I am a mathematics master's student. I intentionally decided to chose a thesis supervised by a PhD student with a non-mathematical, but pretty quantitative background, as the project is very interesting to me. The project involves a field A, a field that is very widely used/developped by engineers, mathematicians, physicists, computer scientists, etc.

I am currently trying to get up to speed in field A. Naturally I'm trying to study it in the "correct mathematically" way. However what I expected mathematically isn't reflected when I do simple experiments on a software implementation of field A. To me these inconsistencies perhaps show a lack of understanding of field A by me, and I probably shouldn't try to interpret the available data by using theories of field A yet.

I brought this up to my supervisor, and we "cleared up" the inconsistencies: he answered why the theory isn't holding up in the software. However I could also tell that these are pseudo-explanations a mathematician would give to non-mathematicians. In this case a mathematician told my supervisor so.

My dilemma is that what should I do now? If I try to explain these inconsistencies myself, it might take too much time, and I am already slightly behind schedule. Furthermore, my supervisor is clearly a very sharp person, he and his own supervisor published several important papers in their field. If they could work with partial understanding, I suppose I could to. After-all, this field A isn't necessarily what I was "contracted" for in the thesis.

Question: What should I do when a supervisor with non-mathematical background encourages me to hand-waive the math a bit (with good reason) whilst I have doubts about the hand-waiving.

As a side note it might take too much time to clear up the inconsistencies myself because I couldn't find a source that is mathematically-rigorous enough for every subtopic I need. I have to assemble bits and pieces from multiple notes & books and I'm struggling to maintain a coherent notes for myself. What I have is composed of small little detours explaning small peculiarities.

  • Would you describe your own field as pure math or applied? And I don't see a real question here. To avoid closure you should probably edit it to provide one.
    – Buffy
    Commented Nov 12, 2023 at 13:44
  • @Buffy My studies are mostly the theoretical aspects of applied math subjects. The thesis topic requires applied math techniques, but isn't in mathematics itself. Even considering it under computer science is a stretch I would say. I will make the question more explicit. Commented Nov 12, 2023 at 13:47
  • This may depend on what exactly you think are "inconsistencies". This may rather be a topic for another site like Mathematics Stack Exchange or maybe CrossValidated if Statistics is involved. Just one blind guess: There may be theory regarding a global optimum of some function but any existing algorithm can only deliver a local one. Sometimes there is no theory for the local one delivered by the algorithm but one would use that anyway as nothing better is available. This kind of "inconsistency" cannot (currently) be removed, although one can try to improve matters in "future work". Commented Nov 12, 2023 at 23:18

1 Answer 1


For pure math this would be an insupportable situation IMO. For applied math, the structure can be made to work if done with care.

However, and this is key (writing as a pure mathematician), hand waving is fine for simplified explanations of things that are known to be true with complete proofs available elsewhere, but not stated. Hand waving for things poorly understood or not yet proven is, again, insupportable. Things in math aren't "sort of" true. Inconsistencies need to be resolved.

If the validity of the thesis depends on some math, then you need to know that the math holds up. If the presentation of the thesis depends on only generally following the mathematical arguments then a bit of hand waving, probably with references to complete treatments, is possible and will probably be appreciated by readers.

But if your "supervisor" is sloppy about the math, take care (i.e. TAKE CARE). You need to know that what you say is valid even if you give "popularized" explanations.

I'd worry less about crossing fields. Math and CS have interesting intersections. Note also that if you are relying on statistics (rather than math) that things can, in fact, be "sort of" true; true in general but not necessarily in a particular case.

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