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.)

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