The video explores the extraordinary life and contributions of Srinivasa Ramanujan, a self-taught mathematical genius who credited his ability to his intuitive connection with his goddess, Namagiri Tayya. Despite lacking formal training, Ramanujan achieved remarkable successes in fields such as number theory, infinite series, and continued fractions, overcoming challenges posed by his unorthodox methods.

Ramanujan's journey from poverty in India to collaborating with British mathematician G.H. Hardy in Cambridge marks a tale of perseverance, showcasing his distinct approach influenced by visions and dreams. His move to England was Fraught with health issues and cultural challenges, yet his groundbreaking work earned recognition through prestigious memberships and degrees.

Main takeaways from the video:

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

Srinivasa Ramanujan was a self taught mathematical genius who relied on intuition to achieve his success.

2. Obscurity [əbˈskjʊrɪti] - (n.) - The state of being unknown, inconspicuous, or unimportant.

Rising from Obscurity and poverty to worldwide recognition, Ramanujan credited his knowledge to his family goddess Namagiri Tayya.

3. Prowess [ˈpraʊəs] - (n.) - Skill or expertise in a particular area or field.

His Prowess in mathematics stood out from an early age.

4. Unconventional [ˌʌnkənˈvɛnʃənl] - (adj.) - Not based on or conforming to what is generally done or believed.

With no formal training in mathematics and Unconventional methods for achieving his results, few could explain his brilliance.

5. Anecdote [ˈænɪkˌdoʊt] - (n.) - A short and amusing or interesting story about a real incident or person.

On one occasion while in hospital, Hardy took a taxi cab to visit him and remarked how the taxi was numbered 1729.

6. Devotion [dɪˈvoʊʃən] - (n.) - Love, loyalty, or enthusiasm for a person, activity, or cause.

He soon lost it after his Devotion to mathematics made him neglect his other subjects.

7. Fraught [frɔːt] - (adj.) - Filled with or likely to result in something undesirable.

His move to England was Fraught with health issues and cultural challenges.

8. Tenacity [tɪˈnæsəti] - (n.) - The quality of being very determined; persistence.

His journey marked a tale of perseverance and Tenacity.

9. Insight [ˈɪnˌsaɪt] - (n.) - The capacity to gain an accurate and deep understanding of someone or something.

Ramanujan quickly disagreed, explaining its importance as the smallest number expressible as a sum of two cubes in two different ways, a quite new Insight.

10. Legacy [ˈlɛɡəsi] - (n.) - Something transmitted by or received from an ancestor or predecessor or from the past.

His contributions are timeless, influencing contemporary mathematics with the Ramanujan summation and Ramanujan number.

Srinivasa Ramanujan: A Mathematician's Divine Inspiration

Srinivasa Ramanujan was a self-taught mathematical genius who relied on intuition to achieve his success, believing that an equation has no meaning unless it expresses a thought of God. While his colleagues meticulously reached their results via proofs, Ramanujan made significant contributions to the theory of numbers, infinite series, continued fractions, elliptic functions, and many more, based on inspiration from dreams and visions, rising from Obscurity and poverty to worldwide recognition. Ramanujan credited his knowledge to his family goddess Namagiri Tayya.

With no formal training in mathematics and Unconventional methods for achieving his results, few could explain his brilliance, and his work continues to amaze over a century later. Srinivasa Ramanujan Ayanga was born on the 22 December 1887 in Tamil Nadu, a state in the south of India. He was raised an orthodox Hindu, and his mother educated him on brahmin culture, which he followed his entire life. His Prowess in mathematics stood out from an early age. He was achieving the best exam scores in the district and mastering advanced trigonometry by the time he was 13 and was solving cubic equations at 15, developing his own theories, and solving the quartic function in algebra.

But the true awakening of his genius was when he was 16 and came across a little known book titled "A Synopsis of Elementary Results in Pure and Applied Mathematics" by G.S. Carr. Carr presented 5000 theorems, largely without proofs, the logical assertions, to support a conclusion, and this seems to have encouraged Ramanujan, who was completely self-taught, to pursue his own work and produce it in the same way, based on feeling above all else. He independently investigated the Bernoulli numbers, and his peers were in awe of his ability, barely able to understand him due to him lacking any formal training in pure mathematics.

Graduating in 1904, Ramanujan received a scholarship for college, but he soon lost it after his Devotion to mathematics made him neglect his other subjects. For the next two years, he had similar academic struggles and was extremely poor, often close to starvation. He continued to study and research independently, writing many of his results and findings in a series of notebooks, which are still studied to this day.

On the 14 July 1909, Ramanujan married a ten-year-old girl named Janaki, who his mother chose for him not long after. He developed a hydrocele, a condition in which fluid becomes blocked in the scrotum, but he was unable to pay for the operation. To treat it, he had to live with the condition for months, until January 1910, when a surgeon agreed to do it for free. Ramanujan recovered, but was hampered by ill health throughout his life. By the end of the same year, he was sick again and fearing for his life, handing his notebooks to a friend to pass on should he die, though he would make a full recovery.

Ramanujan's luck would change when he met the founder of the Indian Mathematical Society, V. Ramaswami Ayyah. He introduced him to prominent members of the mathematical community in Madras, including R. Ramachandra Rao. Rao initially considered Ramanujan to be a fraud, given his unusual methods and lack of proofs in his notebooks, while others were impressed but didn't understand the work due to its lack of clarity. Finally, he met with Rao and was able to convince him of his ability. Suitably impressed, Rao agreed to financially support him, allowing him to continue his research and giving him to publish his work for the first time in the journal of the Indian Mathematical Society.

Ramanujan got a job as an accounting clerk in 1912, where he often breezed through his work using his spare time, completing mathematical research at his desk. With the help of Ayyah and Rao, Ramanujan started to write to various British mathematicians in early 1913, sharing his work, and while most either ignored his letters or were unimpressed due to his lack of formal education, the British mathematician G.H. Hardy was stunned. Like Rao, Hardy initially assumed Ramanujan to be a fraud. While some of the results he already knew, others he could not comprehend, and they were so shocking he deemed that they must be correct because no one would have the imagination to invent them.

Hardy showed the letter to his colleagues, who were equally impressed, and the following month wrote back to Ramanujan, trying to arrange for him to travel to England. However, Ramanujan declined due to his brahmin upbringing and the Kalapani belief of Hinduism, it was considered taboo to leave the country for foreign lands. Instead, he gained a scholarship at the University of Madras in May 1913 so he could continue his research. But Hardy refused to give up and again asked Ramanujan to consider coming to England. This time, much to his surprise, he agreed.

Apparently, his mother had had a dream in which their family goddess Namagiri appeared and commanded her to allow the trip so her son could complete his life's purpose, which Ramanujan was happy to follow. On the 17 March 1914, he travelled alone to England, leaving his wife, Janaki, with his parents, and arrived on the 14 April. Upon his arrival, he showed Hardy the rest of his notebooks and he was blown away by their contents, comparing his ability with great mathematicians of old such as Jacobi and Euler.

While they became fast friends, Hardy and Ramanujan did have conflicting personalities. Hardy was an atheist, devoted to mathematical proof and the traditional methods of pure mathematics, while Ramanujan was a devout Hindu and remained strongly guided by his intuition and self-taught methods developed back home. But this never got in the way of their collaboration during Ramanujan's five-year stay in Cambridge, which proved very successful.

In March 1916, Ramanujan earned a Bachelor of Arts research degree, a predecessor to the modern PhD, mostly for his work on highly composite numbers. He was elected to the London Mathematical Society in December 1917. Then, for his investigation in elliptic functions and the theory of numbers, he was elected a fellow of the Royal Society on the 2 May 1918, one of the youngest men ever elected, and only the second Indian shortly after. On the 13 October 1918, he was elected a fellow of Trinity College in Cambridge, the first Indian to do so.

In the first few months after he moved to England, Ramanujan lived comfortably. But following the outbreak of World War One and the limitations of food rationing, he struggled to sustain himself on his strict vegetarian diet and his health began to get worse. He spent much of his time in hospital from 1915. As his health deteriorated considerably, he grew depressed and suicidal, compounded by his lack of contact with Janaki back home, who his mother wouldn't allow to write to him, fearing she would distract him from his work.

In 1917, his illness was diagnosed as tuberculosis and he stayed in a sanatorium for treatment. However, we now know that this diagnosis was incorrect and he actually suffered from hepatic amoebiasis, which often results from untreated amoebic dysentery, something he suffered from several times before travelling to England. But despite his failing health, mathematics still dominated his thoughts. On one occasion while in hospital, Hardy took a taxi cab to visit him and remarked how the taxi was numbered 1729, which seemed to him a dull number. Ramanujan quickly disagreed, explaining its importance as the smallest number expressible as a sum of two cubes in two different ways, a quite new Insight. As a result, 1729 is now known as the Ramanujan number.

With his health rapidly deteriorating, Srinivasa Ramanujan returned home to India on the 13 March 1919 and failing to get better. He died on the 26 April 1920, just 32 years old. Only decades later, once his work was fully researched and proven, did Ramanujan get the recognition worldwide that he deserved, and now multiple awards and theories are named in his honour. In his short life, he made a monumental impact on the world of mathematics, and his story and rise from humble origins inspired his 2015 biopic, "The Man Who Knew Infinity." The infinity it refers to is both the mathematical infinite series he researched, now known as the Ramanujan summation, but also his apparent access to knowledge from a higher power.

Ramanujan believed his family goddess Namagiri was the source of his inspiration and genius, sometimes being inspired in dreams and sometimes in visions where complex mathematical equations unfolded before his eyes. But whether his genius was natural or supernatural, his importance to modern mathematics cannot be overstated. His ability is no better expressed than by his friend and mentor G.H. Hardy, who once said, on a scale of zero to 100 of mathematical talent, he would score himself 25, the great German mathematician David Hilbert 80, and Ramanujan 100.

Srinivasa Ramanujan, Mathematics, Education, Intuition, G.H. Hardy, Cultural Challenges