I am an undergraduate studying mathematics and one of my interests include complexity and computability theory. I have no experience in programming. The computability theory books I looked into didn't seem to require the need to learn a computer language however books on algorithms always do. My question if I want to learn more about this field do I have to know programming languages or can I learn the topic from a purely theoretical perspective? And if programming languages are required to explore complexity and computablility, which would you in your experience say are the languages that would be best to invest in at an earlier stage of my education? Thank you.
If you want to learn about algorithms, it is a very good idea to learn programming. It always helped me to understand the algorithms, if I also programmed them. And if you are good with understanding algorithms, programming will not be very hard.
As programming languages i recommend python and C/C++