NB: I'm only speaking about the math doctorate as it currently stands in the United States. Due to the current market saturation of math doctorates, any pure m

NB: I'm only speaking about the math doctorate as it currently stands in the United States. Due to the current market saturation of math doctorates, any pure mathematics PhD worth the paper its printed on will also probably come with a non-trivial publication record. The exceptions I can think of are high-risk high-reward areas like cutting-edge number theory (I had a friend go eight years without publishing, which, yikes, but his thesis was semi-revolutionary (or so I'm told)) or, I guess, suitably abstract category theory (though the people I follow in this area seem to publish lots of interesting papers, like the Baez school or the homotopy type theory people; your mileage may vary). It's really too bad. One wonders why we can't simply ax the entire advisor-candidate system (with all its myriad opportunities for physical, emotional, and even sexual abuse) and certify new candidates by saying: "You're a doctor of mathematics when you get five professors to sign off on 3-5 papers you've had published."