This is a very approachable explanation by [mathematician] John Baez https://youtu.be/vzjbRhYjELo?t=426 https://youtu.be/vzjbRhYjELo?t=426 and going into this w

This is a very approachable explanation by [mathematician] John Baez https://youtu.be/vzjbRhYjELo?t=426 https://youtu.be/vzjbRhYjELo?t=426 and going into this with a bit of depth mentioning the 'rigorous' (i.e., analytically 'acceptable' form of the summation of Riemann Zeta function and the radius of convergence and all) along with the naive Euler summation. He goes on to mention a few times as to why it's fundamental in string theory (not to be confused with super string nor m-theory, which are of course different). A bunch of people had issues with the Numberphile episode where these restrictions where elided (due to time, I'd imagine), but they had another episode featuring the zeta function and a math professor (rather than physics professors, who were featured on the one that went viral) explaining the summation with more context: https://www.youtube.com/watch?v=0Oazb7IWzbA https://www.youtube.com/watch?v=0Oazb7IWzbA.