The system of mathematics that we have is a deeply interconnected web, where theorems from very different fields come together in weird ways. For example, you can solve the stolen necklace problem (fairly cutting up a necklace with different types of gems) with the Borsuk-Ulam theorem (topology) by using a hypersphere.
I was thinking mostly of this type of highly abstract maths; we're doing maths to have more maths, while the aliens are doing the maths that they need. As a result, we have a greater understanding of the underlying concepts (see: group theory and the monster), which is rarely useful (for example, we could invent a faster algorithm for doing something, such as the Fast Fourier Transform).
In short, the aliens would still have complex numbers (see Schrodinger equation, for example), advanced calculus and the like. But, of course, one of the best things about r/WritingPrompts is that the prompts can be interpreted in very different ways.
Mabi19_ OP t1_iwyhzbf wrote
Reply to comment by couldathrowaway in [WP] "The new species call themselves 'humans', and while their intelligence is on the low end when it comes to interstellar civilisations, their pure mathematical knowledge is far superior to the entire galactic community's." by Mabi19_
Magic is not what I expected, but this is great.