Is there any particular date when math postdoc results are typically announced?

I believe that in math the first round of postdoc offers usually go out shortly after the NSF announces who will be receiving NSF postdocs. This usually happens in late January. After that, offers tend to go out when (or if) previous offers were declined.

Here at U. Michigan, our first round of offers went out in mid-January. As those offers got declined, we have made offers to replace them, trickling out a few at a time. Many of our first round offers have now learned that they received NSF postdocs's somewhere else, so we made several offers following the NSF announcement. Our first offers had a deadline of February 3, in accord with the uniform deadline. After Feb 3, we will most likely get more declines and make more offers. We aren't sending out rejections because it is possible that this process may go on for a long time, but most likely it will end sometime in February.

Contrary to what other answers say, we started two weeks before the NSF made their announcements, and many of our offers did not involve prior telephone contacts. I think our actions are typical of a large University.

Seems most positions should have a shortlist for interview within this week (probably 1 week before the NSF announcement and 2 weeks before the Coordinance). You should send an email to each position you are interested in to ask for the progress. At least half of them will give you a clear answer and for the rest, you should never think about them again.