List of .NET libraries for mathematical computations. Please feel free to comment if you think a library is missing in the list, or if you want to add some information to a library provided that you use neutral language.
Free (zero-priced) libraries
ALGLIB – An open-source library including linear algebra, statistics, optimization and differential equations.
DotNumerics – Linear Algebra, Differential Equations and Optimizations. Translation of Fortran libraries LAPACK, BLAS and EISPACK to C#.
ILNumerics – Open-source math library for business applications. It also has a commercial professional edition for re-distributions (closed-source allowed).
Math.NET Numerics – For numerical computations in science, engineering and every day use. Includes functions for linear algebra, statistics and integral transforms (FFT).
Microsoft Sho – Linear algebra and data visualization (plotting and charting) with an interactive shell for rapid development.
Microsoft Solver Foundation – .NET solution for mathematical optimizations with built-in solvers.
Extreme Optimization – General purpose matrix/vector calculations with statistics and optimizations. Offers a 60-day trial version.
IMSL® .NET library – Advanced numerical analysis and charting. Contains mathematical, statistical and financial algorithms.
NAG Library for .NET – Features include linear algebra, statistics, optimization and numerical integration.
NMath – Linear algebra, optimizations and statistics. Commercial license with 30-day trial period.