The Impossible Equation Behind String Theory's 26 Dimensions

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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.
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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

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