"Large language models can write informal proofs, translate them into formal ones, and achieve SoTA performance in proving competition-level maths problems!"

https://arxiv.org/abs/2210.12283

This is one of many recent results bringing us closer to a full automatization of mathematics. I expect that the role of human mathematicians will very soon be reduced to that of a guiding hand pointing toward the rough direction of interesting and useful mathematics while artificial intelligence will do the rest.

Quantum Chaos = Volume-Law Spatiotemporal Entanglement https://arxiv.org/abs/2210.14926

No one can hear you screaming in phase space (src)

"We are excited to share a significant advance in the field of AI and mathematics. Meta AI has built a neural theorem prover that has solved 10 International Math Olympiad (IMO) problems — 5x more than any previous AI system. Our AI model also improves upon the current state of the art by 20 percent on miniF2F, a widely used mathematics benchmark, and by 10 percent on the Metamath benchmark.

We have been able to solve the following problem:

Let a and b be natural numbers both prime with 7, and such that 7 is also prime with a + b, if we assume that 7^7 divides (a + b)^7 - a^7 - b^7, we need to show that a + b is at least 19."

https://ai.facebook.com/blog/ai-math-theorem-proving/

Is AI Driven Design a Computational Dead End in Engineering?
https://www.designforam.com/p/is-ai-driven-design-a-computational

Inverse scaling can become U-shaped https://arxiv.org/abs/2211.02011