Persiflage

Another shiny new AI proof, this time a proof by Constantin Kogler of the Odlyzko–Poonen conjecture which says that a polynomial with coefficients chosen randomly from \(\{0,1\}\) is irreducible.

This post is a follow-up on a previous post on the abelian house.

[I just found this draft of a blog post from 2017, I thought it might be a light diversion.]

So one day after an amazing result by humans, the computers have struck back!

Danylo Radchenko and Campbell Wheeler have posted an extraordinary new paper in which they prove that Stark units for real quadratic fields are algebraic numbers.

I was wrong!

The goal of this continuing sequence of posts is to recognize the reality in how our subject is changing and how we should adapt.

Apropos of nothing, I was reminded recently of a fascinating story I heard from Geordie Williamson about AI and go — perhaps this story was the original source.

I have recently heard a few extraordinary opinions about how mathematicians should use AI.

An update on this post, from my inside sources: word on the math streets of SF is that the OpenAI team tried something like 500 problems to get their 10 solutions.

I have my google alert set for the phrase “Galois Representations”.

This is a sequence to this post.

We are all aware of what ChatGPT can do.

My recent post generated a surprising amount of personal emails defending of Philadelphia.

I was heartened to see a recent list of results proved by OpenAI here.

There is an interesting post here on Xena’s blog.

I learnt a few days ago about the following AI challenge: find polynomials with Galois group \(G\) for each of the transitive subgroups of \(S_{24}\), with each of the possible signatures \((r_1,r_2)\) with \(r_1 + 2r_2 = 24\) where \(r_1\) … Continue rea…