The tough part here is "every programmer should know" as there are very few universal "Must Knows". Much of CS theory is math so there is a lot to be said for "You're learning Math whether you think so or not."

Some general comments on math topics:

Partial Differential Equations - Useful for financial technology and engineering applications.

Statistics - Extremely useful in financial technology and marketing applications. (A/B testing, etc) Also good for having an informed worldview.

Regression Analysis - Same as Statistics, though less important for having an informed worldview.

Logic - Whether you call it Philosophy or Math, it's useful in hardware, formal verification, and general thinking.

Linear Algebra - Good for financial technology and machine learning.

Set Theory - Good for understanding databases.

Number Theory - Useful for cryptography.

Graph Theory - Great for networking, and algorithm thinking in general.

Theory of Functions - Good for understanding recursion (LISP, Scheme, etc) and functional programming.

Does anyone need to know all of this? No, but learning the math behind whatever niche you choose will make your intuition and thinking stronger. I think Stats is the only general purpose math that everyone should understand as part of being a critical thinker.