I agree with the idea to study mathematics, as a useful exercise, that would in many cases benefit programmers by giving them a good mental workout, and hopefully reinforce if not expand their understanding of mathematics, logic, and reasoning.
Beyond that I would argue for the study of writing, in a natural (human-oriented) language of your choice.
Programming as a profession, and as an art, is about the meaningful expression of ideas; in a detailed, unambiguous manner that can be processed by a computer. Programming languages are tiny, simplistic, and restrictive in their ability to express ideas, and the execution of these ideas. Writing in a natural language is much more complex, particularly when you strive to remove undesired ambiguity*. The other issue is that as a professional, programming is not done in isolation. Even if you are an independent contractors, you must be able to communicate effectively with clients and users.
*) Ambiguity can be desirable in humor and poetry.
I think that any programmer can benefit from the abilities to make logically sound, comprehensible arguments in a written document; that these abilities will make them better in their ability to understand, and be understood by users, customers, or colleagues.
The argument has been made in the past by Steven C. McConnell in Code Complete, in The Pragmatic Programmer by Andrew Hunt and David Thomas, Coding Horror by Jeff Atwood, and Joel Spolsky (of Joel on Software) in his Introduction to Best Software Writing I and College Advice. And like tons of other software developers, and their managers; repeatedly.
You see, communication is the only really important aspect of software development that people really have trouble with. The rest are details and small bugs, but for really big screw-ups you need miscommunication (or greed)