“Infinite series were Ramanujan's first love.”
One fine day in 1913, Hardy, one of the finest pure mathematicians of his time, received a curious letter. The 10-page letter, sent from Madras started as: ”I beg to introduce myself to you as a clerk…about 23 years of age...I have had no University education…but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as ‘startling’.”
The letter went on to dispute prime number theorem as well as an assertion advanced by Hardy in his paper Orders of Infinity. After having given a pie of the ingenuity behind the letter, it concluded as humbly as it had begun: “I would request you to go through the enclosed papers. Being poor, if you are convinced that there is anything of value I would like to have my theorems published… Requesting to be excused for the trouble I give you.”
This was S. Ramanujan’s third attempt to get recognition by writing to a foreign mathematician of repute, and he seemed to have got it right this time. An awestruck Hardy would later say "I have never met his equal, and I can compare him only with Euler or Jacobi." Considered as dumb in his childhood, S. Ramanujan would go on becoming arguably the best mathematical mind the world would ever see.
Continuing a Legacy of Obsession with Zero and Infinite
Hundreds of years before the West was still mired in unwieldy Roman numerals, Indians had been using the numerals, number system, number line and other advanced Arithmetic which we use to this day. Mathematics was well-steeped in day to day Sanatana religion, for instance, in the need to know the correct time (muhurta) for Vedic ceremonies, the measurement of Vedic altar, etc.
Of all, zero (nothingness), one or unity (finite) and infinity (everything-ness) occupied the centre stage. The zero was being used from 2nd century BC, if not earlier. Its invention, in response to our finite existence in face of infinite universe, was a remarkable achievement. Infinity too was given its fair share of attention. 10^62 appears in Vedic literature dated 1500 BC. Avatamsaka Sutra approaches infinity in an attempt to comprehend divinity (one large meaningful number is pegged at 10^37218383881977644441306597687849648). “Incalculable” numbers were divined to describe the incalculable names and forms of the divinity.
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