How Infinity Explains the Finite | Infinite Series

Peano arithmetic proves many theories in mathematics but does have its limits. In order to prove certain things you have to step beyond these axioms. Sometimes you need infinity.

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Previous Episode – Kill the Mathematical Hydra

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Made by Kornhaber Brown (

Sources and further references:

Kirby, L.; Paris, J. (1982). “Accessible Independence Results for Peano Arithmetic” (PDF). Bulletin of the London Mathematical Society. 14 (4): 285. doi:10.1112/blms/14.4.285

Goodstein, R. (1944), “On the restricted ordinal theorem”, Journal of Symbolic Logic, 9: 33–41, doi:10.2307/2268019, JSTOR 2268019

Goodstein Sequence

The Hydra Game

The Hydra Game

Commenters who took on the additional Hydra challenges!

Anirudh sreekumar

Arjun Ariyil

Dliess Mgg


Karan Kumar

Nishada Banana

Vedant Bhutra

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