1+2+3+4+5+... = -1/12 ? WHAT ?

Even those of you who like mathematics, probably don’t think of it as a subject that can create emotional arguments. But in fact, even a seemingly innocent video clip about mathematics can spark a heated debate.
Most of these debates are associated with mathematical cranks. People who insist that they can solve some unsolved mathematical problem or insist that 1 is not equal 0.99999…. (they are equal). But what if such a dispute involves two of the greatest mathematicians of all times and one of my favorite YouTube channels?

Note: This post includes 3 YouTube videos. The first is about 7 minutes long and it also explains what’s the story here, so I rather you watch it while reading the post. The other two are 40 minutes and 20 minutes long so you can watch them after you finish reading (they are both worth your time… if you like mathematics, that is… )

NumberPhile is one of my favorite YouTube channels, not only because I am well… a numberphile, but also because the way they explain complex mathematical concepts in a friendly and funny way (which involves a brown wrapping paper). The NuberPhile videos are presented by mathematicians and physicists who know their stuff, so I never expected them to touch on anything controversial or not completely substantiated.

But then came this video:

And I thought, “This can’t be right!”. Of course, I wasn’t the only one, as you can see by the hundreds of responses to the video. Some, like mine, were trying to point out the fallacies in the proof. Others were much less polite. Yet, there were some others who supported or at least partly supported the strange equation, presented in the video, while pointing out that it appears in the writings of Reiman and Ramanujan. And so, unlike in most cases of mathematical debates, it wasn’t clear who is right and who didn’t do their homework.

Finally, a theral and mathematically sound explanation of what is going on, came in this video:

As you will see, it explains the fallacies of the NumberPhile proof in a clear and profound way, but does not render the idea presented in it to complete nonsense. Instead, it explains how it is related to the Riemann Zeta function.

So finally, if you want an explanation of what the Zeta function is all about, you can find it explained beautifully here:

So this is mathematics for you in the way it really is. An area full of mind boggling ideas. Not quite the boring stuff they teach in school.