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Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.^[1]

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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^[2] 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^[3] 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.

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.

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.

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 utilizes mathematics to analyze or synthesize musical symbols and patterns.

• jMusic
• Musimat (by Gareth Loy)^[4]
• OpenMusic
• Opusmodus
• Rubato Composer
• SuperCollider
• UPIC

• Comparison of electromagnetic simulation software
• List of cosmological computation software
• List of computational fluid dynamics software
• List of software for Monte Carlo molecular modeling

A growing number of mathematical software is available in web browsers, without the need to download or install any code.^[5]

• List of bioinformatics software
• Biostatistics software
• List of systems biology modeling software
• List of systems biology visualization software

• List of quantum chemistry and solid-state physics software
• Comparison of software for molecular mechanics modeling

• Conway's Game of Life

• AlphaDev – algorithm discovery
• AlphaEvolve – mathematical and algorithm discovery
• AlphaGeometry – geometry problem solving
• AlphaTensor – matrix multiplication discovery
• FunSearch – mathematical discovery
• Ramanujan machine – conjecture discovery

• Computational mathematics
• Comparison of formula editors
• Gödel's incompleteness theorems
• List of information graphics software
• List of MATLAB software and tools
• List of open-source software for mathematics
• Mathlete
• MathOverflow
• Plot (graphics)
• Time complexity

• swMATH Database on mathematical software