[tetron]

This is my take as well. The unreasonable effectiveness of mathematics to describe physics suggests it is more fundamental than something our monkey brains came up with. If aliens are operating with the same physics, they are going to create a mathematics that is isomorphic to our own.

[magusdei]

Isomorphism != equality. Formulas in greek numerals are trivially isomorphic to ones using arabic numerals, because they are different representations of the "same" concepts, but nobody would argue that arabic numerals aren't more practical (at least for us).[1] So even though the concepts the aliens come up with might be technically isomorphic to (a version of) lambda calculus on some extremely abstract level, there is no guarantee that either we or they would be able to recognize this, owing to a vast difference in representation.

[1] Similarly, a basic theorem in algorithmic information theory states that all programming languages are about equally efficient in terms of program size,[2] but that doesn't mean that all programming languages are actually equally good for every problem in practice, as the constant debates about "the best language" among programmers clearly show.

[2] The basic argument is that, if programs written in language A are vastly shorter than those written in language B, it is possible to write an interpreter for language A in language B of constant length c. So all programs written in language B are at most c chars longer than those written in language A.