Why Does -1/12 Keep Appearing Everywhere In Physics?

Book a free consultation with an Odoo expert or start a 15-day free trial of Odoo: https://www.odoo.com/r/cAT Can adding every positive whole number really give you -1/12? We explore how physicists extract meaningful finite values from infinite sums, and how this strange mathematical technique shows up in the measurable Casimir effect and even helps explain why bosonic string theory requires 26 dimensions. . Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime Check out the Space Time Merch Store https://www.pbsspacetime.com/shop Sign up for the mailing list to get episode notifications and hear special announcements! https://mailchi.mp/1a6eb8f2717d/spacetime Search the Entire Space Time Library Here: https://search.pbsspacetime.com/ Hosted by Matt O'Dowd Written by Richard Dyer & Matt O'Dowd Post Production by Leonardo Scholzer Directed by Andrew Kornhaber Associate Producer: Bahar Gholipour Executive Producer: Andrew Kornhaber Executive in Charge for PBS: Maribel Lopez Director of Programming for PBS: Gabrielle Ewing Assistant Director of Programming for PBS: Mike Martin Spacetime is a production of Kornhaber Brown for PBS Digital Studios. This program is produced by Kornhaber Brown, which is solely responsible for its content. © 2026 PBS. All rights reserved. End Credits Music by J.R.S. Schattenberg: https://www.youtube.com/user/MultiDroideka Space Time Was Made Possible In Part By: Big Bang Alexander Tamas Filip Rolenec Juan Benet Kenneth See Mark Rosenthal MATTHEW OCKO Morgan Hough Peter Barrett Vinnie Falco Supernova Ethan Cohen Grace Biaelcki Justin Lloyd Mark Heising Rad Antonov Stephen Wilcox Tristan Lucian Claudius Aurelius Tyacke Hypernova Alex Kern Ben Delo chuck zegar Dean Galvin Donal Botkin D. Rollere Gregory Forfa Jeff White John R. Slavik Paul C. Pedersen Pala Massimiliano Patrick O’hara Scott Gorlick Scott Gray Spencer Jones Vlad Shipulin Zachary Haberman Антон Кочков Gamma Ray Burst Alex Gan Aaron Pinto Almog Cohen Arko Provo Mukherjee Austin Richards Ayden Miller Bert Whetstone Brandon Lattin Brandon R Cal Harrington Cal Stephens Chris Liao Collin Dutrow Craig Falls Craig Stonaha Dan Warren Daniel Donahue Daniel Jennings Darrell Stewart David Giltinan David Johnston Diana S Polijar Donovan King Doug Richardson Doyle Vann Eric Kiebler Eric Raschke Eric Schrenker Faraz Khan Frederic Simon Harsh Khandhadia Isaac Suttell James Trimmier Jason Holtkamp Jeb Campbell Jeff Harris Jerry Thomas Jim Bartosh John Anderson John De Witt John Hanavan John Mieras USN Ret Joseph Salomone Junaid Ali Justin Zheng Kacper Cieśla Kent Durham Koen Wilde Kyle Atkinson Lori Ferris Marcelo Garcia Mark Daniel Cohen Mark Delagasse Mathew Ray Matt Kaprocki Matthew Johnson Matthew Twyman Michael Barton Michael Clark Michael Lev Michael Purcell Michael Spallino Mikk Mihkel Nurges Nicolas Katsantonis Nils Anderson Paul Wood Reuben Brewer Robert DeChellis Ross Kennedy Ross Story Russell Moore SamSword Sandhya Devi Sean Owen Shane Calimlim Terje Vold Terrance Cennon Thomas Dougherty Tybie Fitzhugh WILLIAM HAY III Zac Sweers