Srinivasa Ramanujan

If any student or teacher is asked to name the name of a famous Indian mathematician, chances are that they would name Srinivasa Ramanujan. If we probe a little more they may say that the number 1729 is associated with him.

However, it is a pity that most of them do not know anything else about this great mathematician, India can be proud of.One of the reasons could be that much of Ramanujan’s work involved of mathematics of complex levels, which even postgraduate students in mathematics do not study.

But there are aspects of his work which are accessible to even primary students viz. number patterns & magic squares. These can be used to introduce them to Ramanujan.

Ramanujan loved patterns in number relations and has jotted down many of them in his notebooks.

Here is a pattern only using odd numbers (Here ‘.’ Indicates multiplication )

1 + 2 = 3

2 + 3 = 5

3 + 7 = 2.5

2.5 + 11 =3.7 …..

Two of the relations found in his notebooks, written before his journey to England are

3 3 + 43 + 5 3 = 6 3 and

1 3 + 12 3 = 9 3 + 10 3

Students would realize that the 2ndone is the identity for 1729 which he told Prof. Hardy.

He also gave many algorithms for constructing magic squares of different orders.

Among mathematicians he was considered unique in that most of his discoveries seem to be based more on insight and intuition rather than rigorous proofs. This could be taken as a proof of his “mathematical eye”, which was able to see the final results.

No tribute to Ramanujan could be better than Prof Hardy’s in his “Obituary Notice” and “Twelve Lectures on Ramanujan”.

“Ramanujan was, in a way, my discovery. I did not invent him – like other great men, he invented himself – but I was the first really competent person who had the chance to see some of his work, and I can still remember with satisfaction that I could recognize at once what a treasure I had found….I saw him and talked with him almost everyday for several years, and above all I actually collaborated with him. I owe more to him that anyone else in the world with one exception and my association with him is the one romantic incident in my life.”

In 1976, a box was discovered at the Trinity College, which contained papers & notebooks containing some of the work he had done in 1919-1920, the last year of his life. They contain more than 600 formulas which are being studied by mathematicians from around the world. They are known as the “Lost Notebook” of Ramanujan.

Ramanujan was born on 22ndDecember 1887 & passed away on 26thApril 1920, at the age of 32. In 1918, he became a Fellow of the Royal Society, the 2ndIndian to get that honour.

On the occasion of his 75thbirth anniversary, in 1962, Government of India released a stamp in his honour.

On his 125thbirth anniversary, Government of India declared that his birthday would be celebrated as the National Mathematics Day & 2012 as the National Mathematical Year. On the same occasion, a second stamp was released. Tamil Nadu celebrates his birthday as “State IT Day”.

Mind of a Mathematician

If mathematics is the study of physical & abstract patterns around us,it is then logical to think that some human brains would be wired better for mathematical thinking. Hence some patterns which are not visible to a majority of humans are accessible to some gifted mathematicians.

There is even a perspective that great mathematicians possess a sixth sense which is able to identify patterns which others are not able to. There are many instances of ideas in Mathematics being simultaneously and independently developed by several mathematicians. The invention of calculus is a famous example.

This is also a possible reason why a body of mathematical ideas finds applications a long time later; many a time, after the death of the inventor. Boolean Algebra is an example.

Ramanujan felt that many mathematical ideas just came to him spontaneously. He attributed this to the divine grace of Goddess Namagiri. Ramanujan has written many mathematical identities and patterns, without proofs, many of which mathematicians are still trying to prove.

When Hardy first received such a set of identities from Ramanujan, he remarked “… I had never seen anything in the least like them before. … They must be true; no one would have had the imagination to invent them…”

Mathematical minds like Ramanujan's do not have patience with the standard content of mathematics as taught in our schools and colleges with their emphasis on computations and correct steps.

Music is another ‘intelligence’ which depends on identification of patterns; these being of sounds rather than numbers. It may not be just a coincidence that many great mathematicians were also musically gifted.

We do not find child geniuses in other fields.