Final prime spiral video (quick error check before release)

Eventually, I'd love to cover this. At the moment, there are several other topics higher on the list.

3blue1brown

What a wonderful connection! Speaking of primes... Any chance we might get a video on the connection between the Reimann Zeta Function and the distribution of primes, like you mentioned in the Riemann Zeta video? Those animations were incredible, especially that one of the critical line. So tantalizing!

I love you Grant! This is God's work! 🙏🏼

That was so so beautiful. Thank you so much Grant :)

Oren Milman

Yes! Most certainly. I had bit a bit writers blocked on the "everything about exp" videos that are in the plans.

3blue1brown

Unintended! Perhaps subconsciously though...

3blue1brown

I enjoyed your video again, as usual. Good job! I would love to see you making a video on quarternions and the way in which it could be interpreted a little differently: break the real part of the quarternion number into 3 separate real numbers and visualize the quarternion space as 3 perpendicular complex planes. I wonder if we can get anywhere if we consider spacetime as 3 complex planes, the 3 orthogonal real axis describing 3D space and the 3 imaginary axis (I, j and k) describing 3D time. The result is a dynamic spacetime vector. A nice way of visualizing is to bend each Euclidean axis into a circle. I can’t find much about this on the web so my hope is that you want to dive into this :) PS: after this post I discovered the book The Standard Model of Quantum Physics in Clifford Algebra, Claude Daviau & Jacques Bertrand. Are you planning to cover the topic of fundamental particles explained through Clifford Algebra?

"Now that might seem weird, right? I mean, prime numbers seem _wholly unrelated_ to the continuous world of calculus..." Pun intended? :)

Richard Neilsen

Great video! Will you return to the differential equation series?

Thanks for adding the bit about Dirichlet -- a book about geometry that I am reading bits and pieces of talks about Plato, whose influence on geometry came from his appreciation of it as a mode of reasoning, not from any work on geometry itself. Apparently, outside the Academy, was written "Let no one ignorant of geometry enter these halls", or something to that effect. This bit about Dirichlet and arbitrary questions connecting to important things has the same ring to it, though I can't explain why at this time

The last digits of primes aren't as random as we had thought: https://www.nature.com/news/peculiar-pattern-found-in-random-prime-numbers-1.19550

Imre Polik

At 9:47 I think it would be better to go from 1 to 44 instead of 0 to 43.

Imre Polik

I like the thesis of the value of "pointless" play and the contradiction it entails. If it has values, how can it be pointless. I have not watched the other videos in the series yet, but one thing I felt was not explored sufficiently was the role of units. What if the units were degrees or gradians? What if you used Lockhart's turns? Why isn't there a fundamental unit? MajorPrep's Modular Arithmetic Explained, https://www.youtube.com/watch?v=lJ3CD9M3nEQ, video, while not as slick has some complimentary visualization. And, Infinite Series has an episode that uses modular math to ask questions about the game of Set, https://www.youtube.com/watch?v=zurpOBPt4LI.

Raul

The fist version of the video was great, but now I find it even better: Dirichlet's Theorem, Euler's totient function, the remainder classes... everything gives much more coherence and cohesion to the final result. I just noticed that you're using a comma as the thousands separator. I'd rather prefer to leave a little blank space, as in many countries the comma is used to separate the integer from the decimal part of a number. But that's my only tiny concern. Everything else is breathtaking. All your videos are valuable little gems, please never stop delighting us with them :)

Nèstor Abad Viñas

Great! I love the histogram graphics -- so accessible and deep. Using mod 10 was a way to both introduce the concept of mods more generally and to have the most accessible example for the histograms. I like the editorial at the end too. My only quibble is to avoid implying that exploration is separate from "taking a class." In Freeman's et al metastudy of active learning in STEM (2014), they found that active learning was so much more effective than lecture that if it were a medical study they would have to recommend stopping lecturing before the study was done because it would be unethical to continue.... so many instructors do incorporate exploration into classes -- and more should..... clearly that's my soapbox, but it's also natural to make assumptions based on one's own experience of math classes, so thought I'd mention in case it's helpful....

Nicely done. The *only* thing I could see is when you approximated the number as ".000095" at 11:40, when the number goes on to be "...959" which would obviously round to ...96. Doubt it's worth re-recording but I noticed it. Great video.

Burt Humburg

Looking great to me, I really like what you added. It all makes more sense now!

Boudewijn Redeker

Maybe you could include a link to the Mathologer video in the description.

Daniel Armesto

TOTALLY MINOR nitpick - Dirichlet is -even though it seems French- a German, so the emphasis is NOT on the second syllable, but rather ... https://de.forvo.com/word/dirichlet/ (use the second example) And while I'm at it: here is how you pronounce Basel from your Basel-problem video https://de.forvo.com/search/Basel/ (I'm from Seattle - not SEE-attle, but se-AT-lle). Otherwise, great as always, and I learned something. (Hey - if you zoom out still further, can you see 103,993/33,102)? Thx for teaching math!

Beautiful video Grant! When I was younger, I spent lots of time wondering about these prime spirals, so it touched my heart <3

Ever Salazar