In my work, I use lots of different math software. Other people frequently ask me what programs I use, so I've created this page. There are many math software packages out there; there are just the ones that I use personally or thought were otherwise notable. Since I almost exclusively use Linux, the default assumption is that these programs run on Linux and are free (open-source). Programs running on other platforms or with other constraints are listed in parentheses.
Writing Mathematics
TeX is of course the premier system for typesetting mathematics and other technical information. I personally use the variant LaTeX. TeX distributions include TeXLive and MiKTeX (Win).
Additional packages for TeX can be obtained on CTAN.
I use the LaTeX class beamer with the font package arev for presentations.
PDF utilities (very useful for preparing grant proposals for NSF Fastlane): pdftk (command-line utility to split, join, watermark, etc PDF files), GUI for PDFTK, PDFTK Builder (GUI, Win).
Computational Programs
Sage provides a common interface to several math programs, including Maxima, axiom, and GAP. The interface includes both a web user interface and a programming interface via Python.
Other computer algebra systems: yacas, Maxima, and axiom. TeXmacs can be used as a graphical front-end to each of these programs. Slick!