Many of the other stackexchange sites enable a festive wintertime custom every year in late December, the Winter Bash, in which user profiles are accommodated with fanciful hats, earned for various accomplishments on the site, something like badges, except that they are temporary and often whimsi...

I have noticed a link on my Mathoverflow page linking a webpage that explains an event called Winter bash. I have earned already earned some hat which I am using on different stack exchange communities. My question is: Can I also wear my hat on MathOverflow? If so, how do I do it?

I noticed that the Stackexchange sites are having a Winter Bash, and one of my friends recieved a hat on MSE. Why isn't this on MO? It'll be fun to have something like that here, wouldn't it? (I suspect this is because MO doesn't have a ".stackexchange.com" in its address, but I could be wrong.)

As the idea of an absolute geometry over the field with one element $\mathbb{F}_1$ becomes more clear, two approaches seem to have crystallized, being based on different assumptions and going into different directions: on the one hand, there is Borger's, which interprets an $\mathbb{F}_1$-algebra...

Can someone kindly confirm whether the ultrafilter lemma for arbitrary (i.e., not necessarily Boolean) bounded lattices is equivalent to Zorn's lemma? To be precise, if $\mathbf{L} = (L, \leq, \land, \lor, 0, 1)$ is a bounded lattice, then an $\mathbf{L}$-filter is a non-empty subset $F \subseteq...

The Sylvester problem: see https://en.wikipedia.org/wiki/Sylvester%E2%80%93Gallai_theorem A finite set of plane points has the property that any line through two of them passes through a third point from the set. Then the points are collinear. This claim was posed as a problem by J. J. Sylvest...