>>13417597There are quite many subfields actually but I'll try to name a few larger ones and give a quick description what they roughly deal with that is understable by a layperson
>Number theoryDeals with prime numbers and how they are distributed. And also with equations involving integers. For example one open question that recent research is concerned about: They're many prime numbers whose difference is two, for example 3 and 5, 5 and 7, 11 and 13, 17 and 19 and so on. The question is are they're infinitely many such primes?
>Linear algebraThere isn't really that much research anymore in linear algebra but it is fundamentally important for many other fields. You know these kinda meme pictures where they're several equations with fruits? These are (most of the time) linear equations and linear algebra deals with them and how to solve them.
>AnalysisThis is quite broad but in essence it deals (mostly) with functions that are important because they can describe physical processes. (This doesn't quite do it justice but that's the main historical motivation)
>geometryA vast field, but well you probably already could've guessed that its main focus are geometric objects. There are many subfields which study different kinds of objects
>topologyOften dubbed "rubber band geometry". You also study geometric objects but you basically ask different questions and as a result there are many things that you don't care about like angles, size and curvature. So you imagine you can just deform your objects like they're made of rubber
>probability theoryIs about probabilities
These categories are very broad. In fact many people in some subfields may not understand what other people in other subfields are really doing even if they both do for example geometry. For all fields there are also "numerical versions" where you try to find efficient algorithms to problems in your field, so a computer can compute it. There are also many more fields
