# Senthil Kumaran

## The Man Who Knew Infinity

"An equation for me has no meaning, unless it represents a thought of God." - Srinivasa Ramanujan

"The man who knew infinity" is the story of Srinivasa Ramanujan. This phrase, associated with Ramanujan should be familiar to many due to a very popular book with the same title. There is a motion picture directed by Matt Brown based upon this book.

I watched his movie on a Saturday at Berkeley. I was excited to listen to the QA with the director, and Mathematicians such as Richard Borcheds , Olga Holz and Ken Ribet following the screening.

In India, we have been exposed to Ramanujan quite early in our lives. I had stories in school book about great Indian mathematicians like Aryabhata, Brahmangupta, and Bhaskaracharya. Indian Satellites to Space launched by ISRO bear their names too. Along with those personalities, we have Srinivasa Ramanujan and whom we know for his invention of Magic Squares, and Ramanujan Number, the smallest number expressible as sum of two cubes.

\begin{equation*} 1729 = 1^3 + {12}^3 = 9^3 + 10^3 \end{equation*}

Beyond that, I had not known much about the significance of this number or Ramanujan's work.

Years later, when taking online courses, I had come to know about Hardy and Ramanujan's research in Number Theory being at the core of secure communication and cryptography. Do you use Credit Cards online and feel confident that someone will not maliciously take your money? All this is was because of the research in number theory.

There is also famous anecdote associated with Ramanujan, known to many from South India, Ramanujan prayed to a goddess, and she gave inspiration for his work. He mentions that his theorems had come up like a dream, a boon granted by the Goddess, and he would write formulae in his book. That's how he invented those theorems.

If it happened like that, imagine how excited young students from Madurai will be, where there a temple every hundred feet. :) It needs to be clarified that, Ramanujan was a genius and he also worked very hard on his subjects.

A better understanding of this phenonmemon, in general, is now known. The style of discovery is called " diffused mode learning", wherein after an intense work on challenging problem, the solution suddenly comes up during a restful time.

All these are portrayed well in this movie. The relationship between Hardy and Ramanujan, the scientific culture at Trinity College, London revealed in real detail. The movie has a significant portion dealing with how Hardy mentors Ramanujan, and strives to bring his work to the modern world.

In the question and answer session that followed, two questions were of interest to me.

How do mathematicians study Ramanujan's work when he has not left many formula proofs with his equation?

Richard Borcheds, who is an accomplished mathematician, replied that Ramanujan's work was published in the form of series of notebooks. He left behind three notebooks containing almost 3000 theorems, virtually all without proof. The reason he could have done that is perhaps he grew up in a time when the paper was very expensive for him and he wanted to be economical.

(It did not answer the question, but provided a good perspective).

Question 2: In the movie, Ramanujan is shown to be desisting writing formal proofs. Is that true?

Richard Borcheds shared that, it is bit exaggerated in the movie. Ramanujan always knew the proof of his work and could state it if he wanted to. But he usually did not.

I enjoyed watching this movie and listening to the perspectives associated with the genius from kumbakonam.