I am wondering if having much knowledge in other (seemingly not directly related) branches of mathematics is helpful to a mathematician in his own research. Say there are two algebraic topologists A and B. A also has some knowledge in PDE (say he knows the basics of graduate level PDE well and can even teach a graduate course on PDE) and B does not even know the very basics of ODE. Does this make any difference in their ability in doing research in algebraic topology?
I know that some fields are somehow related; for example, it will help a group theorist if he knows algebraic topology or number theory; but how about other fields that are not apparently related, such as the example that I have quoted?