This page provides a simple list of software which provides (non-trivial) algorithms for numerical calculations, graph theory (including advanced graph layout), number theory or higher algebra in some form. Listing a software or project does not mean an endorsement or that the software has even been reviewed.
The list is currently limited to OSS (because of easier research, not because of bias against closed source software). There is no limit regarding programming languages, license or API design. Computer algebra systems (CAS) are included. Function graphing, charts and other visualization as well as very specialized topics like neural network, cryptography or high energy physics are currently not included. Maybe some will be added later, in separate sections.
Mantissa - linear algebra, least squares, curve fitting, ordinary differential equations integrators, polynomials, random numbers, basic statistical analysis, optimization
Colt - Open Source Libraries for High Performance Scientific and Technical Computing in Java.
JGraphT - graph theory
Java Universal Network/Graph Framework - graph theory, graph layout
JPaul - includes graph theory algorithms
http://sourceforge.net/projects/math4j/ - somebody should tell this guy he's just reinventing the wheel
IA Math - interval arithmetic
ATLAS - highly optimized BLAS library
Gnu Scientific Library (gsl?)
gjrand - random number generators and tests
Goblin - graph theory
lpsolve - mixed integer linear programming
GLPK - linear programming
Numerical Python (URLs TBD)
CAS, solvers, spreadsheets and similar stuff
PSPP - statistical analysis