Known users from DebianScience listed in parenthesis. See also ?EducationMathematics.
Mathematics tools already packaged in Debian
Computer Algebra Systems
See DebianScience/ComputerAlgebraSystems for a comparison of some of these.
Categories from http://axiom-wiki.newsynthesis.org/RosettaStone
General purpose
yacas Computer Algebra System. Yacas is a small and highly flexible computer algebra language. The syntax is very close to Mathematica. The distribution contains a small library of mathematical functions, but its real strength is in the language in which you can easily write your own symbolic manipulation algorithms. It supports arbitrary precision arithmetic.
Group Theory
gap Groups, Algorithms and Programming computer algebra system
magnus Computational group theory software with GUI
Number Theory
aribas Interpreter for big integer and multiprecision floats arithmetic
pari-gp PARI/GP Computer Algebra System binaries
Library
ginac-tools Some tools for the GiNaC symbolic framework. GiNaC (which stands for "GiNaC is Not a CAS (Computer Algebra System)") is a library for doing symbolic (i.e. non-numeric) computation directly in the C++ programming language.
libmatheval1 GNU library for evaluating symbolic mathematical expressions
Numerical computation oriented
freemat mathematics framework (mostly matlab compatible)
Proof Assistant
coq proof assistant for higher-order logic
Geometry
geomview interactive geometry viewing program
Numerical libraries
arpack ARnoldi Package for eigenvalue computations (Christophe Prud'homme)
arpack++ C++ wrapper library for arpack (Christophe Prud'homme)
atlas (Andre Lehovich)
blas (Andre Lehovich) ?More about Blas
blitz++ (Helen Faulkner, Victor Munoz)
fftw3 (Helen Faulkner, Andre Lehovich) More about FFTW
gsl (Helen Faulkner, Andre Lehovich, Victor Munoz) More about GSL
lapack (Andre Lehovich)
superlu sparse direct LU solver (Christophe Prud'homme)
umfpack sparse direct LU solver (Christophe Prud'homme)
Spreadsheets
gnumeric (Carlo Segre, Kenward Vaughan)
openoffice.org Calc (Enrico Zini)
Other
Mathematics tools that could be considered for inclusion in Debian
Focal upstream
giac (155075)
gtybalt (291432)
lepisme upstream
matpack (Victor Munoz)
RKWard (333392) upstream Frontend to R unofficial deb
Simted upstream
SINGULAR upstream
Unignuplot upstream unofficial deb closed ITP: 302538
MIXMOD upstream
Libraries
Mathematics tools that cannot go to main for licensing reasons
SCILAB (Rick Bahague)