Favorite tools

• LaTeX: A requirement for writing mathematical material. Free versions available for any computer system.
• Emacs: An editor that can do so much that it defies description. It has specialized modes to support writing LaTeX (as well as for almost any other activity known to man).
• GNU/Linux: This has been a rock-solid operating system for years. (I switched to Linux when my computations for a consulting job repeatedly crashed under Windows. I have never ever crashed Linux.) All the great tools, including LaTeX and Emacs come free. Also, there are free replacements for MS Office, some of them better than the originals. The GUI has greatly improved in the last year.
• Mathematica: Symbolic math; plotting; programming environment. Mathematica is proprietary and a bit expensive but very useful for specialized applications. Maple is a reasonable alternative. Both run on a variety of platforms, including Linux.
• Scheme, a dialect of LISP, with minimal cognitive overhead and maximum power and expressivity. The language of the gods.