Srinivas Ramanujan, one of the best mathematicians the world has ever seen, was born on this day, 22nd December 1887. His birthday is observed in India as National Mathematics Day. He barely lived for 32 years (died: 26th April 1920) but the work he did in the short span continues to inspire mathematicians even today. Some of his conjectures were proven 80 years after his death, and some of them are being used in research work on Black Holes.

You can read book “The Man Who Knew Infinity” based on his life, or watch the movie with same title. But the movie is not quiet up to the mark. I would recommend this video discussing the movie and the genius of Ramanujan. Do watch this:

It is an amazing interview explaining the genius of Ramanujan through multiple perspectives and also elaborating on what makes him truly great!

Recently I received from a friend following story attributed to Ramanujan…

### What Is Friendship

Mathematician Ramanujan didn’t have any close friends – someone asked him the reason. He replied that although he wanted to have close friends – nobody was up to his expectation. When pressed how he expected his friends to be – he replied – like numbers 220 and 284. The person got confused and asked what is the connection between friendship and these numbers!

Ramanujan asked him to find the divisors of each number!

With much difficulty – the person derived and listed them.

220 – 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220

284 – 1, 2, 4, 71, 142, 284

Ramanujan then asked the person to exclude the numbers 220 and 284 and asked the sum of the remaining divisors. The person was astonished to find:

220 – 1+2+4+5+10+11+20+22+44+55+110 = 284

284 – 1+2+4+71+142 = 220

Ramanujan explained that an ideal friendship should be like these numbers – to complement each other – even when one is absent – the other should represent the friend!

The person thought – no wonder this genius is on the world’s top list of mathematicians!

As far as I know this story is unlikely to be true. I tried to read through many Ramanujan anecdotes and didn’t find this story in any authentic source. The numbers 220 and 284 belong to the type of numbers described as Amicable Numbers. This is the smallest such pair and such numbers were knows since 1400+ years, dating back to Pythegoreans

However there is another anecdote about Ramanujan which is definitely true; in fact the number is now known as Ramanujan Number – and the number is – 1729. The story goes as follows:

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.

The two different ways are:

1729 = 13 + 123 = 93 + 103

The story highlights greatness of Ramanujan. However it also misleads us to believe that Ramanujan was a math savant rather than math genius. If you have watched the above interview you would have known the difference.

So I won’t elaborate further and urge (or force!) you to watch the entire video!

Meanwhile, I will leave you with some of his amazing mathematical discoveries which are not only deeply complex but extremely elegant in form! (I am intentionally using word “elegant”, and if you have, by now, watched the above video, you would know the reference!)

Ramanujan once said “An equation for me has no meaning unless it expresses a thought of God“. It says a lot about how he viewed and approached Mathematics!