Proposal: change the default home page tab of Math.SE from active to interesting.
Explanation and Rationale. Math.SE is the second most active SE site by the number of questions per day, behind StackOverflow. It is therefore reasonable for it to adapt some of the features introduced by StackOverflow to help the users efficiently navigate the list of questions. Back in 2010, Jeff Atwood wrote:
The default question ordering on the home page is a simple, flat list of the most recent (n) questions sorted by activity date — where activity is defined as a new answer, an edit, or a new question. Sophisticated, it ain’t, but it has worked well for us up to a certain volume of activity. Stack Overflow is now well beyond that volume.
I get the impression that Math.SE is growing beyond that volume too (which, by the way, I do not consider a bad thing). The quote continues:
On Stack Overflow (and only Stack Overflow) the default home page tab has changed from active to interesting. The goal is no longer to show you a simple flat list of the last (n) active questions — that’s not even possible any more based on sheer question volume — but, instead, to narrow the list to a subset of active questions that we think you will be interested in.
The algorithm that SE developers designed for this purpose is quite clever: besides the obvious things like favorite tags, it takes into account the user's pattern of answering question and some other things. (See the blog post for the full description.) Given the diverse interests of the Math.SE users, I think it would be beneficial to this site as well. It would not be hard to implement: the tab is already available as an undocumented link https://math.stackexchange.com/?tab=interesting ; all that needs to be done is a few changes in HTML markup of the homepage.