Too old to get another math PhD degree? I got my math PhD degree more than 10 years ago, and my major is algebra. I have published some papers in some journals such as Adv. Math.. I really love math, but I am still thinking I haven't got a good and complete math education, and do not have a good picture of math. Someone may argue that I can teach math to myself. The problem is that I am a teather in a university now; I have to teach a lot of classes and have other duties. Now I have an idea which sounds crazy: I want to do another math PhD. But the problem is I am  almost 40 years old. So I am wondering if this is possible. Does someone have experience of such a second PhD?
The question is really strange. As a university professor you can attend other professor's courses, in addition to self-education. If the time and duties is the main problem, you can take an unpayed leave, or buy out some courses. There are many ways of reducing your duties and obtaining some extra time for self-study,
by sacrificing some of your salary. Given the ratio of professor's salary to the graduate student support (at least in the US) you will be still better off than by switching to a graduate school. Let me add that in most US departments graduate students have the same teaching load as professors, sometimes more.

Speaking of the age, this is not a obstacle: I have at least one friend who enrolled to PhD after 40 (having a master degree before and working as a high school teacher), and he publishes first-class results.