Wolfram Mathematica

"Mathematica" redirects here. For other uses, seeMathematica (disambiguation).

For the programming language used in this program, seeWolfram Language.

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Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allowsmachine learning,statistics,symbolic computation, data manipulation, network analysis, time series analysis,NLP,optimization, plottingfunctions and various types of data, implementation ofalgorithms, creation ofuser interfaces, and interfacing with programs written in otherprogramming languages. It was conceived byStephen Wolfram, and is developed byWolfram Research of Champaign, Illinois.^[8]^[9] TheWolfram Language is the programming language used inMathematica.^[10] Mathematica 1.0 was released on June 23, 1988 inChampaign, Illinois andSanta Clara, California.^[11]^[12]^[13] Mathematica's Wolfram Language is fundamentally based on Lisp; for example, the Mathematica command Most is identically equal to the Lisp command butlast. There is a substantial literature on the development of computer algebra systems (CAS).

Wolfram Mathematica

Developer(s)	Wolfram Research
Initial release	June 23, 1988; 36 years ago (1988-06-23)^[1]

Stable release	14.2.0 (January 23, 2025; 2 months ago (2025-01-23))[±]^[2]

Written in	Wolfram Language,^[3]C/C++,Java^[4]
Platform	Windows,^[5]macOS,Linux (includes separated support for Raspbian onRaspberry Pi^[6]), online service. All platforms support 64-bit implementations.^[7](list)
Available in	English, Chinese, Japanese
Type	Computer algebra,numerical computations,information visualization,statistics,user interface creation
License	Proprietary
Website	www.wolfram.com/mathematica/

Notebook interface

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Mathematica is split into two parts: the kernel and thefront end. The kernel interprets expressions (Wolfram Language code) and returns result expressions, which can then be displayed by the front end.

The original front end, designed byTheodore Gray^[14] in 1988, consists of anotebook interface and allows the creation and editing ofnotebook documents that can contain code, plaintext, images, and graphics.^[15]

Code development is also supported through support in a range of standardintegrated development environment (IDE) includingEclipse,^[16]IntelliJ IDEA,^[17] Atom,Vim,Visual Studio Code andGit. The Mathematica Kernel also includes a command line front end.^[18]

Other interfaces include JMath,^[19] based onGNU Readline and WolframScript^[20] which runs self-contained Mathematica programs (with arguments) from the UNIX command line.

High-performance computing

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Capabilities forhigh-performance computing were extended with the introduction ofpacked arrays in version 4 (1999)^[21] andsparse matrices (version 5, 2003),^[22] and by adopting theGNU Multiple Precision Arithmetic Library to evaluate high-precision arithmetic.

Version 5.2 (2005) added automaticmulti-threading when computations are performed onmulti-core computers.^[23] This release included CPU-specific optimized libraries.^[24] In addition Mathematica is supported by third party specialist acceleration hardware such asClearSpeed.^[25]

In 2002,gridMathematica was introduced to allow user levelparallel programming on heterogeneous clusters and multiprocessor systems^[26] and in 2008 parallel computing technology was included in all Mathematica licenses including support for grid technology such asWindows HPC Server 2008,Microsoft Compute Cluster Server andSun Grid.

Support forCUDA andOpenCL GPU hardware was added in 2010.^[27]

Extensions

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As of Version 14, there are 6,602 built-in functions and symbols in the Wolfram Language.^[28] Stephen Wolfram announced the launch of the Wolfram Function Repository in June 2019 as a way for the public Wolfram community to contribute functionality to the Wolfram Language.^[29] At the time of Stephen Wolfram's release announcement for Mathematica 13, there were 2,259 functions contributed as Resource Functions.^[30] In addition to the Wolfram Function Repository, there is a Wolfram Data Repository with computable data and the Wolfram Neural Net Repository for machine learning.^[31]

Wolfram Mathematica is the basis of the Combinatorica package, which adds discrete mathematics functionality in combinatorics and graph theory to the program.^[32]

Connections to other applications, programming languages, and services

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Communication with other applications can be done using a protocol called Wolfram Symbolic Transfer Protocol (WSTP). It allows communication between the Wolfram Mathematica kernel and the front end and provides a general interface between the kernel and other applications.^[33]

Wolfram Research freely distributes a developer kit for linking applications written in the programming languageC to the Mathematica kernel through WSTP using J/Link.,^[34] aJava program that can ask Mathematica to perform computations. Similar functionality is achieved with .NET /Link,^[35] but with.NET programs instead of Java programs.

Other languages that connect to Mathematica includeHaskell,^[36]AppleScript,^[37]Racket,^[38]Visual Basic,^[39]Python,^[40]^[41] andClojure.^[42]

Mathematica supports the generation and execution ofModelica models forsystems modeling and connects withWolfram System Modeler.

Links are also available to many third-party software packages and APIs.^[43]

Mathematica can also capture real-time data from a variety of sources^[44] and can read and write to public blockchains (Bitcoin,Ethereum, and ARK).^[45]

It supports import and export of over 220 data, image, video, sound,computer-aided design (CAD),geographic information systems (GIS),^[46] document, and biomedical formats.

In 2019, support was added for compiling Wolfram Language code toLLVM.^[47]

Version 12.3 of the Wolfram Language added support forArduino.^[48]

Computable data

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Mathematica is also integrated withWolfram Alpha, an onlineanswer engine that provides additional data, some of which is kept updated in real time, for users who use Mathematica with an internet connection. Some of the data sets include astronomical, chemical, geopolitical, language, biomedical, airplane, and weather data, in addition to mathematical data (such as knots and polyhedra).^[49]

Reception

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BYTE in 1989 listed Mathematica as among the "Distinction" winners of the BYTE Awards, stating that it "is another breakthrough Macintosh application ... it could enable you to absorb the algebra and calculus that seemed impossible to comprehend from a textbook".^[50] Mathematica has been criticized for being closed source.^[51] Wolfram Research claims keeping Mathematica closed source is central to its business model and the continuity of the software.^[52]^[53]