Transcript:

Consider this infinite sum: 1 + 2 + 3 + 4... all the way to infinity. When this problem was posed to Ramanujan, intuitively, Ramanujan came up with the answer −1/12. And you think, wait a minute, these are all positive numbers; they are going to add up; how is the answer going to be negative? But in Ramanujan's mind, he could see the solution going all the way to infinity, looping back and coming back from −infinity towards 0, and stopping at −1/12.

Many years after Ramanujan, the Riemann Zeta function was formulated. This is the one. It is the sum of all n > 1. This function was analytically continued to values < 1, and the value that came out for zeta of −1 is −1/12.

It's amazing. Ramanujan had this amazing, amazing genius insight into infinity. It is quite sad that we lost him at the age of 32.