Just a number

WHEN Carl Friedrich Gauss was a little boy, his teacher asked the class to add up all numbers from one to hundred. Gauss came up with the answer instantly.

"Little Gauss, how did you do it so quickly?" said the teacher. The others in the class were still adding up the numbers.

"I observed that the sum of the first and the last numbers in the series was 101 (100+1) and the second numbers from the top and the bottom also added up to 101 (99+2). I also observed that there were 50 such pairs of 101 in the series if all numbers were to be added up. So, the sum has to be 50 multiplied by 101 which is 5050," said Gauss.

"It is like magic," said the teacher.

"A formula to be precise which can be used to find the sum of first n numbers," Gauss suggested modestly.

ONCE, mathematician G.H. Hardy visited a London hopital to see Srinivas Ramanujan who was suffering from tuberculosis. When Hardy entered the room where Ramanujan lay in bed, he said, "I came here in a taxi. Its number was 1729, rather a dull number. I hope is is not a bad omen."

"No, Hardy," said Ramanujan, "it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways." To be accurate, Ramanujan should have said "the sum of two positive cubes in two different ways", but that was what he meant anyhow.

1729 has since become known as the Hardy-Ramanujan Number, even though this feature of 1729 was known to mathematicians more than 300 years before Ramanujan. Numbers of its type (the smallest numbers expressible as the sum of 2 cubes in n ways) are also called taxicab numbers.

Ramanujan loved numbers and experimented with these all through his life. As a child, he found prime numbers upto many thousands, trying to find a pattern that the other mathematicians had missed. Not all numbers can be expressed as the sum of two squares or cubes. He found numbers that could be expressed like this. He would notice that 1729 came up twice on this list, and would remember it all his life.

An average school child today knows methods, for which, Aristotle, Newton, Gauss and Ramanujan would have sacrificed their lives. There is nothing special about 5050 or 1729 if you do not observe closely. Assume for a while that you have discovered a special property of a number that thousands of persons before you have missed. You will be remembered long after Hitler, Napoleon, Gandhi and Akbar are forgotten.

When Newton saw an apple fall, he found,
A mode to prove that the Earth turned round,
In a most natural whirl called gravitation,
And thus is the sole mortal who could grapple,
Since Adam, with the fall or with the apple

— Byron