In discussion of mathematics PhD studies, a certain issue frequently arises which concerns the nature of pure mathematical research in general: (non)-interchangeability of PhD supervisors in mathematics.

Indeed university administrators (especially at the level of science and engineering faculties) appear to be surprised by claims that a particular PhD supervisor of a PhD student cannot be easily replaced in this role.

The administrators’ argument runs as follows.

“We need a supervisor for XX when ZZ is made redundant. I understand that the pure group here is very strong.

But I am told that there is nobody else who can supervise XX. Therefore the pure group is not as strong as I thought it was.

So perhaps we should review our support to it”.

The fallacy in this argument comes from the fact that the pure group is, on the whole, only as strong as the sum of its parts. Pure mathematicians work alone, or in groups of two or three at most, and not in large teams which, one can assume, is common in

experimental science and engineering departments. Each area of research within pure mathematics is highly technical and specialised, and it is impossible to enter another area quickly. The amount of background reading (which might involve going back 50 years—maths never goes out of date!) is just too large. This is even true at the level of supervising PhD students. When they apply here (or anywhere) they apply to the person, not the group, because they know roughly what they want to work in. Continue reading →