil Nadu, in the south east of India. His father was K. Srinivasa
Iyengar, an accounting clerk for a clothing merchant. His mother was
Komalatammal, who earned a small amount of money each month as a singer
at the local temple.

His family were Brahmins, the Hindu caste of priests and scholars. His
mother ensured the boy was in tune with Brahmin traditions and culture.
Although his family were high caste, they were very poor.

Ramanujan’s parents moved around a lot, and he attended a variety of
different elementary schools.


Early Mathematics


At age 10, Ramanujan was the top student in his district and he started
high school at the Kumbakonam Town High School. Looking at the
mathematics books in his school’s library, he quickly found his
vocation. By age 12, he had begun serious self-study of mathematics,
working through cubic equations and arithmetic and geometric series. He
invented his own method of solving quartic equations.

As Ramanujan’s mathematical knowledge developed, his main source of
inspiration and expertise became Synopsis of elementary results in pure
mathematics by George S. Carr. This book presented a very large number
of mathematical results – over 4000 theorems – but generally showed
little working, cramming into its pages as many results as possible.


With little other guidance, Ramanujan came to believe this was how
mathematics was done, so he himself learned to show little working.
Also, he could afford only a small amount of paper, doing most of his
work on slate with chalk, transferring a minimal amount of his working
and his results to paper.

His memory for mathematical formulas and constants seems to have been
boundless: he amazed classmates with his ability to recite the values of
irrational numbers like π, e, and √2 to as many decimal places as they
asked for.

An Apparently Bright Future Fizzles Out
In 1904, Ramanujan left high school; his future looked promising: he
had won the school’s mathematics prize and, more importantly, a
scholarship allowing him to study at the Government Arts College in the
town of Kumbakonam.

Obsessed with mathematics, Ramanujan failed his non-mathematical exams
and lost his scholarship. In 1905, he traveled to Madras and enrolled at
Pachaiyappa’s College, but again failed his non-mathematical exams.

The Discovery of Ramanujan as a Mathematician of Genius

The Hungry Years
At the beginning of 1907, at age 19, with minimal funds and a stomach
all too often groaning with hunger, Ramanujan continued on the path he
had chosen: total devotion to mathematics. The mathematics he was doing
was highly original and very advanced.

Even though (or some might say because) he had very little formal
mathematical education he was able to discover new theorems. He also
independently discovered results originally discovered by some of the
greatest mathematicians in history, such as Carl Friedrich Gauss and
Leonhard Euler.

Ill-health was Ramanujan’s constant companion – as it would be for much
of his short life.

By 1910, he realized he must find work to stay alive. In the city of
Madras he found some students who needed mathematics tutoring and he
also walked around the city offering to do accounting work for businesses.

And then a piece of luck came his way. Ramanujan tried to find work at
the government revenue department, and there he met an official whose
name was Ramaswamy Aiyer. Ramanujan did not have a resume to show
Ramaswamy Aiyer; all he had were his notebooks – the results of his
mathematical work.

Ramanujan’s good fortune was that Ramaswamy Aiyer was a mathematician.
He had only recently founded the Indian Mathematical Society, and his
jaw dropped when he saw Ramanujan’s work.


“I was struck by the extraordinary mathematical results contained in it.
I had no mind to smother his genius by an appointment in the lowest
rungs of the revenue department.”

V. Ramaswamy Aiyer, 1871 – 1936

Mathematician

Things Begin to Look Up
Ramaswamy Aiyer contacted the secretary of the Indian Mathematical
Society, R. Ramachandra Rao, suggesting he provide financial support for
Ramanujan. At first Rao resisted the idea, believing Ramanujan was
simply copying the work of earlier great mathematicians. A meeting with
Ramanujan, however, convinced Rao that he was dealing with a genuine
mathematical genius. He agreed to provide support for Ramanujan, and
Ramaswamy Aiyer began publishing Ramanujan’s work in the Journal of the
Indian Mathematical Society.

Ramanujan’s work, however, was hard to understand. The style he had
adopted as a schoolboy, after digesting George S. Carr’s book,
contributed to the problem. His mathematics often left too few clues to
allow anyone who wasn’t also a mathematical genius to see how he
obtained his results.

In March 1912, his financial position improved when he got a job as an
accounting clerk with the Madras Port Trust.

There he was encouraged to do mathematics at work after finishing his
daily tasks by the port’s Chief Accountant, S. Narayana Iyer, who was
treasurer of the Indian Mathematical Society, and by Sir Francis Spring,
an engineer, who was Chairman of the Madras Port Trust.

Francis Spring began pressing for Ramanujan’s mathematical work to be
supported by the government and for him to be appointed to a research
position at one of the great British universities.

A Crank or a Genius?
Ramanujan and his supporters contacted a number of British professors,
but only one was receptive – an eminent pure mathematician at the
University of Cambridge – Godfrey Harold Hardy, known to everyone as G.
H. Hardy, who received a letter from Ramanujan in January 1913. By this
time, Ramanujan had reached the age of 25.

Professor Hardy puzzled over the nine pages of mathematical notes
Ramanujan had sent. They seemed rather incredible. Could it be that one
of his colleagues was playing a trick on him?

Hardy reviewed the papers with J. E. Littlewood, another eminent
Cambridge mathematician, telling Littlewood they had been written by
either a crank or a genius, but he wasn’t quite sure which. After
spending two and a half hours poring over the outlandishly original
work, the mathematicians came to a conclusion. They were looking at the
papers of a mathematical genius:

“I had never seen anything in the least like them before. A single look
at them is enough to show that they could only be written by a
mathematician of the highest class. They must be true because, if they
were not true, no one would have the imagination to invent them.”

G. H. Hardy, 1877 – 1947
Mathematician


Hardy was eager for Ramanujan to move to Cambridge, but in accordance
with his Brahmin beliefs, Ramanujan refused to travel overseas. Instead,
an arrangement was made to fund two years of work at the University of
Madras. During this time, Ramanujan’s mother had a dream in which the
goddess Namagiri told her she should give her son permission to go to
Cambridge, and this she did. Her decision led to several very heated
quarrels with other devout family members.

Ramanujan at Cambridge

Ramanujan arrived in Cambridge in April 1914, three months before the
outbreak of World War 1. Within days he had begun work with Hardy and
Littlewood. Two years later, he was awarded the equivalent of a Ph.D.
for his work – a mere formality.

Ramanujan’s prodigious mathematical output amazed Hardy and Littlewood.

The notebooks he brought from India were filled with thousands of
identities, equations, and theorems he discovered for himself in the
years 1903 – 1914.

Some had been discovered by earlier mathematicians; some, through
inexperience, were mistaken; many were entirely new.

“It was his insight into algebraical formulae, transformations of
infinite series, and so forth that was most amazing. On this side most
certainly I have never met his equal, and I can compare him only with
Euler or Jacobi.”

G. H. Hardy, 1877 – 1947

Mathematician


Explaining Ramanujan’s Extraordinary Mathematical Output

Ramanujan had very little formal training in mathematics, and indeed
large areas of mathematics were unknown to him. Yet in the areas
familiar to him and in which he enjoyed working, his output of new
results was phenomenal.

Ramanujan said the Hindu goddess Namagiri – who had appeared in his
mother’s dream telling her to allow him to go to Cambridge – had
appeared in one of his own dreams.

“While asleep, I had an unusual experience. There was a red screen
formed by flowing blood, as it were. I was observing it. Suddenly a hand
began to write on the screen. I became all attention. That hand wrote a
number of elliptic integrals. They stuck to my mind. As soon as I woke
up, I committed them to writing.”

Srinivasa Ramanujan, 1887 – 1920

Mathematician

According to Hardy, Ramanujan’s ideas were:

“… arrived at by a process of mingled argument, intuition, and
induction, of which he was entirely unable to give any coherent account.”

G. H. Hardy, 1877 – 1947

Mathematician

It is possible that Ramanujan’s brain was wired differently from most
mathematicians.

He seems to have had a personal window through which some problems in
number theory appeared with a clarity denied to most people in the
field. Results they fought for through days of arduous thought seemed
obvious to Ramanujan.

Professor Bruce Berndt is an analytic number theorist who, since 1977,
has spent decades researching Ramanujan’s theorems. He has published
several books about them, establishing that the great majority are
correct. He was told an interesting story by the great Hungarian
mathematician Paul Erdős about something G. H. Hardy had once said to him:


“Suppose that we rate mathematicians on the basis of pure talent on a
scale from 0 to 100. Hardy gave himself a score of 25, Littlewood 30,
Hilbert 80 and Ramanujan 100.”

Paul Erdős, 1913 – 1996

Mathematician

Given that David Hilbert is regarded by many as the greatest
mathematician of the early twentieth century, and Hardy and Littlewood
were immensely influential mathematicians, it is fascinating to see how
exceptional Hardy thought Ramanujan’s raw mathematical ability was.

Number Theory and String Theory
In 1918 Ramanujan became the first Indian mathematician to be elected
a Fellow of the British Royal Society:


“Distinguished as a pure mathematician particularly for his
investigation in elliptic functions and the theory of numbers.”

In his short lifetime he produced almost 4000 proofs, identities,
conjectures, and equations in pure mathematics.

His theta function lies at the heart of string theory in physics.

The Ramanujan theta function

“… each of the 24 modes in the Ramanujan function corresponds to a
physical vibration of a string. Whenever the string executes its complex
motions in space-time by splitting and recombining, a large number of
highly sophisticated mathematical identities must be satisfied. These
are precisely the mathematical identities discovered by Ramanujan.”

Michio Kaku, Born 1947

Theoretical Physicist

Some Personal Details and the End

In July 1909, Ramanujan married S. Janaki Ammal, who was then just 10
years old. The marriage had been arranged by Ramanujan’s mother. The
couple began sharing a home in 1912.

When Ramanujan left to study at the University of Cambridge, his wife
moved in with Ramanujan’s parents. Ramanujan’s scholarship was
sufficient for his needs in Cambridge and the family’s needs in Kumbakonam.

For his first three years in Cambridge, Ramanujan was very happy. His
health, however, had always been rather poor. The winter weather in
England, much colder than anything he had ever imagined, made him ill
for a time.

In 1917, he was diagnosed with tuberculosis and worryingly low vitamin
levels. He spent months being cared for in sanitariums and nursing homes.

In February 1919, his health seemed to have recovered sufficiently for
him to return to India, but sadly he lived for only one more year.

Srinivasa Ramanujan died aged 32 in Madras on April 26, 1920. His death
was most likely caused by hepatic amoebiasis caused by liver parasites
common in Madras. His body was cremated.

Sadly, some of Ramanujan’s Brahmin relatives refused to attend his
funeral because he had traveled overseas.

“For my part, it is difficult for me to say what I owe to Ramanujan –
his originality has been a constant source of suggestion to me ever
since I knew him, and his death is one of the worst blows I have ever had.”

G. H. Hardy, 1877 – 1947

Mathematician

“That was the wonderful thing about Ramanujan. He discovered so much,
and yet he left so much more in his garden for other people to discover.”

Freeman Dyson, Born 1923

Mathematician and Physicist

Published by FamousScientists.org

Creative Commons Images
Image of Paul Erdős by Topsy Kretts, Creative Commons Attribution 3.0
Unported License.

Image of Michio Kaku by Campus Party Brasil, Creative Commons
Attribution-Share Alike 2.0 Generic License.

Further Reading
Srinivasa Ramanujan Aiyangar, Godfrey Harold Hardy, P. Venkatesvara
Seshu Aiyar, Bertram Martin Wilson
Collected Papers of Srinivasa Ramanujan
American Mathematical Soc., 1927

Bruce C. Berndt
Ramanujan’s Notebooks Part 1
Springer Verlag, 1985

Srinivasa Ramanujan Aiyangar
Ramanujan: Letters and Commentary
American Mathematical Soc., 1995

Godfrey Harold Hardy
Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work
AMS Chelsea Pub., 1 Jan 1999

B A Kupershmidt
A Review of Bruce C. Berndt’s Ramanujan’s Notebooks, Parts I – V.
Journal of Nonlinear Mathematical Physics, V.7, N 2, R7–R37, 2000