We’ve launched an expansion of FrontierMath: Open Problems! The benchmark now contains 50 significant, unsolved problems from research mathematics. AI has solved three so far, and solving all of them would be an incredible mathematical feat. Thread with more.

So far GPT 5.6 Sol is the most interesting new model mathematics-wise for me - those of the new proof claims on erdosproblems.com that I've looked at in detail have all been correct, and moreover contained some interesting ideas. 1/7

A new blog post on Erdős, aliens, and evil spirits. www.erdosproblems.com/forum/thread...

I have started a collection of essays, blog posts, etc discussing AI in mathematics. I do not agree with everything written, but all are valuable to read - the more different views the better! Please reply with your own suggestions. thomasbloom.org/AIlinks.html

I have written a blog post giving my personal sketch of the recent disproofs of the sum-product and unit distance conjectures. www.erdosproblems.com/forum/thread...

New project: problemsilike.com, a website collecting open problems that I, personally, like, with comments on their context, difficulty, and interest.

Some dismiss Erdős problems as trivialities - this couldn't be further from the truth! While many are amusing novelties, some of them are the most central problems in number theory and combinatorics. A blog post with, in my view, the 10 most important: erdosproblems.com/forum/thread...

A new blog post by @acerfur.bsky.social describing his experience as a pioneer of using AI tools to solve Erdős problems: www.erdosproblems.com/forum/thread...

AI is capable now of generating new interesting mathematics. But it's much easier for it to generate plausible-sounding nonsense. I am concerned that the latter, copied and promoted by users with no understanding of the mathematics, is going to drown out the former.

My prediction is that by the end of the month there'll be between 4 and 8 new Erdos problems with solutions mostly or entirely AI generated. But then we'll have seen all the easy wins available, and progress will slow until a significant jump in model capability or new human insights.

One of the big challenges now in using AI for mathematics is the credit/attribution problem. AI has a tendency to use observations/techniques without giving credit as to where it 'learnt' about them (mainly because it's forgotten itself).

If you want something to read for the next couple of years, I highly recommend The Wandering Inn - 16 million words and still in progress! wanderinginn.com (It even has a mathematician canine character, with cool shades, though you have to wait about 10+ million words for them to show up.)

Overview

Table of Contents Latest Patreon Chapter loading… Latest Public Chapter loading… Where I left off loading… New here? START YOUR JOURNEY Welcome to the Innverse, a captivating web serial where stories ...

wanderinginn.com

A famous quote by Renyi (often falsely attributed to Erdős) is "A mathematician is a machine for turning coffee into theorems." I recently learnt that in German this is actually a great pun: the word 'satz' for 'theorems' can also be translated as 'coffee grounds'.

Here is one of my favourite, little-known Erdős problems for #mathsky: Take a 1x1 square. You can fit lots of lines of length 1 inside. Say that a collection of lines is 'maximal' if you can't fit any other lines inside without overlapping. 1/?

Is there a good mathematics community on here? Can anyone share some good people to follow? I'd like to talk about Erdos problems and other maths, and would rather not do it on Twitter/X for obvious reasons.

A new paper of mine, on an L^3 control assumption, which has a number of applications in additive combinatorics. In particular, I give a new value for the sum-product exponent, which measures how any set of real numbers must grow under addition or multiplication. arxiv.org/abs/2501.09470

Control and its applications in additive combinatorics

We prove new quantitative bounds on the additive structure of sets obeying an $L^3$ 'control' assumption, which arises naturally in several questions within additive combinatorics. This has a number o...

arxiv.org