What is the hardest sub-field of Maths to get a PhD in? Topology/Geometry? Algebra? Statistics? Analysis? etc?
>>9159602
This is subjective, there is no objective answer. For one person it is logic, for another one it is Geometry etc.
There is a Gauss-quote: "Math is the Queen of Science and Number Theory is the Queen of Math.", if you are looking for the "best" topic.
>>9159602
Algebraic Geometry had insane requeriments and fields use A.G, don't worry about hard PhD worry about research.