Does -1/12 Protect Us From Infinity? - Numberphile

Also newly uploaded today about -1/12: https://youtu.be/FmLIGN8ZGdw And see the full -1/12 playlist at: youtube.com/playlist?list=PLt5AfwLFPxWK2zCU-4X1iuu… -1/12 shield sticker and tee: numberphile.creator-spring.com/listing/1-12-shield…

"I saw a tweet that made me so mad that I disproved it and wrote a paper about it" is the best way to do research

For what it's worth, the original -1/12 video is the reason I went on to study maths and physics in uni and here I am now 😂

You can genuinely feel Tony going "I told you so!" to everyone by the way he's talking. Man's been brooding for literally a decade

If you plot the graph f(N) = N(N+1)/2, it is a parabola that intersect X axis at points 0 and -1. The area bounded by parabola between 0 and -1 is exactly -1/12

Good lord have i really been watchng your videos for 10 years or more? Time sure flies by.

I was more or less mathematically illiterate and despised everything mathematics, and then I watched this video back in the day and it really intrigued me. Now, a few years later I am a grad student in pure mathematics, and it all started with watching these videos, particularly the one about -1/2! You can say what you want about the rigor of these computations, but for me, this is what started my love for mathematics!

Finally, the long-awaited -1/12 redemption arc.

One thing i love about numberphile is how passionate these very intelligent people are about such an awesome topic. Very nice change from the constant bombardment of low level nonsense. Thank you numberphile

C N² - 1/12 + O(1/N) such that C happens to be 0 makes way more sense than just a blanket -1/12. This is very cool

I have not seen Tony so excited for years. I like it. Good luck on his way

I was an undergraduate when the infamous -1/12 video came out and now I’m close to finish a PhD in arithmetic geometry. This made me feel so nostalgic.

For those wondering why e^(-n/N)*cos(n/N) is so elegant, it's the fact that in C*N^2, C is the Mellin transform of the regulator function, which basically amounts to integrating x*e^(-x)*cos(x) from 0 to infinity, and it ends up being 0.

Man I love how Brady just goes in with the tough questions and points. Great video!

Professor Padilla is a brilliant physicist and mathematician and incredibly skilled at explaining his thinking to us, even when ,like here, it gets into the realm of wonder. Thank you, Brady, for bringing him to us.

Ten years ago I was very unhappy with my career and watched the original video. I was so intrigued and inspired, I quit my job and went back to school for a math degree to better understand this result. I've never regretted this decision and seeing this video feels like everything has come full circle.

Lot more gray hairs on Tony. Cannot believe we have been growing up with this man for more than a decade. On a side note, any more of them big numbers?

Wow can't believe it's been 10 years since that video

Your videos were one of the things that really got me into mathematics, and now I'm in graduate school for my physics PhD. Looking in the comments, I'm not alone in this either! Thanks for ten years of accessible math education -- even if some of it isnt entirely rigorous :p This sum regulation method is fascinating... I wouldnt buy putting an equals sign anywhere, but it's still extremely compelling that -1/12 is just as important here as it is via analytic continuation. Edit: That connection to physics -- wow! It makes me think that there must be some universally "preferred" method of renormalizing sums, some way that's "natural" in both mathematics and physics for reasons that arent entirely clear. I'm very curious why certain regularizations produce that behavior but not others...

Oh my how the time has passed. 10 years ago I was in high school, watching these videos with astonishment and a genuine feel of adventure and love for all these awesome discoveries. A decade and two degrees later, and nothing has changed, except maybe for greying Professor Padilla, but still as enthusiastic as ever. Thank you, sincerely.