TITLE: How important is programming for mathematicians?
QUESTION [47 upvotes]: I'm a freshman student in mathematics, and I'm considering whether or not to take a programming course. How important is programming for mathematicians? Do working mathematicians use programs to aid their research?

REPLY [4 votes]: I have a Ph.D. in mathematics and I did two postdocs and worked as an assistant professor for five years in which I spent much of my time on research. I currently work as a software developer.
It depends completely on the type of math you are interested in. If you are interested in pure mathematics as opposed to applied mathematics the answer is generally that a programming language is worth much less than another semester of math under your belt. Proofs are the only gold standard in that area and computers rarely furnish them. Read the abstracts of papers for the top math (pure) journals in just about any given month and you can verify this for yourself. 
The applied mathematicians I knew seemed to make more use of a computer, but it still depended wildly on the specific area of applied math they were interested in. Some areas of applied math seem to have researchers who really primarily do proofs and hence probably made little use of software themselves. Others were very interested in computer simulations of specific examples.
On the other hand it is by no means uncommon for people who major in mathematics to eventually find themselves doing professional software development. Given the number of math doctorates compared to the number of CS students, I am surprised often I have run into another math doctorate lurking among the software engineers. It's not bad to have programming as a fail-safe in case you don't end up in a job that is actually doing mathematics for a living. Though honestly a single course is unlikely to land you a software job.