Large Numbers and the Nature of Mathematics
The great mathematician GH Hardy once shared an anecdote of his meeting with S. Ramanujan: I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." Indeed, each number is special if we analyse it for long enough. Ramanujan and his work are regarded by many as the pinnacle of mathematical intuition. He could see patterns unravel themselves, and had also obtained a fundamental intuition for the numbers. Many of us have been exposed to this mathematical beauty occasionally throughout our study of the subject -the so called “joy of mathematics”- even though we may not feel it. For example, a repeatedly used number like one, two or zero doesn’t merely represent a concept, a definition, an object or a transformation. It is something that transcend...