Unknown Facts About “The Math Wizard” Srinivasa Ramanujan

A Wizard, an Enigma, a Genius, The man who knew Infinity- Srinivasa Ramanujan (December 22, 1887, to April 26, 1920). S Ramanujan was an Indian mathematician. He was a Math Wizard. The Mathematical Genius made many important contributions to mathematical analysis, number theory, Ramanujan Summation, and continued fractions which excites many mathematicians almost one hundred years later too.  The results discovered by Ramanujan were so amazing and are still such hot topics. 

An equation means nothing to me unless it expresses a thought of God.

S Ramanujan

“No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man’s game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.”

G.H. Hardy- A Mathematician’s Apology

“I have wondered how much Ramanujan could have done if he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package.”

George Andrews

“I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, ‘Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.”

G.H. Hardy

The mock theta functions in the notebook have been found to be useful for calculating the entropy of black holes, the most annoying riddle to science.

Rankin Robert A

“The discovery of this ‘Lost Notebook’ caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world.”

Bruce C. Berndt

“Try to imagine the quality of Ramanujan’s mind, one which drove him to work unceasingly while deathly ill, and one great enough to grow deeper while his body became weaker. I stand in awe of his accomplishments; understanding is beyond me. We would admire any mathematician whose life’s work was half of what Ramanujan found in the last year of his life while he was dying.”

Richard Askey

Have you had an opportunity to read this amazing book (The Man Who Knew Infinity: A Life of the Genius Ramanujan) by Robert Kanigel. The book is coined as ‘One of the finest, best-documented biographies ever published about a modern mathematician.’

The book was later adapted into a film in 2016 starring Dev Patel, Jeremy Irons, Stephen Fry, Toby Jones and Devika Bhise.

Cool Facts you should know about Ramanujan

The man who gave Pi a value, Ramanujan was born in Erode, Madras, India. In 1889 he contracted smallpox but recovered. 

In 1897, he was the highest scorer in his district in the subjects- English, Tamil, geography, and arithmetic. In high school, he developed a special interest in mathematics, so much so that he started to discover advanced theorems. 

In 1903, the book on Mathematics by G.S.Carr, ‘A Synopsis of Elementary Results in Pure and Applied Mathematics’ became instrumental in his future discoveries.

By the time he was 17th, he did develop the Bernoulli numbers and calculated the Euler-Mascheroni constant to 15 decimal places. Google it guys! 

In 1904 he graduated from town Higher Secondary School and received the K. Ranganatha Rao prize in mathematics. Only to lose it, since he failed to study any subject but mathematics.

In 1905 he enrolled in another college. He failed again to study other subjects and left out without a degree. But his mathematical genius impressed V. Ramaswamy Iyer, the founder of the Indian Mathematical Society. Iyer gave him letters of introduction to R. Ramachandra Rao, who gave him financial backing while Ramanujan continued his research in mathematics.

On 14 July 1909, Ramanujan married Janaki (Janakiammal; 21 March 1899 – 13 April 1994), a girl his mother had selected for him a year earlier and who was ten years old when they married.

In 1912 he was hired in the office of the Chief Accountant of the Madras Port Trust. He began to send his mathematical papers to the famous British mathematician, (Godfrey Harold Hardy) G.H. Hardy. His first two letters went unanswered, but his third, of January 16, 1913, hit its target. Ramanujan included nine pages of mathematics.

Hardy already knew some of the results while others were completely astonishing to him. Hardy recognized Ramanujan’s brilliance in mathematics and to encourage his works he started to present his papers to his colleagues at Trinity College.

In a famous anecdote, once Hardy took a cab to visit Ramanujan. When he got there, he told Ramanujan the cab’s number he was in, 1729, which he thinks was a dull one. Ramanujan replies, “No, it is a very interesting number.” He describes, ‘It is the smallest number expressible as a sum of two cubes in two different ways. That is, 1729 = 1 3 + 12 3 = 9 3 + 10 3.’ 

This number now is called the Hardy-Ramanujan number, and such numbers, (smallest numbers that can be expressed as the sum of two cubes in n different ways) have been dubbed as ‘taxicab numbers.’ The next ‘taxicab number’ in the sequence, (the smallest number that can be expressed as the sum of two cubes in three different ways,) is 87,539,319.

On March 17, 1914, Ramanujan left India for England. He spent five years in Cambridge and was eventually awarded a Ph.D. in mathematics. He received many awards for his work and in 1917 he was elected to the London Mathematical Society.

In 1918 he was elected Fellow of the Royal Society “for his investigation in Elliptic function and the Theory of Numbers.” Later that year, He was diagnosed with tuberculosis and a severe vitamin deficiency but the medical studies pointed to a case of undiagnosed hepatic amoebiasis.

He returned to India in 1919 and died the very next year. He was 32 years old. Till then, He had compiled over 3,900 results, mostly identities, and equations. 

His infinite series for pi is one of his most celebrated findings. This is also the reason why we revere him as ‘The Man who knew INFINITY.’

Now, facts you mightn’t know about the Mathematical wizard Srinivasa Ramanujan

• Ramanujan was a self-taught Genius. He had almost no formal training in pure mathematics.
• It’s saddening that half of Ramanujan’s work was those which were already recently proven. He wasted his time and energy on proven equations. This was not because he was trying to prove them wrong or so, this was because he didn’t know if they were already proven. He lacked resources. 
• The works of Ramanujan were genius, so genius that, the ones that were ordinary mathematical readers could barely understand exactly how Ramanujan achieved the results.
• Ramanujan initially declined the request of Dr. Hardy to travel to England. Because his Brahmin upbringing forbade him from visiting any foreign land. After this, Ramanujan’s work was further endorsed by a former mathematics lecturer at Trinity College, Cambridge – Gilbert Walker. Walker’s endorsement led to an arrangement for a scholarship for Ramanujan at the University of Madras. Ramanujan received Rs. 75 per month scholarship so that he could continue with his research. In the meantime, Hardy asked his friend E. H. Neville who was posted in Madras as a lecturer to mentor Ramanujan into visiting Cambridge.
• Hardy came up with a scale of mathematical ability that went from 0 to 100. He put himself at 25. David Hilbert, the great German mathematician, was at 80. Fascinatingly, he put Ramanujan at 100. 

• When Ramanujan died, he left behind three notebooks and a sheaf of papers which is the famous- “the lost notebook.” These notebooks contained thousands of results that are still inspiring mathematical work decades later.
• He died because of Hepatic Amoebiasis. Hepatic Amoebiasis was actually a widespread disease in Madras and was usually caused by improperly treated dysentery lying dormant for years.
• Till he died, Ramanujan continued working. After his death, his youngest brother Tirunarayanan compiled and chronicled all his work.
• His “lost notebook”, containing discoveries from the last year of his life, caused great excitement among mathematicians when it was rediscovered in 1976. You may get it too! Here is the enigmatic “Lost Notebook Part 1” and here is the “Lost Notebook Part 2.”
• George Andrews and Bruce C. Berndt (2005, 2009, 2012, 2013) have published several books in which they give proofs for Ramanujan’s formulas included in the notebook. Berndt says of the notebook’s discovery: “The discovery of this ‘Lost Notebook’ caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world.”
• Rankin Robert A (1989) described the lost notebook in detail. The majority of the formulas are about q-series and mock theta functions. The mock theta functions in the notebook have been found to be useful for calculating the entropy of black holes, the most annoying riddle to science, or it was till then.
• At the Ramanujan Conference in 1987, referring to the mock theta functions, mathematician and theoretical physicist Freeman Dyson spoke of “a grand synthesis still to be discovered”, and he speculated about their application to physics in the context of string theory. He concluded that “the mock theta functions give us tantalizing hints of a grand synthesis, still to be discovered”. “This is an indication of the prescience and genius of Ramanujan. Many mathematicians are very excited that the results discovered by Ramanujan almost one hundred years ago are now such hot topics.”
• Mrs. Janakiammal Ramanujan, the widow of Ramanujan, lived for several decades in Triplicane, close to the University’s Marina Campus, and died on April 13, 1994. A bust of Ramanujan, sculpted by Paul Granlund was presented to her and it is now with her adopted son Mr. W. Narayanan, living in Triplicane.

How a self-taught man went on to know INFINITY? 

Ramanujan had always said that he accessed a portal of supreme intelligence and it was the mother, Goddess Mahalakshmi (or Namagiri) who would bestow on him fully formed equations.

Creative people would connect to it. They all have/had similar experiences.

His words- 

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 write.

There was a biopic made on him, did you watch it?

‘The Man Who Knew Infinity’ 

The screening was attended by, Sundar Pichai (CEO, Google), Sergey Brin (founder, Google), Mark Zuckerberg (founder, Facebook), Brendan Iribe (CEO of Oculus VR), and some other legends of the Silicon Valley, who all reportedly came out with tears. The biopic moved the who’s who of the US super-elite, so much that they reportedly pledged to form a foundation in the name of him. 

Just wow! Isn’t it? To commemorate the contributions of Srinivasa Ramanujan, every year on his birth anniversary ie., 22 December National Mathematics Day is celebrated. While the International Day of Mathematics is celebrated on March 14. 

If you are with me, still, I think I gotta ask you, Do you like Maths? Use the com box to enlighten me why not. Also share, were the facts cool enough, or did you already know them? 

References 

https://www.britannica.com/story/interesting-facts-about-srinivasa-ramanujan

https://www.imsc.res.in/~rao/ramanujan.html

Ramanujan’s Lost Notebook