But what is the Riemann zeta function? Visualizing analytic continuation

Unraveling the enigmatic function behind the Riemann hypothesis

Help fund future projects

An equally valuable form of support is to simply share some of the videos.

Special thanks to these supporters

Posters/shirts for this visualization at

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.

Thanks to these viewers for their contributions to translations

Hebrew: Omer Tuchfeld

------------------

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist

Various social media stuffs: