Srinivasa Ramanujan: Inventions, Books & Achievements

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  • 0:05 Who Was Srinivasa Ramanujan?
  • 0:30 Early Life and Mathematics
  • 1:20 Publications in India
  • 2:38 Publications in Cambridge
  • 4:38 Legacy
  • 5:12 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Srinivasa Ramanujan (1887-1920) was a mathematical genius who changed the world of mathematics in his short life. In this lesson, learn about his very interesting and unusual life and all the contributions he made to the world of mathematics.

Who Was Srinivasa Ramanujan?

Srinivasa Ramanujan was one of the world's great mathematicians. Despite starting out as a relatively unknown Indian clerk, he burst into the world of mathematics like a thunderstorm, changing the future of math and securing his place in history before dying suddenly of tuberculosis at the young age of 32. Even though Ramanujan's life was short, his contributions to mathematics were extensive.

Early Life and Mathematics

Ramanujan was born in 1887 in southern India. From a very early age, he was interested in mathematics and showed signs that he was extraordinarily gifted. He taught himself mathematics from books, and was already engaged in an in depth analysis of the Bernoulli numbers by the time he was a teenager. He was still not yet twenty years old, and already well on his way to becoming one of the world's greatest mathematical thinkers.

However, his obsession with mathematics was so intense that it caused problems in his life. He lost his university scholarships when he refused to study other subjects, causing him to fail his exams. After years of struggling, he was finally able to attract the attention of a noted Indian mathematician and member of the Indian Mathematical Society named Ramachandran Rho; it was then that the larger world began to learn about the mathematical genius of Srinivasa Ramanujan.

Publications in India

In 1911, Rho helped him to publish his first paper, which examined the properties of Bernoulli numbers, in the Journal of the Indian Mathematical Society. This paper contained lots of complex calculations and new ways of doing mathematics, both of which would be hallmarks of Ramanujan's work throughout his career. He made friends with some British expatriates living in India, and they encouraged him to write to British mathematicians to help him advance his career in mathematics.

In 1913, he wrote a long letter to the Cambridge mathematician G.H. Hardy. In the letter, he included ten pages of his own mathematical work. Although Ramanujan believed that he had come up with all of the ideas he wrote about, a lot of the work had already been done by other mathematicians in the past. Ramanujan, however, wasn't aware of this and had independently discovered a great number of theorems and presented them in a way that was different from whatever had ever been done before. Pretty impressive for someone who had little formal education in mathematics! In addition, there was also some truly novel mathematics mixed in with his work that no one had ever seen before.

Hardy was impressed and surprised by the high level of mathematics Ramanujan was capable of, and he immediately began planning to arrange for him to come to Cambridge. In the meantime, Ramanujan continued to fill notebook after notebook with his mathematics and published several more papers in India.

Publications in Cambridge

In 1914, Ramanujan arrived in Cambridge, and once there, his work really took off. Many of his most important contributions were were related to game theory, composite numbers, and infinite sequences and series. Among many other things, he discovered a method of writing the constant pi as an infinite series. This method was first described in the article Modular Equations and Approximations to pi, which was published in 1914 in The Quarterly Journal of Pure and Applied Mathematics. Just like all of his other work, this paper was full of dense, long mathematical equations and computations that seemed obvious to Ramanujan, but incredibly complicated to everyone else, even other mathematicians.

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