What do you need to know to write your own synthesizer?

Question

Programming

There was an interest in the synthesis of sound. What materials can be studied to understand sound synthesis/programming? Where to begin?

Answer 1

I think it's worth starting with the basics of "what is sound". Then understand what is a harmonic series, etc. Then slowly look towards the school "trigonometric arithmetic". Then read literature about synthesizers and modulation.
Perhaps after that - a little about Fourier transforms. Maybe not ...
ps you can cross out the familiar from the list