Digital Library of Mathematical Functions: A special function reference site that aims to be the next-generation Abromowitz & Stegun.
Mathworld: Eric Weisstein's encylopedia of math topics. Not as well-maintained as it once was, but still a useful compliment to Wikipedia.
Wolfram Functions: A compendium of properties of special functions.

Math.NET: Another free .NET library, probably our closest competitor. Offers some interpolation and matrix functionality that we lack, lacks some data wrangling, statistics, fitting, special function, and solver functionality that we offer.
Extreme Optimization: A commercial library with a well-organized API and a lot of functionality. Retails for about $1000/developer.
NMath: A commercial library with a lot of functionality and a not-so-organized API structure. Retails for about $1300/developer.
IMSL C#: A commercial library with a pedigree stretching back to the 1970s which has now been ported to .NET.

GNU Scientific Library: A C library maintained since the 1990s.
MPMath: A python library for computing special functions to arbitrary precision.
LAPACK: The standard linear algebra library, in FORTRAN.

William Kahan (Wikipedia, Academic): The father of floating point.
Fredrik Johansson (Personal): Developer of mpmath and arb.
David Borwein (Wikipedia), Jonathan Borwein (Wikipedia, Academic), and Peter Borwein (Wikipedia): Pioneers in experimental mathematics.
Donald Knuth (Wikipedia, Academic): Expositor of algorithms extraordinaire.
M. J. D. Powell (Wikipedia): Originator of nearly every modern derivative-free optimization algorithm.
Nico Temme (Academic): Developed some extraordinary approaches to the evaluation of special functions.
Toshio Fukushima: Developed new algorithms for the fast comptation of elliptic functions.
Irene Stegun (Wikipedia): Published some of the first papers on the computation of special functions. With Milton Abromowitz, edited A & S.

Goldberg, David, What Every Computer Scientist Should Know About Floating-Point Arithmetic, 1991: A very in-depth guide to floating-point, very useful but actually far more than any typical programmer would be expected to know about floating-point.
Kahan, Branch Cuts for Complex Elementary Functions, or Much Ado About Nothing's Sign Bit: Algorithms for basic complex functions.
Bailey, Borwein, and Crandall, Advanced in the Theory of Box Integrals, 2009: Analytic solutions (found by experiment) to difficult multi-dimensional integrals. We use these as test-cases of our multi-dimensional integration logic.
Powell, UOBYQA: Unconstrained Optimization by Quadratic Approximation, 2000: Our derivative-free algorithm for unconstrained local optimization is based on this paper.
Fukushima, Toshio, Fast Computation of Complete Elliptic Integrals and Jacobian Elliptic Functions, Celestial Mechanics and Dynamical Astronomy 105 (2009) 305
Stegun, I. and Zucker, R., Automatic Computing Methods for Special Functions. Part III. The Sine, Cosine, Exponential Integrals, and Related Functions, Journal of Research of the National Bureau of Standards 80B (1976) 291