>>11354338>deep Containing many theorems on which many others are proven. This typically extends to other fields as well. No, I’m not trivially talking about set theory or univalent foundations which are necessary to address how we write in the first place, but results that are common in the math canon that we use all the time. For example, we have generalized heine-borel in analysis
>cute Nontrivial facts fall out of simple yet novel ways to look at old theorems. In a basic analysis, you would go through continuity arguments to prove IVT, whereas in a topology class, it’s almost a direct consequence of connectedness. The latter is cute.
>intuitive Many proofs in courses from complex analysis make direct appeal to the structure of the elements of the plane rather than more contrived methods. Now, I enjoy stretching my reasoning when working over fields like the reals, but there’s no denying the complex numbers play way nicer given how a lot seems to pop out from their construction.
>natural Many methods you use when reasoning over complex numbers come up when doing new problems. Similarly, even arithmetic over the complex field is so easy, especially when considering polar form
