Visualizing the Riemann zeta function and analytic continuation

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Shared December 9, 2016

Unraveling the enigmatic function behind the Riemann hypothesis
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Music by Vince Rubinetti:

Check out some of Vince's other work here:

For those who want to learn more about complex exponentiation, here are a few resources:
- My video on the topic:
- Mathologer's:
- Better Explained:

For those who want to learn more about the relationship between 1+2+3+4+... and -1/12, I'm quite fond of this blog post by Terry Tao:

Also, in a different video "What does it feel like to invent math", I give a completely different example of how adding up growing positive numbers can meaningfully give a negative number, so long as you loosen your understanding of what distance should mean for numbers:

Interestingly, that vertical line where the convergent portion of the function appears to abruptly stop corresponds to numbers whose real part is Euler's constant, ~0.577. For those who know what this is, it's kind of fun to puzzle about why this is the case.


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