alt Hacker NewsYou might be thinking of Euclid's axioms, which defines points, lines, planes, etc, and that lines can be parallel. This is an interesting one because the system is violated if your space is not flat, like if you're on a sphere.
You could also be thinking of Zermelo-Fraenknel set theory (ZF/ZFC), which most of modern mathematics is ultimately based upon.
This highlights I think what is an ultimate pitfall of something like Lean. It is something like this: when an assumption is broken or violated in mathematics, the whole field of mathematics can _grow_. Non-euclidean geometry, imaginary numbers, etc are all examples of this. Trying to cram maths into a programming language sounds like it would constrain it, removing the creativity and reducing all maths to a search space.