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Anthropic Took On the Riemann Hypothesis. Here’s What Actually Happened

Ellie Sleightholm

536,814 views

Claude Didn’t Solve the Riemann Hypothesis. So What Did It Do?

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Analytic continuation 3Blue1Brown: But what is the Riemann zeta function? Vis...
More resources: https://desvl.xyz/2022/11/24/riemann-...

Chapters:
00:00 AI and the crisis in mathematics
01:38 Prime numbers and the prime counting function
03:24 From the Basel problem to the zeta function
05:01 Euler’s product: connecting zeta to primes
08:12 A quick fleece interlude 🍂
09:05 Riemann’s paper and complex numbers
12:09 Zeros, the critical strip and the Riemann hypothesis
14:18 A history of progress on the critical line
16:07 What Anthropic actually announced
17:24 Inside Claude’s team of AI agents
19:23 Failed approaches and a new direction
20:43 The claimed 50% result, and attempts to break it
21:39 Pushing the bound to 67.25%
22:54 Checking the proof: AI, mathematicians and Lean
24:59 Is this a significant breakthrough?
25:48 Why even 100% wouldn’t prove the hypothesis
28:13 My thoughts on AI’s progress
28:52 Guardrails and misuse
29:39 Mathematics is more than a benchmark
31:03 Transparency and giving mathematicians credit
33:23 What does it mean to be a mathematician?

Credits:
Written and directed by Ellie Sleightholm
Partially animated by Ellie Sleightholm using the manim package: https://www.manim.community/
Edited and partially animated by Matilda Andrews

Music from Epidemic Sound
Somes stock footage from Storyblocks

Subscribers: 159,145

20 Comments

@elliesleightholm Creator 5 days ago Pinned

🍂Get 10% off OutsideIn’s range with code 'ELLIE10' at checkout: https://www.weareoi.com?sca_ref=11725872.7Z91mEpVN0Do1&sca_source=YouTube

For every item purchased, they donate clothing to someone experiencing homelessness. This is NOT a sponsored video, this is a brand I've supported for the last 5 years. They've kindly given me an affiliate link so I can share their mission 💛

@pasblo39 4 days ago (edited)

The best thing to come out of this openai paper is that it allowed me to find so many nice math, physics and computer science channels

@gijsjanssen5561 4 days ago (edited)

For anyone interested, there's currently a youtube channel, Zeta Explained, doing a series on the Riemann Zeta Function which goes more into depth on the function and the hypothesis. Currently on episode 115

@tylerhaslam2083 3 days ago

33:58 "A mathematician isn't simply a person who gets to the answer first. They're also the person who understands what the answer means, how it fits into everything we already know and are yet to know, and how to pass that understanding on."
Amen!!

@RobertWyesham 4 days ago

This is a fantastic post! So detailed, and so clear! And, your sound and lighting are superb! Thanks for posting.

@flcor 4 days ago

I love your fresh and open-minded approach to this new brave world. Keep going!

@soumyadeep_dasguptaa 4 days ago

I’m just a teenager in high school with ambitions of becoming a mathematician simply because I think mathematics is fun and cool, and I really enjoy understanding why a proof works.
I understood what you explained in here, and I understood most of the simplicity you presented, except for a few parts. Loved this video, Ellie!
As a suggestion, I'd say maybe share your journey from your high school years to your college days in one of your upcoming videos, as I feel it'll help many people like me. And all the best for your PhD!

@toddbaker3435 2 days ago

Ellie, Thank you so much for this video. I am a professor (but not a researcher) at a small liberal arts college in upstate New York. I have always been fascinated by the Riemann Hypothesis (which is what drew me to your video), and this semester I am working with my Honors students (many of whom are animation, game design, and computer science majors) trying to get a handle on AI and how it will impact their fields. This was extremely helpful. Thank you again and good luck on your Ph.D.

@khulanisithole1657 4 days ago

Everytime I watch your videos, you inspire me to continue persuing my dream of studying mathematics (applied mathematics to be precise, with a focus on optimization methods). Am a high school mathematics teacher 🇿🇦

@rafin_explains 4 days ago

really good content, this type of videos really motivate me to learn more maths, and pls do share your phd journey

@seanhunter111 3 days ago

One fun thing about that Riemann paper (“On the number of primes less than a given magnitude”) where he considers extending the zeta function to the complex numbers and states the hypothesis: It was his only paper in number theory, and essentially founded an entire field (analytic number theory).

@Politan182 3 days ago

What a wonderful video. Subscribed and looking forward for more!

@druewilding 4 days ago

I'm really happy they are publishing all the details so we mere humans can learn from the findings. the navier-stokes thing was a bit lacking in that, I thought.

@gelbgleb 2 days ago

This is a brilliant video! Explanations, details, thoughts, examples - it's just far beyond what one may think from the title of the video. Thank you, Ellie!

@jagatiello6900 4 days ago

14:30 A crucial step in the first proofs of the PNT is the fact that zeta doesn't vanish on the line Re(s)=1. And, by the functional equation proved by Riemann, it doesn't vanish on Re(s)=0 either. So the non-trivial zeros are all inside the critical strip, that is, 0<Re(s)<1.
14:56 That's exactly right. In fact, Davenport and Heilbronn showed that some functions satisfying a similar functional equation to that of the RZF do have infinitely many non-trivial zeros outside the critical strip, despite having an infinite number of them on the critical line.

@quranjadeed 4 days ago

I am 60. In high school I loved math. For our graduating national exam I studied so much that I wanted to get a perfect math score something my school had never yet achieved. A week before the exam our math teacher said that he didn’t believe anyone in the school will be “doing great” so I was so much looking forward to proving him wrong! I ended up missing only one question (out of 60) and so did not get the perfect score. The question I missed was a silly problem that I never missed before. Such is life. I ended up with an Electrical Engineering degree and worked as an engineer since. However, I still love math and am seriously considering going back to school…

@RickyReviews101 4 days ago

Mathematicians created their own Frankenstein monster.

@higo021298 4 days ago (edited)

Your channel is really cool. Science communication without oversimplifying the ideas, keep going!

@juliomacnob 3 days ago

We need mathematicians to understand what these machines are doing and proving; ordinary people don’t have the capacity to understand it.

@Kamel419 22 hours ago

I have watched so many videos explaining math and your explanations are the best I've ever seen. This absolutely includes 3blue1brown - I've been watching his videos for many years.