Reference articles on history, science, culture and more
Surprise meSurprise meSubscribe
Encyclopedia

Mathematical software

Software used in mathematical applications

Wikipedia contributorsAdapted for Fathomly · View authors
5 min read
Source updated August 22, 2026

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

01Evolution 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.

02Software 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.

03Educational mathematics software

Mathematical education video games

04Computer 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.

05Solvers

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

06Cryptography

07Statistics

Statistical software

08Theorem provers and proof assistants

Proof assistants

Theorem provers

09Geometry

10Numerical 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.

11Music mathematics software

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

12Physics

13Websites

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

14Biomathematics

15Mathematical chemistry

16Mathematical and numerical libraries

C

Open-source

Proprietary

C++

Open-source

Fortran

Open-source

Proprietary

Java

Open-source

Proprietary

.NET

Open-source

Proprietary

Perl

Open-source

Python

Open-source

17List of mathematical software

18Mathematical notation software

19Spreadsheet software

20Mathematical art software

21Artificial intelligence for mathematics

Watch videos about Mathematical softwareExplainers and documentaries on YouTube (opens in a new tab)

Sources and credits

This article is adapted from the Wikipedia article “Mathematical software”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

Fathomly is not affiliated with or endorsed by the Wikimedia Foundation. Spotted a problem? Tell us.

Continue exploring

Related topics

Computational mathematics

Computational mathematics is a field of study that focuses on the interaction of mathematical sciences, computer science, and algorithms. A large part of computational mathematics consists roughly of using mathematics for allowing and improving computer computation in areas of science and engineering where mathematics are useful.

Formula editor

A formula editor, also known as an equation editor, is a computer program that is used to typeset mathematical formulas and mathematical expressions. Formula editors typically serve two purposes: They allow word processing and publication of technical content either for print publication, or to generate raster images for web pages or screen presentations.

Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in philosophy of mathematics.