Mathematics topics or fields that increase computer programming proficiency?
So, there are many fields of math that are relevant to the Science of CS, but for programming specifically:


Graph theory: this is the big one. Graphs and trees are everywhere. Networks, maps, paths in video games. Even things like solving a Rubiks cube can be modelled as a graph algorithm and solved with A*.
Discrete math: aside from graph theory, knowing this area in general is helpful. It's full of proofs by induction, which are very useful for understanding recursion, which is very useful in programming, particularly with data structures. Knowing about sets, counting, inclusion-exclusion, boolean logic, etc. can come in handy once in a while.
Type theory: unsurprisingly, knowing type theory helps with understanding programming in typed languages, and more broadly, with using types as a way of ensuring certain correctness properties. Knowing about the theory of subtyping helps you to understand covariance and contravariance in Java-like languages. Knowing about things like parametric polymorphism is obviously helpful when learning a type-heavy language like Haskell or Purescript, but langauges like Scala, TypeScript, and Rust are becoming more prevalent in industry, and types are at their cores.

If you take this one to its extreme, you get things like Coq and Agda and Idris, which can be used to prove extremely precise correctness properties about programs.
Computability and Complexity Theory: knowing when a problem is either unsolvable, or NP-hard, is useful, because you won't waste hours racking your brain for a fast way to do it. Likewise, knowing some of the theory behind approximation algorithms, fixed-parameter tractability, or low-base exponential algorithms, can help when you really need to solve an NP-hard problem.
Automata theory: many problems can be modelled with various state machines, so understanding their properties is useful.


There are also some field-specific areas:


Statistics: If you're doing machine learning or big-data, this is a must.
Linear algebra/vector calc: both of these are important for machine learning, graphics, simulations, or image/audio processing.
Lattice theory: if you're doing any work with compilers or program optimization, this one comes up all the time. Fixed points everywhere!
Category theory: not needed to code, but useful for anything deeply drenched in type theory.


Edit: can't believe I forgot:


Cryptography: if you're interested in security, hashing, digital signatures and such, then make sure to learn some number theory, Group Theory, Field theory, elliptical curve Theory, etc.