Srinivasa Ramanujan, born in 1887 in South India, grew up with a fervent passion for mathematics, largely developed through a single book of math Theorems by George Carr. Despite facing numerous educational setbacks, including flunking out of college due to his preoccupation with math, Ramanujan's intuitive understanding led him to make groundbreaking contributions to mathematics. His unique ability to see patterns enabled him to solve complex problems that baffled peers, culminating in his work being recognized by prominent mathematicians.

Ramanujan's determination and perseverance resulted in global recognition. At the age of 23, he boldly reached out to Cambridge mathematician G.H. Hardy, outlining his mathematical discoveries in a letter. His work, though sometimes lacking rigorous proofs, was marked by brilliance which intrigued Hardy and led to a collaborative period at Cambridge University. Despite personal and health challenges, Ramanujan continued to make substantial contributions, especially in number theory and Elliptic functions, and was honored by the Royal Society.

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Key Vocabularies and Common Phrases:

1. Divergent [daɪˈvɜːrdʒənt] - (adj.) - Tending to be different or develop in different directions, in mathematics; a series that does not converge.

Divergent series emerge from a complex mathematical process.

2. Intuition [ˌɪntuˈɪʃən] - (n.) - The ability to understand something immediately, without the need for conscious reasoning.

Ramanujan had a natural Intuition for math, which can be illustrated by this problem he solved.

3. Theorems [ˈθɪərəmz] - (n.) - Propositions that have been formally proved based on previously established statements.

Carr's book was like a crossword puzzle with its empty grids begging to be filled in.

4. Partitions [pɑːrˈtɪʃənz] - (n.) - Mathematics; ways of writing a number as a sum of positive integers.

Ramanujan and Hardy contributed substantially to number theory, a branch of mathematics that calculates the Partitions of a number.

5. Elliptic [ɪˈlɪptɪk] - (adj.) - Oval-shaped; relating to or having the form of an ellipse.

He was elected partly for his work on Elliptic functions, which are used to explain complex shapes and patterns.

6. Intrepid [ɪnˈtrɛpɪd] - (adj.) - Fearless; adventurous.

Hardy remarked, seemed scarcely possible to believe. He concluded that the letter was certainly the most Intrepid that I have ever received.

7. Collaborate [kəˈlæbəˌreɪt] - (v.) - To work jointly on an activity or project.

He and Hardy couldn't have been any more different yet their partnership flourished.

8. Astute [əˈstuːt] - (adj.) - Having or showing an ability to accurately assess situations for strategic purposes.

Ramanujan's Astute insights into the nature of numbers.

9. Orthodox [ˈɔrθəˌdɑks] - (adj.) - Conforming to what is generally or traditionally accepted as right or true.

Most of his Orthodox relatives stayed away from his funeral.

10. Revelation [ˌrɛvəˈleɪʃən] - (n.) - A surprising and previously unknown fact revealed in a dramatic way.

The Revelation of Ramanujan's mathematical abilities profoundly changed Hardy's views.

Ramanujan's Journey From Obscurity to Fame Through Numbers

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 to perform groundbreaking research on mathematical problems.

Ramanujan was born on December 22, 1887, in Orodi, 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 Serangapini 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 this book of math Theorems by British mathematician George Carr. It was meant as a teaching aid for students. However, many students actually struggled to read this book because it listed answers without showing the steps to get there. But for Ramanujan, this book awakened the genius in it. Carr's book was like a crossword puzzle with its empty grids begging to be filled in.

As Robert Canigal 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 PC 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 eight houses, house six is special because one plus two plus three plus four plus five equals seven plus eight. 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 Kumbakonim. 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 Rs20 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 mind. 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 4000 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, GH 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 pounds 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, 1234 and so on to infinity added up to negative 112. 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 one that can only be divided by one and itself. Prime numbers are notoriously hard to predict. It's like trying to understand if there's a pattern to let 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 up a sausage and then reassembling it by 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.

Ramanujan's letter to Hardy ended this 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, Siri Nivasa. Ramanujan.

Hardy didn't know what to make of this unusual letter from a young man 5000 miles away. Was this a practical joke or had he just stumbled upon the second Sir Isaac Newton? Hardy showed the letter to his colleague Ge 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.

However, Ramanujan didn't bother explaining how he arrived at his conclusions. He just slept 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 star 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, Eh 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 sons 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 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 four 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 once 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 Mach theta functions. Mach theta functions are a highly abstract concept, like a secret math 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 much 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. My association with him is the one romantic incident in my life. We are left to wonder how many Ramanujans are in India today or elsewhere, waiting to be discovered.

Mathematics, History, Education, Science, Inspiration, Srinivasa Ramanujan