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

Ten years later... Professor Tony Padilla returns to the thorny issue of summing the integers arriving at -1/12. More links & stuff in full description below ↓↓↓

NUMBERPHILE

Videos by Brady Haran

[cmelonwheels]

"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

[Tea]

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

[atrumluminarium]

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 😂

[seifqiblawi]

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

[Mk-qkbw]

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

[justforfunforever]

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!

[dmitryrybin]

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

[FourthDerivative]

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

[maxtrax]

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

[Toobula]

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.

[Kram]

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

[y]

Best Numberphile video I have seen in a while. Thanks Brady.

[alokaggarwal]

Thanks! I love your channel, and this particular video is one of my all-time favorites. It explained a complex topic in a clear and compelling way. Amazing.

[gariyamelperaltaalvarez]

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.

[njpf]

I appreciate Tony’s passion for the subject! It’s always awesome to see someone apply their passion and continue to push it to new edges and in new ways!

[Examantel]

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.

[eugenemasoniv]

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

[MatheusLeston]

10 years ago, because of your videos, I got really into this -1/12 thing. I kept researching it for quite a while. But this new video is just amazing; what a fascinating result!

[FlorianBendl]

Watching your videos for many years I sometimes regret I left academia. So much to still be discovered. Thanks for making these intriguing videos that even I can keep track with.

[lescarter]

Love your content, presented in a very accessible way. Coming from St. Helens, hearing someone who comes from the Northwest providing such great insights into mathematics feels comforting and even more relatable (and hopefully inspiring for kids growing up in the region). Thanks!