The question is self-explanatory, but I want to make some remarks in order to prevent the responses from going off into undesirable directions. It seems that every few years I hear someone ask this question; it seems to hold a perennial fascination for research mathematicians, just as quests for ...

In 2002, the discovery of the AKS algorithm proved that it is possible to determine whether an integer is prime in polynomial time deterministically. However, it is still not known whether there is an algorithm for factoring an integer in polynomial time. To me, this is the most counter-intuitive...

The subject of this discussion are questions on "open problems" on MO. There is an existing policy on "open problems" reproduced from the (old) FAQs, which involves an open-problem tag. The motivation for starting this discussion are comments on said post, various users have expressed concerns r...

Due to several discussions on the main site, I am asking this question concerning the best practices for tagging questions on MathOverflow. Unfortunately, the relevant documentation page https://mathoverflow.net/help/tagging does not answer the following questions (except partially questions numb...