Avery Carr

Here's what András Sárközy, Erdős's most prolific collaborator, asked 25 years ago: "How small can one make the maximal gap between the consecutive elements of a multiplicative Sidon set selected from {1, 2, ..., n}?" In particular: does there exist a multiplicative Sidon set A ⊆ {1, 2, …, n} such that every sub-interval of [1, n] of length at least √n contains at least one element of A? The answer is yes. The solution was autonomously discovered and formally verified in #Lean by Aristotle. We then improved the bound below √n and Aristotle formalised our proof too.

> First woman and first Iranian to receive the Fields Medal in 2014. > Gold medalist at the International Mathematical Olympiad in 1994 with a score of 41/42. > Professor at Stanford University with major contributions to hyperbolic geometry, Teichmüller theory, and dynamical systems. > Gold medalist at the IMO in Toronto in 1995 with a perfect score of 42/42. Today, we celebrate the life and legacy of Maryam Mirzakhani, who would have turned 49. In 2014, she became the first woman to receive the Fields Medal for her groundbreaking work in geometry and dynamical systems. Maryam Mirzakhani passed away in 2017 at the age of 40, but her contributions to mathematics continue to inspire generations around the world.

@littmath @AcerFur Thank you!

@littmath Thank you! I am wondering about the Erdős problems as well @AcerFur. I know #1196 has/will land in a good journal, but what about the rest?

I'd like to solicit thoughts on a question I had about problemsilike.com, my new problem list website. At this point I've solved a number of nominally open problems with the help of AI tools. I say "nominally," because in many cases the answer was implicit in the literature, or because the solution showed that the conjecture in question was not so interesting, etc. Basically, situations where it is not worth my time to polish the result and send it through the traditional review process. On the other hand, these are problems I like, or at least problems I like enough to try my hand at. Is it useful to put already-solved problems like this on the site? Or should those be handled in some other way?

@stevenstrogatz @avorobey Because they are very “selective”.😂. Book was only a NYT bestseller and has lots of famous praise, but sure you are “selective”.

@avorobey If an author takes the bait, they start asking you to pay for the opportunity to have your book discussed.

Best thing in this book club scam: "The way you explore [insert key theme, character dynamic, or narrative strength]".

@jdlichtman @AcerFur Wish I could heart this more than once. Same here.

@AcerFur Mine is also quite unique...story for another time

lol most people don’t know this, but I am quite bad at the Cambridge maths tripos. I am terrible at thinking about several questions on fields that I don’t particularly care for each within 30 mins in exam conditions… Tbf Roth only barely passed the tripos and he ended up fine.

And we have already have a first potential solution to #6, produced by GPT 5.5 Pro (prompted by @thomasfbloom). It will take some time for me to check it but at first glance it indeed looks plausible! The problem and my pre-registered comments below.

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

@thomasfbloom @AcerFur That’s a great question. Right now, models are solving problems posed by humans. But will there come a point where the models themselves decide which problems are important, pose those problems, and then solve them? If so, where does that leave human understanding of the results?

There are many here who both believe that soon AI will be superhuman at maths, solving all Millenium problems and beyond, and yet also reject any claims that maths is 'dead', and believe that mathematics will thrive. I'm curious, for those people, what is maths in that future?

@AIsakovic1 @physicscat0x7d For me, I have been working in graph theory lately, one paper accepted recently, and one on the way to submit. But plan to circle back to this soon. I feel there are so many theorems from functional analysis that could aptly be applied to areas like black holes.

@ATCarrMath @physicscat0x7d Congratulations! Will you continue working on related topics?

Finally submitted the hard copy of my PhD thesis!

The top 10 Erdos problems by @thomasfbloom are really cool, completely different level from what we have seen so far with AI! erdosproblems.com/forum/thread/b…

I had never thought I would say this! But here I go: I solved my first Erdős problem! I did so using ChatGPT-5.5-Pro. 🧵1/n

@DavidTurturean Congratulations!

He is not wrong…

@davidbessis Legends recognize legends.

It's great to be complimented by great writers😊!

@zeratizerata @alz_zyd_ Compute power (in terms of energy) is one limit. Limits grounded in epistemology in general (incompleteness and undecidable propositions). Proof digestion is needed as well. The problems thus far solved by LLMs are not representative of the universe of unsolved problems.

@ATCarrMath @alz_zyd_ you don't think they WILL? what's your reasons it does not seems they have an intelligence limit

If you still think LLMs suck at math, at this point it really is a skill issue

@kfountou @littmath Good thing mathematics is the Queen of the sciences.

@littmath The king is dead, long live the king!

The reports of my death are greatly exaggerated. —Mathematics