As a math major that makes me worry a little bit.
How tiny is the fraction?
How tiny is the fraction?
This was Rutgers - at Princeton, the ratio would be a bit better, at NJIT it would be worse. Don't even ask about podunk state.
It's a shitty career path. Unless you are fantastically good, don't waste your time.
[1] My adviser told me I could have been on the tenure track if I wanted to. Since I didn't put it to the test by applying for such jobs, I won't claim it as true.
Every other course will just give you a better chance of getting a job, and help you perform better once you get there. A math grad can solve all kinds of problems that other people will just shrug their shoulders at. That's always useful.
Academia in general is a dangerous career path though. Too many people on the ground floor (i.e. every undergrad who can't think of a better thing than grad school), too much glamor keeping them there, very bureaucratic organizations, and a complete mismatch between work (research) and funding (students).
I don't suppose physics would be any better?
Putnam is less relevant than original research.