tl;dr- Philosophy departments don't tend to focus on math much, and Philosophy students have a mathematical proficiency much closer to an Art major's than to an Engineering major's. This answer doesn't comment on formal logic.
Lack of math in Philosophy departments
You normally don't need much math to do well in a Philosophy department's graduate program.
For evidence, we can look at standardized test scores to see what students going into different fields tend to be proficient in. In these GRE scores by discipline, we can see that students planning to do Philosophy in grad school rank only somewhat better in Quantitative Reasoning than other Arts and Humanities students, but much worse than Engineering, Physical Sciences, and Economics students.
You might be able to do math in a Philosophy department
I'm not aware of any hard rule stating that you can't do something math-related in a Philosophy grad program. For an example, "Historical Development of the BFGS Secant Method and Its Characterization Properties" (2009) by Joanna Papakonstantinou is a great read. The author published this as their dissertation for a Ph.D. in Philosophy from Rice University.
The caveat here is that their advisory committee doesn't list anyone from the Philosophy department, so presumably they worked with people from other fields. Presumably if you want to do something Math-related in a Philosophy department, you may have to reach out to advisors from others fields to support you, as the Philosophy department's professors are unlikely to have enough background knowledge to evaluate your work.
But if you want to do math, why in a Philosophy department?
Part of the lack of mathematics in Philosophy may just be a definition thing. This is, "philosophy" may be the general field of knowledge, but "Philosophy" in the sense of "what Philosophy departments focus on" is a far narrower topic.
If you want to do something like hardcore math, you can - just, you'd probably prefer a Math Ph.D. program, which is likely to give you a better background and a more valuable degree. You can even do a math-heavy Ph.D. in fields like Engineering, Physical Science, or Economics if you focus on advancing the understanding of a type of math that's relevant to those fields.
For example, you may not usually think of a Business department as a place where math's advanced, right? But Business departments are really interested in Big Data and data science. So, it shouldn't be too hard a sell to get a Ph.D. in some sort of Business-related field, then just spend your whole time doing math or data analysis, as long as you somehow refer it back to some sort of practical business interest. That's the beauty of grad school!
Addendum: Philosophy students scored well on the rest of the GRE
Above, I'd noted that Philosophy students didn't score very well on Quantitative Reasoning, as that's relevant to the question. Looking back at it, I wanted to note that this may belie an interesting tidbit...
Despite middling performance in Quantitative Reasoning, Philosophy students achieved the highest scores across all disciplines on the other two sections of the GRE, i.e. Verbal Reasoning and Analytical Writing.
