Ramanujam: The Man who Knew Infinity

Ramanujam was a mathematical genius of the last century.  One of the greatest if not THE greatest!  Recently, it was announced that a movie would be made on him.

British director Stephen Fry and India’s Dev Benegal are to make a film about an Indian mathematician whose ideas underpin the digital revolution.

The shooting will start in Tamil Nadu next year.  Who will be there in that movie?  This is what they say:

A “major American or British star” will play the cricket-loving Hardy, whose stamp of approval took Ramanujan to Cambridge University in 1914, Benegal told the BBC.

He said he and Fry would be looking for a “terrific Indian actor” to play Ramanujan.

“It won’t be [Bollywood stars like] Amir Khan or Shah Rukh Khan surely. I am sure we will find the right actor,” he said.

One of the Directors – Dev Benegal – says of Ramanujam’s accomplishments and relevance to modern day technology:

“For me, Ramanujan’s work and ideas are the DNA of what powers digital technology today,” says Benegal.

“When your automated teller machines divide and arrange your money before coughing it up, they are all using Ramanujan’s partition theory.”

Who was Ramanujam?

About the end of World War I, Ramanujan, was lying gravely ill in a London hospital when Hardy, the leading mathematician in England, visited him there. “I came over in cab number 1729,” he told Ramanujan. “That seems a rather dull number to me.”

“Oh, no!” Ramanujan replied back. “1729 is the smallest number you can write as the sum of two cubes, in two different ways.” You or I would use a computer to figure that out. Ramanujan did it from his sickbed without blinking.

The Early Life

Ramanujan was born to a poor family in South India in 1887. He was a genius of a different kind.  While he was brilliant in Mathematics he did not care much about the other subjects.  His early mathematics education consisted of two books. One was a standard trigonometry concepts and other, was a handbook of 6000 theorems — stated without proof!  This second book probably set the foundation for his style of learning and erudition!  He started writing his own theorems right out of his mind – thousands of theorems – all without proofs!

Here is one incident from his school days:

The teacher was asking some simple questions in arithmetic. The class was learning the simple operation of division. When the teacher asked how many bananas would each boy get if three bananas were divided equally among three boys, someone had an answer. One each. Thousand bananas divided equally among thousand boys? The answer was still the same. One. The class was progressing thus, questions being asked by the teacher and answers being provided by the student. But there was a boy who had a question. If none of the bananas was divided among no boys, how much would each boy get? The whole class burst into laughter at what the students thought was a fast one or a silly question. But the teacher seemed to have been impressed. He took it upon himself to explain to the boys that what the student had asked was not a silly question but rather a profound one. He was questioning the teacher about the concept of infinity. A concept that had baffled mathematicians for centuries, until the Indian scientist Bhaskara had provided some light. He had proved that zero divided by zero was neither zero nor one, but infinity.

The student was Srinivas Ramanujam.

He failed in his first year college examination after his obsession with mathematics grew on.  His father got him married to a young girl of eight years as his father thought that he was clearly mad!

Thousands of Theorems – Without Proof!

The real turning point that started off his own creations was when a friend introduced the book Synopsis of Elementary Results in Pure and Applied Mathematics by George Shoobridge Carr to Ramanujam. Any young man of 15 years would have found this book too much to deal with at that young age but Ramanujam was ecstatic at the introduction.

He began solving problems given in the book. With the floodgates now open, ideas began to pour in. Such was the gush of ideas that Ramanujam found it difficult to write them all down. The number of papers that Ramanujam required per month for jotting his ideas was roughly Two thousand! He scribbled his results in loose sheets and notebooks. These later came to be known as Ramanujam’s Frayed Notebooks.

After marriage Ramanujam had to look for a job and he came across Francis Spring (Director at Madras Port Trust) who was empathetic of his brilliance shown in his notebooks and appointed him at the Port Trust as a clerk.  In May of 1913, the University of Madras awarded him a fellowship nothwithstanding the fact that he did not have a formal degree!

Hardy and Ramanujam

He kept on writing his theorems and worked as a clerk. In 1913 he wrote to Hardy at Cambridge. Hardy would’ve ignored the letter, but he took a moment to glance at 120 theorems Ramanujan had included. It was the oddest pastiche. Here were familiar results, reinvented. Part of these portions was the Reimann series, a topic in Definite Integral in calculus. Ignorant of Reimann’s original work, Ramanujam had reproduced the work all over again.

Another part of this collection was Ramanujam’s interpretation about the equations called “modular