[dane-pgp]

Any species would face a selective pressure towards theorems which help them understand the world around them (if they have any motivation to prove theorems at all), and they will similarly face a pressure towards choosing the smallest/simplest set of axioms which allows all those theorems to be proven (and new ones to be discovered).

In fact, if we assume that neural networks are the only sorts of intelligence that can occur naturally in the universe and be sophisticated enough for arbitrary abstract calculation[0], then we might be able to infer things about the sorts of concepts they will develop and in what order. For example, having the concept of finite sums would likely occur before having the concept of infinite sums.

[0] I know that cellular automata can emulate a universal Turing machine, but I can't imagine a situation existing in nature where the cells evolve into an arrangement that produces a Turing machine, much less a machine running a program of instructions that lead to it generating mathematical theorems.