1) If your programming is related to some engineering project, some kind of calculations, modelling some real world events, etc. then handling symbolic stuff and being able to go from them to working code would be an ovbious advantage.
Or if you want to develop new algorithms and data structures
then mathematics and symbolic analysis are going to be useful for you.
However, the world of programming is so diverse that you can spend decades without seeing any math at all. Think about building a web based content management system, think about programming a commuminty message board, routine SQL programming, etc.
2) It depends. Just like the first question, the important thing is which field of programming you are working in. If you are into the algorithm development, doing theoretical work, building some security protocol, cryptography, etc. then formal CS education can be the right place to start. But never forget that there are thousands of programmers who don't have any formal education in CS. Maybe the problem is with the meaning of the word "programming", it is too wide! :) I'm doing very high level web programming, Linus Torvalds is doing very low level multitasking, multiuser operating system programming. We are both programming, but are we doing the same thing?
3) Well you must change the question: Are there languages who are more friendly to the mathematically inclined? ;-) I don't think well known, procedural (imperative) programming languages look like "mathematical".
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