Problems or conjectures posed (either individually or jointly with others) by the great mathematician Paul Erdős who posed many challenging questions that have served as a benchmark of progress in many diverse fields of mathematics, particularly combinatorics and number theory.

This website was made by Thomas Bloom, a mathematician who likes to think about the problems Erdős posed. Technical assistance with setting up the code for the website was provided by ChatGPT and the logo was made by Midjourney. Since this website was launched, many people have helped with spotting typos and pointing to updated references, or suggesting new problems. These people are credited individually under each relevant problem.

Some people have contributed a huge amount to the website, in comments, suggestions, corrections, and without them this website would not be what it is today - a special thank you to Sarosh Adenwalla, Boris Alexeev, Stijn Cambie, Zachary Chase, Dogmachine, Zach Hunter, Vjeksolav Kovač, Mehtaab Sawhney, Mark Sellke, Stefan Steinerberger, Terence Tao, Wouter van Doorn, and Desmond Weisenberg.

Some from Erdős himself, in the discussion surrounding the problem in a problem list he wrote. I have sometimes expanded this by including updated references and also other remarks. If you're interested in any particular problem, I encourage you to go and look at the original problem descriptions by Erdős (sources in the bottom left of the problem box), which often contain more information than I have chosen to display here, and to do a literature search - while I'm trying to make sure the site records the current state of the art, this is a work in progress!

Often I found the way Erdős stated a problem to be hard to understand or unnecessarily verbose. I have sometimes taken the liberty of changing the statement into what is (in my opinion) the most elegant/easiest to parse version. If you think that I have accidentally changed the actual content of the problem, please let me know.

No, but that is the eventual goal. If you have an update on the status of any problem, please leave a comment below the problem or email me at [email protected].

If you are interested in any problem I encourage you to go and search around in the first instance, to discover what has been done and if it has been solved. Do not assume that an 'unsolved' problem is in fact unsolved, and do your own literature search before investing significant effort into finding a solution.

The best way to do this is to add a comment under the problem. You can also send an email to [email protected] (including the change and the problem id).

Definitely not, adding these is a work in progress, and the hope is that this website will become more comprehensive over time. If you'd like to speed up this process, you can send in new Erdős problems yourself to [email protected] - it'll appear faster if you can include the source and a complete LaTex markup of the problem (with no macros!).

I also don't plan to include every open problem that Erdős ever posed; he was very prolific and wrote over 1500 papers, many of which had open problems, and wrote many letters. My (personal and subjective) aim is to include all of the interesting Erdős problems. For example, sufficient (but not necessary) conditions for a problem being included are Erdős including it on a standalone published list of problems, or being on record as offering a monetary value for its solution. A usually necessary (but not sufficient) condition is that the problem be reasonably understandable and interesting as a stand-alone statement (e.g. stating at the end of a long technical lemma in a long technical paper 'can this be improved?' does not count).

There are also some problems on this website which are not originally due to Erdős, but were problems liked and repeated by him. In such cases the original author of the problem is credited in the commentary.

Erdős often attached prizes to his problems. Often this is a reasonable measure of how interesting/difficult Erdős thought the problem was. He was not always consistent with the value of the prizes - where there is ambiguity I have chosen to show the highest prize value that Erdős is on record as offering for that problem.

No.

Erdős prizes are now awarded by the Combinatorics Foundation, administered by Steve Butler. Prizes will only be awarded after the publication of a solution in a reputable journal, with accompanying documentation verifying that Erdős offered that amount. If you are eligible to be awarded a prize, you should contact Steve Butler directly. The owner of this website has no involvement with, or influence over, the distribution of these prizes.

Leave a comment in the appropriate thread on the forum or email [email protected].