# Partitions — a play on Ramanujan

While I was in San Francisco during May 2-5 to give a talk at an American Mathematical Society meeting, I had the opportunity to see a play at the Aurora Theatre in Berkeley titled "Partitions". This is about the Indian mathematical genius, Srinivasa Ramanujan.

The playwright is Ira Hauptman and the cast consisted of six characters: Ramanujan, Prof. G.H. Hardy of Cambridge University, who was Ramanujam's mentor, the Goddess of Namakkal who appears in Ramanujan's dreams and gives him wonderful mathematical formulae, Billington, a (fictional?) colleague of Hardy's at Cambridge University, a police officer from Scotland Yard and Pierre Fermat, a famous French mathematician of the 17th Century.

The play begins with a scene at Scotland Yard where Ramanujan is being questioned by a police officer for attempting to commit suicide by throwing himself on the subway tracks. Ramanujan says that he wanted to die because he inadvertently ate meat and, therefore, had sinned. Hardy tells the police officer that Ramanujan is a Fellow of the Royal Society (FRS) — which he was not at that time, but only later — and gets him released. That sets the stage for the introduction of this unusual personality from India who is a genius of the first magnitude.

The next scene of the play is a discussion between Hardy and Billington about the letter from Ramanujan which contains several incredible mathematical formulae, and the decision by Hardy to invite Ramanujan to Cambridge. The play then proceeds with Ramanujan's arrival in England to work with Hardy. There is a scene which focuses on Ramanujan's remarkable insight which led to the Hardy-Ramanujan asymptotic formula for partitions — hence, the title of the play. Fermat is brought into the play in a somewhat surprising manner.

As is well known, Fermat's Last Theorem is his assertion that the equation x^n+y^n=z^n has no solutions in positive integers x,y,z if the exponent n is at least 3. This statement by Fermat gained fame because when he recorded it in his notebook, he made the claim that he had a "truly marvellous" proof and that the margin of his notebook was too small to contain it. Fermat's Last Theorem resisted attempts for a solution for three centuries, and it was only in the 1990s was this great problem solved.

In the play Hardy suggests that Ramanujan should work on Fermat's Last Theorem. This is really the playwright's fancy. There is even a conversation in the play between Ramanujan and the Goddess of Namakkal concerning Fermat's Last Theorem. As far as we know, Ramanujan never worked on Fermat's Last Theorem nor did Hardy suggest that he should. Fermat's character is quite impressive and so his introduction in the play for the sake of effect is acceptable artist's fantasy.

No account of Ramanujan is complete without the Taxi Cab episode. There is a charming scene of Hardy meeting Ramanujan in a hospital, and when Hardy mentions that he arrived by the taxi numbered 1729, Ramanujan immediately points out that 1729=10^3+9^3=12^3+1^3, the smallest positive integer that can be expressed as a sum of two cubes in two different ways. Of course, the Ramanujan taxicab equation x^3+y^3=z^3+w^3 yields Fermat's equation for cubes by setting w=0, but it is to be noted that the taxicab equation has positive integer solutions, whereas Fermat's does not.

In 1995, I wrote an article for The Hindu titled "Fermat and Ramanujan - a comparison" following the announcement of Andrew Wiles and Richard Taylor that the proof of Fermat's Last Theorem was completed. In that article, I pointed out that although Ramanujan never worked on Fermat's Last Theorem, there are several similarities between Fermat and Ramanujan. For instance, both recorded their findings in notebooks, both communicated their discoveries in letters, and both provided only sketches of proofs of their claims in many instances.

The play concludes with the letter Hardy receives from India conveying the sad news of Ramanujan's death, and Hardy's address to the London Mathematical Society giving an account of the spectacular contributions of Ramanujan.

In the past few decades, we have witnessed how Ramanujan's contributions have made such a profound impact on various branches of mathematics. The book, "The man who knew infinity", by Robert Kanigel reached out to the general public the world over by describing the fascinating life story of Ramanujan. And now, in the form of a play, the public is made aware, once again, of this wonderful story. This is a very impressive play and I had the pleasure of seeing it with Prof. George Andrews, the world's greatest authority on Ramanujan's work and on partitions.

I heard about the play only upon arrival in San Francisco. When Prof. Andrews called the Aurora theatre to check for ticket availability, he was told there were just two seats left and we took them. We could not believe our luck because it was Saturday evening and we called just a few hours before the play. But I had a feeling that the Goddess of Namakkal had preserved these seats for us.

(The writer is Professor and Chair of the Department of Mathematics at the University of Florida)

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