Wednesday, 8 February 2012

My Ramanujan Moment

Most people will have have heard of the brilliant Indian mathematician Srinivasa Ramanujan from the clip on the right from 'Good Will Hunting'. Most of the information given in the clip is wrong according to the biographies I have read on the internet. However, that is only background, I want to talk about the story that led to the number 1729 becoming known as the Hardy-Ramanujan Number. The following quote is from the mathworld.wolfram.com description of the incident:
 "Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, 'rather a dull number,' adding that he hoped that wasn't a bad omen. 'No, Hardy,' said Ramanujan, 'it is a very interesting number. It is the smallest number expressible as the sum of two [positive] cubes in two different ways' "

My own Ramunajan moment has its genesis in my inclination for pointing out to friends who were celebrating their twenty-seventh birthday that, barring unforeseen medical advances, they would be celebrating there last birthday where there age could be expressed as a number raised to the power of itself. At some point a friend said to me that their twenty-ninth birthday would be their last before the "Big One". I thought for a second before pointing out that it would be their last birthday where the sum of the digits forward the product of the digits would equal the number itself.

Now I was wrong - but so was Ramanujan* - as can be seen from the following equation:

Sum of digits = a + b
Product of digits = ab
Number = 10a + b

* It can be seen above that positive is inserted in brackets for no possible reason other than to make his statement correct. The man was a genius we know this from what great mathematicians tell us of his work. This story adds very little to his legend for me.

Further Info:

A Further Five Numbers
A Brief History of Mathematics: Hardy and Ramanujan

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