Posted on October 23, 2024
| 2 minutes
| 298 words
| Markus Shepherd

This subject has nothing to do with games nor data science, but chances are that amongst the readers of this blogs are many who appreciate mathematics – and its beauty. Long before Recommend.Games, I’ve had a blog on the Riemann Hypothesis – the famous conjecture which is usually formulated in terms of the zeros of the complex Riemann \(\zeta\)-function, but is really about the distribution of prime numbers. If you’re curious to learn more, check out the blog. 🤓

The reason I bring this up now is that I just re-created and updated an old animation I’ve uploaded to YouTube almost ten years ago:

The line you’re watching going round and round in circles is a plot of the values of said \(\zeta\)-function on what’s called the critical line \(s=\frac12+ti\). Every time the line hits the origin, we’ve just witnessed another one of those enigmatic \(\zeta\)-zeros. We know that there are infinitely many of those zeros on the critical line; the Riemann Hypothesis states that there are none elsewhere (except for the trivial zeros at negative even integers).

If this all sounds really confusing and you have no idea how on earth this could possibly be connected to prime numbers, I’d again refer you to my other blog where I’ve tried to explain those questions with very little mathematical prerequisites.

But the real reason I wanted to draw your attention to the video: I just find it so pretty. 😇 Even if you don’t care for analytic number theory, I hope you can still appreciate the beauty of this spiral making seemingly unpredictable narrow and wide turns. If you really want to unwind and get hypnotised by the \(\zeta\)-function, I’ve also create an hour-long version:

Enjoy! I promise, the next post will be about board games again… 😎