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I am wondering: what analogy can one construct for mathematics? I.e., what fields of mathematics are most difficult to find jobs? Obviously there must be fewer jobs in pure math than in applied math, but what pure math sub-fields have more scarcity of jobs? And is it harder to find a job in pure mathematics or in theoretical physics?

I've been accepted to a PhD program in theoretical physics and am happy to go, but if the job prospects end up looking especially poor for me I am thinking about changing to math after I get my master's degree in about two years. Would like to know what people think of this, as well (how hard it might be to switch to math after a MS in physics, and BS in both math/physics). Any thoughts?