5th - Applied math (meaning numerical analysis and other type of number crunching) - the smarter the better, but it's absolutely possible to complete a good PhD by dint of perseverance and hard work even without brilliant insights


4th - Pure but not very abstract fields (Partial Differential Equations / Combinatorics / etc) - depending on the topic these might involve some clever tricks but largely the use of duly adapted well-known techniques


3rd - Most mainstream pure math (Differential Geometry / Dynamical Systems / Probability / Analytical Number Theory) - nobody gets far proving fairly abstract theorems without a respectable amount of mathematical talent


2nd - Logic and especially abstract math (Algebraic and Arithmetic Geometry / Algebraic Topology / Logic): you have to be pretty damn smart to make relevant original contributions in these fields


1st - Extremely difficult fields (Langlands Program / String Theory / Derived Algebraic Geometry) - Don't come near these if you're not absolutely brilliant (and then some)

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