Srinivasa Ramanujan, was one of India’s greatest mathematicians who lived in the early part of the twentieth century. He displayed intense curiosity from a very young age and would ask questions such as, ‘who was the first man in the world?’ or, what is the distance between clouds? Mathematics was the subject he loved and he poured all his energies into it, learning, mastering and also contributing original work in this field, leaving behind an enduring legacy. Even today, nearly a century after his death, his theorems are being applied in diverse fields like computers, polymer chemistry, cancer research……..
Is it possible for children to appreciate his work? Certainly not if they are asked to wade through his published papers, each averaging 20 pages of dense mathematical notations and formulae! But maybe they can get to taste some of the flavor of his work – especially in Number Theory, which deals with everyday numbers that all of us familiar with – the 7s, 15s, 249s……..; he had played about with numbers and equations all through his life, discovering their properties, identifying relationships among them …..
For example take the number 1729 – all of us know this as Ramanujan’s number. Prof. Hardy was visiting an ailing Ramanujan and on entering the room he expressed his disappointment at the number of his taxi cab which was 1729. Hardy remarked that it was a dull number. Ramanujan’s response was immediate: “No, Hardy, it is a very interesting number! It is the smallest number expressible as the sum of two cubes in two different ways!”
Finding numbers that are the sum of one pair of cubes should not be difficult. Take any two cubes, add them up and there you have it:
2^3 + 3^3 = 35
3^3 + 5^3 =152; and so on ………
But can you get 35 or 152 by adding another set of cubes? The answer is NO!
You can keep trying with every integer in the number list; it is only when you reach 1729 that you strike the two pairs of cubes!
9^3 + 10^3 & 12^3 + 1^3!
How did Ramanujan know? He certainly didn’t pluck it out of thin air! Years before, in his playful dealings with numbers, he had observed this little property of 1729 and wrote it down in his (now famous) notebook. Given his easy familiarity with numbers and their properties, it was not difficult for him to remember such nuggets of mathematical insights that he had worked out himself.
Here’s a small exercise for you:
Q) Find out numbers that are a sum of one pair of cubes – at least 10 of them.
Q) Can you find the second smallest number that is the sum of two sets of cubes?
Work it out yourself – don’t rely on calculators, computers or adults to help you.
Do it the way Ramanujan did, play with the numbers; then, maybe, you just might begin to experience a tiny bit of the excitement that held him in thrall for most of his life. You will also begin to appreciate the effort, patience and self belief that is needed to produce his kind of work!