Mathematical software

Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.

Evolution of mathematical software

Mathematical knowledge of techniques such as algorisms which existed before the invention of the electronic computer, helped to develop mathematical software. On the other hand, due to the growth of computing power (such as Moore's law), the new treatment (for example, a new kind of technique such as data assimilation which combined numerical analysis and statistics) needed the progress of the mathematical science or applied mathematics.
The progress of mathematical information presentation such as TeX or MathML will demand to evolution form formula manipulation language to true mathematics manipulation language (not withstanding the problem that whether mathematical theory is inconsistent or not). And popularisation of general purpose mathematical software, special purpose mathematical software so called one purpose software which use special subjects will adapt for environmental progress at the normalisation of the platform, keeping the diversity of mathematical software.

Software calculator

A software calculator allows the user to perform simple mathematical operations, like addition, multiplication, exponentiation and trigonometry. Data input is typically manual, and the output is a text label.

Educational mathematics software

Mathematical education video games

Computer algebra systems

Many mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human readable notation.

Solvers

This section is an excerpt from Solver.[edit]

A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type.

Equation solvers

Optimization software

SMT solvers

Theorem-provers

Cryptography

Statistics

Statistical software

Theorem provers and proof assistants

Proof assistants

Theorem provers

Geometry

Numerical analysis

The Netlib repository contains various collections of software routines for numerical problems, mostly in Fortran and C. Commercial products implementing many different numerical algorithms include the IMSL, NMath and NAG libraries; a free alternative is the GNU Scientific Library. A different approach is taken by the Numerical Recipes library, where emphasis is placed on clear understanding of algorithms.

Many computer algebra systems (listed above) can also be used for numerical computations.

Music mathematics software

Music mathematics software utilizes mathematics to analyze or synthesize musical symbols and patterns.

Physics

Plotting and charting

Websites

A growing number of mathematical software is available in web browsers, without the need to download or install any code.

Biomathematics

Mathematical chemistry

Mathematical modeling and simulations

Mathematical and numerical libraries

C

C++

Open-source

Fortran

Java

.NET

Perl

Open-source

Python

Open-source

List of mathematical software

Mathematical notation software

Spreadsheet software

Mathematical art software

Artificial intelligence for mathematics

See also

References

  1. ↑ See, e.g., the editorial charter of the ACM Transactions on Mathematical Software or the problem taxonomy of the National Institute of Standards and Technology Guide to Available Mathematical Software (both retrieved 2015-02-15).
  2. ↑ Both MathML and TeX may be only simple a kind of computer language which enable also to present the mathematical formula. However they also may be the mathematical software if the term of software interpreted as whole technology on how to use computer, at most wide sense.
  3. ↑ Included your written script code on the general purpose mathematical software.
  4. ↑ Musimathics website, freeware download
  5. ↑ Internet Accessible Mathematical Computation Archived 2017-06-28 at the Wayback Machine, Institute for Computational Mathematics, Kent State University, retrieved 2015-02-15.
  6. ↑ "Ultimate Math Library: Utilities Tools". Unity Asset Store.
  7. ↑ "Math Equation Writer – GUI Tools". Unity Asset Store. Retrieved 2025-08-06.
  8. ↑ "MathPlus Library: Game Toolkits". Unity Asset Store.
  9. ↑ "Smithy Procedural Generation Framework".
  10. ↑ "NeuroFractals Pack – 3D Environments". Unity Asset Store. Retrieved 2025-08-06.