• Antik - A library for computational mathematics, science, and engineering
• axiom - Axiom is a general purpose Computer Algebra application
• Bordeaux-FFT - Bordeaux-FFT is a fast, pure-Lisp implementation of Fast Fourier Transforms
• cl-ana - cl-ana aims to provide the basic tools necessary to analyze large/medium-large datasets
• cl-buchberger - cl-buchberger is a Common Lisp implementation of Buchberger's algorithm for the computation of Gröbner bases
• cl-factoradic - cl-factoradic is a Mathematics/Combinatorics library that implements calculation and iteration of permutations based on the factoradic numbers system
• cl-fftw3 - cl-fftw3 provides a CFFI interface for Common Lisp programs to use the FFTW3 Fourier transform library
• cl-geometry - cl-geometry is a Common Lisp package for simple two dimensional computational geometry
• cl-graph - CL-Graph is a set of Common Lisp utilities for manipulating graphs
• cl-gsl - cl-gsl provides bindings to the GNU Scientific Library (GSL) of mathematics routines
• cl-jointgen - CL-JOINTGEN is a Common Lisp implementation of the Joint Generation Algorithm for computing the dual of a monotone boolean function
• cl-mathstats - CL-MathStats is a set of miscellaneous Common Lisp mathematics and statistics utilities
• CL-NUM-UTILS - Simple numerical functions, including intervals, Chebyshev polynomials and univariate rootfinding
• cl-permutation - CL-PERMUTATION is a Mathematics library for doing permutation and permutation group calculations written by Robert Smith
• cl-rmath - [unmaintained, maintainers welcome] A simple, autogenerated foreign interface for the standalone R API
• cl-satwrap - A thin generic SAT (propositional satisfiability problem) solver interface to your favorite “industrial-strength” SAT solver
• CLLIB - CLLIB is a varied collection of Common lisp tools and routines in CLOCC
• clmath - CLMATH is a modern re-packaging of an old Common Lisp scientific library by Gerald Roylance
• COMPUTABLE-REALS - COMPUTABLE-REALS is a Mathematics library for dealing with arbitrary precision reals
• Decimals - A decimal number parser and formatting package for Common Lisp
• embeddable-maxima - embeddable-maxima is the fork of Maxima CAS to make it embeddable into common lisp application
• Factorial - The Factorial of n is the product of all the integers between 1
• FEMLISP - FEMLISP is a Mathematics Application which solves partial differential equations with the help of the finite element method (FEM)
• FFT - A Common Lisp library to do Fast Fourier Transform on a multi-dimensional array of numbers
• Fibonacci - The Fibonacci sequence of numbers was described in a mathematics book by Leonardo da Pisa (Fibonacci) called Liber Abaci
• float-features - float-features is a portability library for IEEE float features that are not covered by the CL standard
• floating-point - Floating-point is a Common Lisp library with functions for calculating
• floating-point-contractions - Numerically stable, contracted versions of floating-point operations
• Forward Discrete Cosine Transform - forward-dct! is a function implementing forward Discrete Cosine Transform, as used in JPEG
• graph-utils - graph-utils: graph analysis utilities for Common Lisp
• GSLL - GNU Scientific Library for Lisp allows you to use the GNU Scientific Library (GSL) from Common Lisp
• IMPS - IMPS is an Interactive Mathematical Proof System developed by W
• Integrate - A package to aid in solving differential equations, currently slightly limited in scope
• LispLab - The main purpose of Lisplab is to to integrate all kinds of mathematics capabilities into one framework
• Mandelbrot set explorer - This mathematics application was written in Common Lisp (by Edi Weitz)
• map - Octave-like functionality for Common Lisp
• math-extensions - Additional numerical classes (quaternions, intervals, etc.) for Common Lisp
• MatLisp - A BLAS and LAPACK linear algebra library wrapper which makes their features accessible through a set of CLOS classes
• Maxima - Maxima is a GPL'd Common Lisp mathematics application for computer based algebra (an implementation of MIT's Macsyma system)
• maxima-json-rpc - maxima-json-rpc is http post json-rpc server for embeddable-maxima
• micmac - Common Lisp Mathematics library by Gabor Melis that implements alpha-beta, beam search, UCT and Metropolis-Hastings MCMC
• Mitch's LISP Mathematical Library - Large Mathematics library by Mitch Richling: numerical analysis, dynamical systems, symbolic algebra, combinatorial enumeration and counting algorithms, computational group theory, probabilistic modeling and simulation
• Nuprl - The Nuprl system, based on the type theory of Martin-Löf, is a system for manipulating proofs
• Oct - Lisp implementation of quad-double floats
• patxi-2 - PatXi-2 is a library for doing numerical computations in Common Lisp
• plot-2d - Plot-2D is a 2-dimensional data representation and plotting application for Mathematics and scientific data
• plotting - Library and Application packages to produce 2D and 3D plots
• primecount - Sublinear (in time and space) counting and summing of integer primes using optimized sieving method
• PRL - The Proof (or Program) Refinement Logic program, led by Robert Constable of Cornell
• Quantile estimator - Biased Quantiles over Data Streams
• ratmath - Utilities for Rational Numbers in Common Lisp (rational approximations and interval arithmetic)
• SimLab - SimLab Is a scientific simulation and analysis tool that uses the weyl computer algebra system
• TPS - TPS, standing for Theorem Proving System, is a theorem prover for first-order logic and type theory
• ulimyhmpqs - ulimyhmpqs is an implementation of the Hypercube Multiple Polynomial Quadratic Sieve (HMPQS), an algorithm for the factorisation of large (up to about 110 digits, where the Number Field Sieve (NFS) algorithms become more efficient) integers
• Weyl - A computer algebra substrate for Common Lisp
• wu-decimal - Wu-Decimal is a decimal number package developed by Wukix

Linear algebra: (main topic: linear algebra)

• 3d-matrices - This is a library implementing common matrix operations, mainly intended as the counterpiece to 3d-vectors and thus being aimed at operations in 3D space
• 3d-vectors - This is a simple library for 3D vectors
• april - A subset of APL (A Programming Language) compiling to Common Lisp
• cl-blapack - A wrapper around the Fortran BLAS and LAPACK libraries for dense linear algebra
• cl-clsparse - Common Lisp bindings for clSPARSE
• cl-octave - An FFI to the Octave linear algebra language (CMUCL-only)
• cl-tuples - cl-tuples is a library for writing optimised vector math
• clem - A library for representing and performing various operations on matrices
• CLLIB - CLLIB is a varied collection of Common lisp tools and routines in CLOCC
• FSVD - FSVD is a Common Lisp implementation of Simon Funk's quasi SVD as described at http://sifter.org/~simon/journal/20061211.html in the context of its application to the netflix prize
• GSLL - GNU Scientific Library for Lisp allows you to use the GNU Scientific Library (GSL) from Common Lisp
• l-math - L-MATH is a library for simple linear algebra in geometric applications
• Linear-algebra - Linear-algebra is a Common Lisp library of numeric linear algebra routines
• lisp-matrix - A matrix linear algebra library for common lisp building on work by Mark Hoemmen, Evan Monroig, Tamas Papp and Rif
• LispLab - The main purpose of Lisplab is to to integrate all kinds of mathematics capabilities into one framework
• LLA - “Lisp Linear Algebra”, LLA for short, provides convenient and fast matrix operations by binding to LAPACK
• magicl - Matrix Algebra proGrams In Common Lisp: numerical linear algebra routines with auto-generated bindings to BLAS, LAPACK and Expokit
• MatLisp - A BLAS and LAPACK linear algebra library wrapper which makes their features accessible through a set of CLOS classes
• MGL-MAT - MAT is a linear algebra library for working with multi-dimensional arrays which supports efficient interfacing to foreign and CUDA code
• NLISP - NLISP is an environment for numerical computation and visualisation like IDL or Matlab
• origin - A native Lisp graphics math library with an emphasis on performance and correctness
• sb-cga - SB-CGA is a computer graphics algebra library for Common Lisp
• Sheafhom - Sheafhom is a package by Mark McConnell for large sparse linear algebra computations over the integers and other exact number types
• spartns - Spartns is a SPARse TeNSor representation library

Statistics: (main topic: statistics)

• cl-ana - cl-ana aims to provide the basic tools necessary to analyze large/medium-large datasets
• cl-mathstats - CL-MathStats is a set of miscellaneous Common Lisp mathematics and statistics utilities
• cl-randist - This package is a manual translation from C to common lisp of some random number generation functions of GSL library
• cl-random - [unmaintained, maintainers welcome] A library for uni- and multivariate probability distributions and statistics functions
• CLLIB - CLLIB is a varied collection of Common lisp tools and routines in CLOCC
• common-lisp-stat - Common Lisp Statistics -- based on LispStat but updated for Common Lisp and incorporating lessons from R
• Mersenne Twister - The Mersenne Twister is a pseudorandom number generation algorithm created by Makoto Matsumoto
• py-random - A translation of the random module in the Python standard library
• RCL - RCL is an FFI to communicate with the R statistics environment
• rclg - An R (statistics programming language) FFI for Common Lisp
• RHO - The ρ (RHO) Common Lisp library contains a set of data structures and functions to provide some of the functionalities of R
• sapaclisp - sapaclisp is a collection of Common Lisp functions for spectral analysis
• SimpSamp - SimpSamp is a statistics library for simple random sampling without replacement
• Stats - Stats by Larry Hunter is a statistics library

Other stuff:

• RCL is a library for interfacing Common Lisp with the R environment using CFFI. (October 7 2007) rukubites: RCL doesn't work in SBCL, and requires some small modifications in alien-defs.lisp to accomodate CFFI API changes for defcvar.
• RCLG is an unfinished R interface that works for sbcl but not clisp (as of git version October 7 2007). It seems to have a similar interface as RCL.
• FriCAS is a fork of the Axiom computer algebra system.
• cl-ana is Common Lisp data analysis library.
• Kenzo is a program for doing computational algebraic topology.
• CommonLispStat (see also GitHub location), is a port/rewrite/re-intentioning of XLispStat to Common Lisp. The goal is to develop an "R like" set of packages which deliver additional functionality to Common Lisp for applied statistical data analysis.