At the suggestion of Terence Tao, I have added a blog feature to this site. The idea is to host some longer pieces of writing about some of the mathematics and problems featured on this site, or about Erdős himself. If you would like to volunteer to write a blog post please email me or comment below. I am particularly interested in:
Informal descriptions of the ideas behind recent Erdős-related breakthroughs, either by the authors or a third party (both perspectives are useful).
Survey posts reviewing a family of Erdős problems (e.g. "Erdős and Distances").
A deep dive into one individual problem, ideally a famous one, describing why it is important and what makes it difficult.
Historical posts collecting some lesser-known anecdotes or stories about Erdős.
Please advertise this opportunity to people you know outside of the regular site users, all are welcome!
While there are many interesting blog posts to be written about AI and its uses in mathematics, I would prefer to focus on non-AI topics such as the above, since there are many other places for people to write about and discuss AI. (I am open to the occasional AI-related post though.)
A site retrospective
This site was first created in late March 2023, but I only shared the link privately with a couple of people at first while it was in early stages. It officially launched 28th May 2023, which is when the current URL went live and I emailed around an announcement.
At that time it had just over 200 problems. We now have 1135 problems in the database (although not all are originally by Erdős himself, some are problems of others that he was fond of and repeated). With all the forum activity lately I haven't been adding many new problems, but there are certainly many more out there (see the list of problem lists). I'm sure there are at least a couple hundred more problems still to be added, although we should have almost all of the most well-known.
The idea for this site had been kicking around in my head for several years - every time I looked back at an old paper of Erdős, browsing for interesting problems, I became frustrated by not knowing which problems were still open, which were quietly solved in an obscure paper and then forgotten about, and which had led to famous theorems in areas outside of my own.
The only solution was to start compiling a list of all the Erdős problems, recording relevant literature and results, but the scale of Erdős' output made this a daunting task. Moreover, clearly this was a resource that would be useful to many other mathematicians as well. As such I put it to one side, hoping that someone better qualified would create it.
As time went on, no such list appeared (although there did exist partial lists, such as Chung's list of graph theory problems). The catalyst to go ahead and make it myself was a combination of two things: conversations with Zachary Chase, then a DPhil student at the University of Oxford, who had had similar thoughts about creating an Erdős problems list, and discovering how good ChatGPT was at coding.
Of course, ChatGPT is far better now than in early 2023, but even back then it was capable of doing most of the work in suggesting Python libraries, code routines, and a sensible web structure. I knew a little bit of Python, enough to check what it suggested and fill in the gaps, but don't like to imagine how long creating this site would have taken me without ChatGPT's assistance.
With the coding aspect streamlined, it only remained to write the actual LaTeX descriptions of the problems and add the remarks. Fortunately, this is something I quite enjoyed (and still do) - one of the aspects of being a mathematician I most enjoy is reading and digesting the work of great mathematicians.
Still, progress was slow, and at some point (probably when I decided to tackle the 1980 problem list of Erdős and Graham, which runs at over hundred pages, all of them densely packed with interesting number theory problems) I despaired of ever finishing the task ahead of me. At that point I had done just over 100 problems, and clearly there were many more hundreds ahead. I was embarrassed at the thought of putting out such an obviously incomplete list - moreover, one in which I was surely missing many important references that I 'should' have been aware of.
As Voltaire wrote, however, "Perfect is the enemy of good". It was far better to just start the site, however incomplete and flawed, and invite contributions from other mathematicians, slowly building the list and filling in the gaps as time went on. Similarly, I decided not to spend too long investigating any one particular problem, especially those problems which were obscure and outside my usual area (although I did always make an attempt). In an ideal world I would have spent hours on a literature search for each one, but then progress would have been much slower. Furthermore, I hoped (as has often been the case) that what would have been a lengthy fruitless search for me would be an instant comment from another, more well-informed, mathematician. I am immensely grateful to all those who have helped build this site and fill in the gaps with their expertise.
For a couple of years the site slowly grew, and became a useful resource - certainly for myself, and I believe also for others. Adding to the site itself was always a pleasurable procrastination, forcing me to explore some avenues that I would never have normally gone down. As I had hoped, many of the more obscure problems received a new lease of life, sometimes including published solutions and papers.
Part of my initial vision, which is slowly coming into shape, is that modern day mathematics, often using techniques unknown by Erdős, could clear up many of these more obscure problems. We will then be left with a core of interesting, difficult, problems, which can serve to demonstrate the limits of our knowledge.
In August 2025 I finally got around to adding a comment feature to the site, which has been a very successful experiment, allowing people to discuss problems and exchange ideas. This is especially exciting for me, since as a graduate student I used to take great pleasure in following the various Polymath threads (e.g. on Gowers' blog posts), and seeing the raw stuff of mathematics take shape in real time. I wanted to make another venue on the internet for such discussions to happen (albeit on a smaller scale), and am grateful to all those who have been so open and generous with sharing their thoughts. I think (I hope) that we have created a friendly community, and fostered many new collaborations.
With the recent attention from the AI community, the site is more popular than ever. In the last week we've received over 150,000 unique visitors (as in over 150,000 distinct human beings have visited the site at least one in the last week). There are over 3,400 comments on the site, and over 500 registered users.
The arrival of AI
Soon after the forum was added, around October 2025, AI tools started to become useful for this site (on the mathematical side - as mentioned above from a coding perspective they were useful from day one). At first this was as a super-powered literature search, turning up many previously unknown solutions and papers. In the last month we have started to see actual solutions generated by AI. Whether or not these are truly novel solutions can be murky - often a subsequent literature search finds the AI proof, or at least significant elements, scattered around other papers. The AI contributions wiki attempts to track AI solutions and to what extent they are novel.
These question 'is this solution new?' is ill-defined, and it is often hard to pin down whether a solution is 'new' - this is nothing unique to AI in particular, as similar discussions could be had over many human proofs and papers (although I suspect rarely has so potential economic value hinged on this philosophical question).
What is undeniable, however, is that these AI tools are now invaluable as a tool in finding solutions to some of the problems on this site (where I am taking advantage of an ambiguity in the use of the word 'find'). Plucking the low-hanging fruit is rapidly becoming an automated process. Time will tell how long before AI is able to help with some of the truly hard problems, and what the balance between human and AI researchers will be in such investigations.
The future
I am forever amazed by the breadth and depth of Erdős' questions.
For sure, recalling the quote of Erdős from the front page, some of them are certainly 'marshmallows', and turn out to be quite simple, even trivial, to prove. I do not think this would have bothered Erdős, and it is only a shame that he is no longer present to fire back 'Aha, yes of course. Now what about...?'
Many of the questions, on the other hand, are 'acorns' from which mighty oaks, or sometimes entire forests, have grown. Yet others appear small, but are merely acorns yet to sprout (or perhaps closer to Grothendieck's walnuts), and from them will one day grow marvels we have not yet dreamt of.
It has been a privilege to help raise awareness of this remarkable mathematician and the questions he asked. Every day I check on the site with anticipation, eager to learn about new (or sometimes old) ideas and mathematics. Who knows how things will look a year from now, and which problems will have been solved.
What I am sure of is, as long as mathematics is being done, the problems of Erdős will play a role, guiding and challenging researchers. To quote the man himself: "New ideas will be needed, which can, in turn, lead to more general results, and naturally, to further new problems. In this way, the cycle of life in mathematics continues forever."
Order by
oldest first or
newest first. (The most recent comments are highlighted in a red border.)
Thomas,
I love this idea. AI tools were instrumental in my use of sieve tools to reducing Erdős Problem #218 to showing that each strict inequality dn+1>dn and dn+1<dn has density 1/2 (so still open but reduced to a well known conditional)
I wrote an essay this past weekend on X about my own math and AI journey (Terry Tao’s recent Math Inc interview was a big inspiration). Length precluded my including the use of AI on #218; nevertheless, I hoped to lay out some important guidelines for non-professionals like myself to flip their findings “over the fence” for professionals to consider in a way that is respectful of the latter’s time and attention.
Hi Thomas — thanks for adding the blog feature, this is a great idea.
I’d be very interested in contributing a post. In particular, I could write a deep dive on an Erdős problem (likely the Sunflower Conjecture), focusing on why the problem is natural, why it’s difficult, and how different partial results and perspectives fit together, rather than on any single claimed breakthrough.
I’d aim for an informal but mathematically serious exposition, accessible to graduate students and problem solvers, and aligned with the kinds of survey/deep-dive posts you describe.
Separately (and only if useful), I’d also be happy to help think about or prototype a lightweight evaluation or review workflow for incoming blog posts — e.g. something that keeps standards clear without adding overhead. If that’s of interest, I’d be glad to submit a pull request or discuss ideas, but no pressure at all.
Thanks for the offer, but I will be keeping the process of moderating this blog old-school, and focusing on a small number of high-quality submissions from trusted site users (or other known mathematicians).
Thanks for clarifying — that makes sense. I appreciate the care you’re taking with curation, and I’m looking forward to reading the posts that come out of it.
Thank you for building such an amazing resource and making the future feel fun. Ever since my Dad encouraged me to read and finally re-read and understand Gödel Escher Bach I've dreamed of a more open community to problem solve at scale. I do worry what the next generation will do if math is "solved" by the time they are in middle school, but sure is an exciting time to be alive when we can all participate on the frontier still, and for that I am grateful.
I am in fact amazed that the comment sections here are active. This seems difficult to achieve for specialized (non-social-media) forums like this.
Regarding AI, we don't need to give it attention or avoid it in particular. As you have written, we should proceed normally and don't particularly treat it as "unique". If AI is helpful, it should be so naturally, not by trying to advocate for it in particular. Same with the other direction.
In fact I like to think that *because* the site is so well organized, it becomes *easy* to test AI on it, which is part of why the attention is here now.
Regarding mathematics, I like that Erdos liked to propose problems that are intuitive and well-motivated, though some are easy and some do require sophisticated machinery. It makes it easy to see *why* the machinery matters; this is sometimes the bane of when one studies higher mathematics and couldn't "see" the purpose.
I believe that everything has a purpose and happens naturally, whether in math, AI, or what is happening here in the forum. Things are just how they're meant to be. Cheers!
All comments are the responsibility of the user. Comments appearing on this page are not verified for correctness. Please keep posts mathematical and on topic.
