Ramanujan Biography Professional Life A

Moderators are staffed during regular business hours (New York time) and can only accept comments written in English.

Working alone, he discovered highly original and unknown mathematical results that were far ahead of his time.

In 1913, he sent a letter filled with strange-looking mathematical theorems to G.

Hardy, one of the worlds leading experts on number theory, later said that some of Ramanujans theorems defeated me completely; I had never seen anything in the least like them before.

Ramanujan Biography Professional Life A

The work that Ramanujan did in his brief professional life a century ago has spawned whole new areas of mathematical investigation, kept top mathematicians busy for their whole professional lives, and is finding applications in computer science, string theory, and the mathematical basis of black hole physics.

There is no doubt that Srinivas Ramanujan was a magical genius, one of the greatest of all time.

Just looking at any of his almost 4,000 original results can inspire a feeling of bewilderment and awe even in professional mathematicians: What kind of mind can dream up exotic gems like these.

While most of Ramanujans results are far beyond the scope of this column, it turns out that we can get a flavor for some simple infinite forms using nothing more than middle-school algebra.

In 1911, Ramanujan sent the right-hand side of the following equation to a mathematical journal as a puzzle.

That means that you can start anywhere and get exactly the same continued fraction, as shown in the picture below: The continued fraction in the red box is exactly the same as that in the blue box.

Yes, as we saw in last months column, as far as infinity is concerned, a part can be equal to the whole.

There is a certain house on the street such that the sum of all the house numbers to the left side of it is equal to the sum of all the house numbers to its right.

A friend of Ramanujan, P.

C. Mahalanobis, who was also a student at Cambridge and who later became an eminent statistician, read about this problem while visiting Ramanujan.

Mahalanobis solved the problem, and then turned to Ramanujan and said, Heres a problem for you.

What problem Tell me, said Ramanujan, still stirring vegetables.

He then dictated a continuous fraction that expressed all the infinite solutions to the problem if you ignore the constraint of 50 to 500 houses.

The true puzzles of Ramanujans ability are psychological, and Id love to get the views of Quanta readers on these.

Steven Wolfram has conjectured that if Ramanujan had modern calculating tools like Mathematica, he would have been quite an adventurer going out into the mathematical universe and finding all sorts of strange and wonderful things, then using his intuition and aesthetic sense to see what fits together and what to study further.

I asked myself, Which continued fraction and the answer just came to me.

The question has to be asked about all great mathematicians who died young (notably variste Galois, inventor of group theory, who died at 20 in a gun duel).

How much poorer is the world of mathematics because of Ramanujans untimely death.

And if youd like to suggest a favorite puzzle for a future Insights column, submit it as a comment below, clearly marked NEW PUZZLE SUGGESTION (it will not appear online, so solutions to the puzzle above should be submitted separately).

Correction: This post was revised on July 14 to remove an extraneous 1 in the first line of the continued fraction and an apocryphal reference to a dream of Ramanujans.

Abusive, profane, self-promotional, misleading, incoherent or off-topic comments will be rejected.

Ramanujan Biography Pdf