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  1.  
    On the main mathoverflow page, there are tabs "hot" and "active".

    If you let your mouse hang over those buttons, little descriptions come up.

    Hot - "questions with the most activity and interest within the last few days"

    Active - "questions that have been asked, answered or updated recently".

    I find the blurbs don't match up with reality.

    Q: What is the algorithm to decide the rankings on the "hot" and "active" pages?

    I find the "active" page to be reasonably useful. But the "hot" page gives me a listing of questions that have few votes, and no answers. If anything the "hot" page should be called the "inactive" page.
  2.  

    You can find the formula on meta.SO. I always look at the active tab instead of the hot tab, so I don't have a strong opinion about how the hot algorithm should work.