1+2+3+4+... = -1/12
Proof:
https://www.youtube.com/watch?v=w-I6XTVZXww
A bit longer: Sum of Natural Numbers (second proof and extra footage) - YouTube
The zeta function regularization is kinda weird from an intuitive standpoint, but it's pretty common in string theories.
(Moar thorough, non-youtubed explaination: http://math.ucr.edu/home/baez/twf_ascii/week126)

Proof:
https://www.youtube.com/watch?v=w-I6XTVZXww
A bit longer: Sum of Natural Numbers (second proof and extra footage) - YouTube
The zeta function regularization is kinda weird from an intuitive standpoint, but it's pretty common in string theories.
(Moar thorough, non-youtubed explaination: http://math.ucr.edu/home/baez/twf_ascii/week126)
