You may have seen that Youtube video by Numberphile that circulated the social media world a few years ago. It showed an ‘astounding’ mathematical result:

\[1+2+3+4+5+\ldots = -\frac{1}{12}\]

(quote: “the answer to this sum is, remarkably, minus a twelfth”)

Then they tell you that this result is used in many areas of physics, and show you a page of a string theory textbook (*oooo*) that states it as a theorem.

The video caused a bit of an uproar at the time, since it was many people’s first introduction to the (rather outrageous) idea and they had all sorts of (very reasonable) objections.

I’m interested in talking about this because: I think it’s important to think about how to deal with experts telling you something that seems insane, and this is a nice microcosm for that problem.

Because, well, the world of mathematics seems to have been irresponsible here. It’s fine to get excited about strange mathematical results. But it’s not fine to present something that requires a lot of asterixes and disclaimers as simply “true”. The equation is *true* only in the sense that if you subtly change the meanings of lots of symbols, it can be shown to become true. But that’s not the same thing as quotidian, useful, everyday truth. And now that this is ‘out’, as it were, we have to figure out how to cope with it. Is it true? False? Something else? Let’s discuss.