Tuesday, February 08, 2005

Ramanujan's Work

Most Indians know that Srinivasa Ramanujan as a mathematical genius. Ask them atleast one equation that he conjectured/proved or in general to summarise his contribution to Mathematics in general, you will draw a blank most of the time.Not that this is a bad thing or everone is expected to answer, but just for the sake of holding yours in the conversation.

For example take the simple identity of

1+2+3+4+5+6.... infinity = - 1/12 (negative one-twelfth)

Chew on that!Yeah! Ramanujan proved that if you sum all whole numbers to infinity, the result is a negative fraction.Not simply that, he conjectured so many equations and identities, that a good chunk of what he wrote is still left open to proof. (He conjectured that 2 power N minus 7 is a square only for 3,4,5,7 and 15 which is verified till 10 power 40)

Consider the equation n! +1 = m ^2 . (That is n factorial +1 equals a perfect square. )
Ramanujan conjectured that n=4, 5, 7 are the only solutions. So far it has been verified till 10^9 and it is almost 'virtually certain' that he was right.

There are so many like these. There is this new site (that is still being constructed ) that seems to have his collected papers, questions, notebooks and other miscellaneous information scanned in to the site. It is an excellent resource to get acquainted with his life/work.

When he was on his death bed he was working on mock-theta functions, these are functions that are not theta functions but imitate them. His work on continued fractions is still modern enough.

Just some random notes on him..

6 comments:

perspective said...

wow!! that was really interesting...
i would agree.. till date i had no idea of the contributions of Srinivasa Ramanujan...really.
thanks for the education...

Primalsoup said...

Phew! OHT or what! Many many things added make a negative, I must use that somehow in some conservation to throw at somebody...

So, how goes life in your rabbit hole? :)

Paddy said...

[Anya] Thanks! Atleast made you think which was the objective of the post.Not that it is neccesary but when we take pride in the fact of an Indian Genius, it helps to know a wee bit about his contribution to the subject.

[BBB] Ki Holo! BTW what does OHT mean? Cant figure it.
Yeah! Let me put it this way,If you want to make all the money in this world you need to borrow something like 8 cents and some fractional cents.Yes!Its a very good ammo for a cocktail party (if you go to the same parties I do)

>So, how goes life in your rabbit hole? :)

Either I am the March Hare or the Mad Hatter. Waiting to surface back :)

Primalsoup said...

OHT aka Over Head Transmission… happened a lot while used to attend the multiple regression classes in college :)

We had once had a workshop for our clients in which we explored the possibility of using Alice in Wonderland to morph them into “nicer” people… almost everyone wanted to be the Mad Hatter! And the rest the Cheshire Cat! :) Needless to say the people didn’t become any nicer… anyway I forget what was the point I was going to make! :)

Primalsoup said...

And by "them" I meant clients...

Paddy said...

>OHT aka Over Head Transmission…
Cool. I'll add that to my lexicon of TLAs.


>the multiple regression classes in college :)

Multiple regression was so convoluted that I end up using exponential smoothing in its place.Worked well for my last project :)

Give me an example of your client.Either your clients should be grinning a lot or should like a lot of tea based on that.

>anyway I forget what was the point I was going to make! :)

Hall mark of great people :)

>And by "them" I meant clients...

Again , I am not familiar with who they might be so its kinda difficult to visualise that workshop.

Thanks,