Why 1+2+3+...=-1/12 Is Not an Ordinary Sum

HN points to it as the in-depth rebuttal to the Numberphile video that explains why the 'proof' is wrong yet the result is meaningful.

Mathologer examines the infamous Numberphile claim that 1+2+3+... equals -1/12, explaining what is wrong with the calculation and how it connects to real math like the zeta function and analytic continuation.