# Srinivasa Ramanujan

## Biography

## Complete Works

\hr
### Taxicab number 1729

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No", he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

$${(6{A}^{2}-4AB+4{B}^{2})}^{3}={(3{A}^{2}+5AB-5{B}^{2})}^{3}+{(4{A}^{2}-4AB+6{B}^{2})}^{3}+{(5{A}^{2}-5AB-3{B}^{2})}^{3}$$

$$\frac{1+53t+9{t}^{2}}{1-82t-82{t}^{2}+{t}^{3}}={x}_{0}+{x}_{1}t+{x}_{2}{t}^{2}+\dots $$
$$\frac{2-26t-12{t}^{2}}{1-82t-82{t}^{2}+{t}^{3}}={y}_{0}+{z}_{1}t+{y}_{2}{t}^{2}+\dots $$
$$\frac{-2-8t+10{t}^{2}}{1-82t-82{t}^{2}+{t}^{3}}={z}_{0}+{z}_{1}t+{z}_{2}{t}^{2}+\dots $$
$$\phantom{\rule{thickmathspace}{0ex}}}\u27f9{\textstyle \phantom{\rule{thickmathspace}{0ex}}}{x}_{n}^{3}+{y}_{n}^{3}+{z}_{n}^{3}=(-1{)}^{n}.$$

Complete cubic parametrization of the Fermat cubic surface, Elkies
### Carr's Synopsis

G.S. Carr’s: A Synopsis of Elementary Results, a book on Pure
Mathematics

4865 formulae without proofs, in algebra,
trigonometry, analytical geometry and calculus.

* "It was this book which awakened his genius. He set himself to establish the formulae
given therein. As he was without the aid of other books, each solution was a piece of
research so far as he was concerned.}" * -P.V. Seshu Aiyar, R. Ramachandra Rao

## References

Ramanujan Obituary by Hardy

Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (AMS Chelsea Publishing), GH Hardy

Michael D. Hirschhorn (1995) An Amazing Identity of Ramanujan, Mathematics Magazine, 68:3, 199-201, DOI: 10.1080/0025570X.1995.11996312

Berndt, B.C. (2002). The Influence of Carr’s Synopsis on Ramanujan.

### Books

### Videos/ Documentaries

### Websites

Letters and Papers, Cambridge Archive