Last hours of 2024: One Wish, Reviving(?) Polymath3, Peter Sarnak’s Question, and Quantum Plans

Combinatorics and more 2024-12-31

A wish

2025c

It is time for the horrible war to end

Polymath thoughts: Reviving Polymath3?

A question for our readers: Should we revive polymath3?

Polymath3 dealt with the following problem:

Is there a polynomial $P(d,n)$ such that the graph of every $d$ -polytope $P$ with $n$ facets has diameter at most $P(d,n)$ .

If anybody is interested to take part in a renewed polymath project, please comment over here or drop me an email.

AI and mathematics

Peter Sarnak is in town and when we met he had a question for me:

Will AI take over mathematics?

Peter told me what he thinks, and was surprised and a bit disappointed that I don’t have an opinion. I promised to think about it and to try to have some answer in a week (Thursday, January 2) .

Meanwhile, I asked ChatGPT and this is what it answered. Here is one quote:

(ChatGPT) Many breakthroughs in mathematics involve conceptual leaps that are hard to formalize in a way AI can process.

I disagree; I don’t see reasons to think that conceptual leaps will be harder for AI compared to other aspects of math. (I disagree with several other assertions in ChatGPT’s answer.)

Quantum thoughts and Future Posts

“Some quantum mysteries” is the name of an ambitious post that I am planning for some time and I hope to conclude in a few weeks. I will mention several quantum physics mysteries many of which are related to quantum information theory and the first one is about the elusive “Majorana zero modes”. A spinoff of this post which may be ready even earlier is a summary of few skeptical views about quantum computing of Robert Alicki, Michel Dyakonov, Leonid Levin, Oded Goldreich, and others.