A question

Hey /prog/, i have a question, why do programmers need to know a lot of maths, calculus and lineal algebra?

Math doesn't help you write code.  Math can help you analyze code and figure out what you want to write in the first place.

Matrix math and trig are crucially important in graphics and simulations.

You will never implement calculus (the study of continuous values) in software.  All computing approaches tend to be iterative, which brings about its own field of study.