Uploaded March 2019 | Updated September 2026, 4 hours ago
The sum of natural numbers, 1+2+3+..., is a fairly regularly cited sum to show off the strange nature of mathematics. This is mainly due to the fact that it can (seemingly) easily be shown to be equal to -1/12. That's right. Not only is the result finite, it is also a fraction as well as negative! This seems completely crazy and that's because there is an important factor of infinity that is hidden from view when proving this in the usual ways. So let's find out what this sum is equal to while still retaining this mysterious hidden infinity. The way of doing this is through what is known as regularization of the series (which is secretly done is the normal way of evaluating this sum as well).
This parallels nicely to a technique in physics known as renormalization, where we take infinities that show up like this and hide them in other places, like the masses and charges of particles. This allows us to have finite physics, but we lose the ability to predict these quantities.
► Music Credit: Dj Quads
Track Name: "It's Near"
Music By: Dj Quads @ soundcloud.com/aka-dj-quads
Original upload HERE - youtube.com/watch?v=UI79n3E1U_g
Follow me on Twitter: twitter.com/ZapPhysics
The sum of natural numbers, 1+2+3+..., is a fairly regularly cited sum to show off the strange nature of mathematics. This is mainly due to the fact that it can (seemingly) easily be shown to be equal to -1/12. That's right. Not only is the result finite, it is also a fraction as well as negative! This seems completely crazy and that's because there is an important factor of infinity that is hidden from view when proving this in the usual ways. So let's find out what this sum is equal to while still retaining this mysterious hidden infinity. The way of doing this is through what is known as regularization of the series (which is secretly done is the normal way of evaluating this sum as well).
This parallels nicely to a technique in physics known as renormalization, where we take infinities that show up like this and hide them in other places, like the masses and charges of particles. This allows us to have finite physics, but we lose the ability to predict these quantities.
► Music Credit: Dj Quads
Track Name: "It's Near"
Music By: Dj Quads @ soundcloud.com/aka-dj-quads
Original upload HERE - youtube.com/watch?v=UI79n3E1U_g
Follow me on Twitter: twitter.com/ZapPhysics
