View source for Wolfram Mathematica

{{short description|Computational software program}}
{{redirect|Mathematica}}
{{For|the programming language used in this program|Wolfram Language}}
{{Expand German|topic=mathematics|date=April 2020|Mathematica}} 
{{Infobox software
| name = Wolfram Mathematica
| logo = Mathematica Logo.svg
| logo_upright = 0.4 
| developer = [[Wolfram Research]]
| released = {{Start date and age|1988|06|23}}<ref>{{citation|title=Mathematica Turns 20 Today|first=Stephen|last=Wolfram|url=http://blog.wolfram.com/2008/06/23/mathematica-turns-20-today/|date=23 Jun 2008|publisher=Wolfram|access-date=16 May 2012}}</ref>
| latest preview version = 
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} -->
| programming language = [[Wolfram Language]],<ref>{{cite web|url=http://blog.wolfram.com/2013/06/23/celebrating-mathematicas-first-quarter-century/|title=Celebrating Mathematica's First Quarter Century|date=23 June 2013 |access-date=11 August 2015}}</ref> [[C (programming language)|C]]/[[C++]], [[Java (programming language)|Java]]<ref>[http://reference.wolfram.com/legacy/v9/tutorial/TheSoftwareEngineeringOfMathematica.html The Software Engineering of Mathematica—Wolfram Mathematica 9 Documentation] {{Webarchive|url=https://web.archive.org/web/20170729133220/http://reference.wolfram.com/legacy/v9/tutorial/TheSoftwareEngineeringOfMathematica.html |date=2017-07-29 }}. Reference.wolfram.com. Retrieved on 2015-03-23.</ref>
| operating system = 
| platform = [[Microsoft Windows|Windows]],<ref>{{cite web|url=https://www.wolfram.com/mathematica/system-requirements.html|title=Mathematica 12 System Requirements and Platform Availability|access-date=16 December 2020}}</ref> [[macOS]], [[Linux]] (includes separated support for Raspbian on [[Raspberry Pi]]<ref>[https://www.theverge.com/2013/11/21/5130394/raspberry-pi-includes-mathematica-wolfram-language-free Raspberry Pi Includes Mathematica for Free] {{Webarchive|url=https://web.archive.org/web/20140509213354/http://www.theverge.com/2013/11/21/5130394/raspberry-pi-includes-mathematica-wolfram-language-free |date=2014-05-09 }} The Verge</ref>), online service. All platforms support 64-bit implementations.<ref>{{cite web|url=http://www.wolfram.com/products/mathematica/platforms/|title=Wolfram Mathematica|access-date=11 August 2015}}</ref> [http://www.wolfram.com/mathematica/system-requirements.html (list)]
| size = 
| language = English, Chinese, Japanese
| language count = <!-- DO NOT include this parameter unless you know what it does -->
| language footnote = 
| genre = [[Computer algebra system|Computer algebra]], [[List of numerical-analysis software|numerical computations]], [[information visualization]], [[List of statistical packages|statistics]], [[Graphical user interface|user interface creation]]
| license = [[Proprietary software|Proprietary]]
| website = {{Official URL}}
| standard = 
}}
'''Wolfram Mathematica''' (also known as '''Mathematica''') is a software system with built-in libraries for several areas of technical computing that allows [[machine learning]], [[statistics]], [[Computer algebra|symbolic computation]], data manipulation, network analysis, time series analysis, [[Natural_language_processing|NLP]], [[optimization]], plotting [[Function (mathematics)|functions]] and various types of data, implementation of [[algorithm]]s, creation of [[user interface]]s, and interfacing with programs written in other [[programming language]]s. It was conceived by [[Stephen Wolfram]], and is developed by [[Wolfram Research]] of Champaign, Illinois.<ref>{{cite web |title=Stephen Wolfram: Simple Solutions; The iconoclastic physicist's Mathematica software nails complex puzzles |url=https://www.bloomberg.com/news/articles/2005-10-02/stephen-wolfram-simple-solutions |website=BusinessWeek |access-date=August 4, 2021 |date=October 3, 2005|url-access=subscription}}</ref><ref>{{cite web|url=http://www.wolfram.com/company/contact.cgi|title=Contact Wolfram Research|access-date=11 August 2015}}</ref> The [[Wolfram Language]] is the programming language used in ''Mathematica''.<ref>{{cite web|url=http://www.slate.com/articles/technology/bitwise/2014/03/stephen_wolfram_s_new_programming_language_can_he_make_the_world_computable.html|title=Stephen Wolfram's new programming language: Can he make the world computable?|work=Slate Magazine|date=6 March 2014 |access-date=11 August 2015}}</ref> Mathematica 1.0 was released on June 23, 1988 in [[Champaign, Illinois]] and [[Santa Clara, California]].<ref>{{Cite web |title=Mathematica—Three Decades of Contributions, Invention, Discovery, and Education |url=https://www.wolfram.com/mathematica/scrapbook/ |access-date=2022-05-16 |website=www.wolfram.com |language=en}}</ref><ref name=":0">{{Cite web |title=Celebrating a Third of a Century of Mathematica, and Looking Forward—Stephen Wolfram Writings |url=https://writings.stephenwolfram.com/2021/10/celebrating-a-third-of-a-century-of-mathematica-and-looking-forward/ |access-date=2022-05-16 |website=writings.stephenwolfram.com |date=22 October 2021 |language=en}}</ref><ref>{{Cite web |title=There Was a Time before Mathematica…—Stephen Wolfram Writings |url=https://writings.stephenwolfram.com/2013/06/there-was-a-time-before-mathematica/ |access-date=2022-05-16 |website=writings.stephenwolfram.com |date=6 June 2013 |language=en}}</ref> Mathematica's Wolfram Language is fundamentally based on Lisp; for example, the Mathematica command Most is identically equal to the Lisp command butlast.  

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==Notebook interface==
Mathematica is split into two parts: the kernel and the [[Front and back ends|front 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 by [[Theodore Gray]]<ref>[https://patents.google.com/patent/US8407580 Patent US8407580]  Google Patent Search</ref> in 1988, consists of a [[notebook interface]] and allows the creation and editing of [[Notebook interface|notebook documents]] that can contain code, plaintext, images, and graphics.<ref>{{Cite news|url=http://bit-player.org/wp-content/extras/bph-publications/Pixel-1990-01-Hayes-Mathematica.pdf |archive-url=https://web.archive.org/web/20140715213929/http://bit-player.org/wp-content/extras/bph-publications/Pixel-1990-01-Hayes-Mathematica.pdf |archive-date=2014-07-15 |url-status=live|title=Thoughts on Mathematica|last=Hayes|first=Brian|date=1990-01-01|work=Pixel}}</ref>

Code development is also supported through support in a range of standard [[integrated development environment]] (IDE) including [[Eclipse (software)|Eclipse]],<ref>{{cite web|url=http://www.macworld.com/news/2006/06/21/workbench/index.php|title=Wolfram intros Workbench IDE for Mathematica|date=21 June 2006|work=Macworld|access-date=11 August 2015|archive-date=2 July 2006|archive-url=https://web.archive.org/web/20060702172412/http://www.macworld.com/news/2006/06/21/workbench/index.php|url-status=dead}}</ref> [[IntelliJ IDEA]],<ref>{{cite web| url = http://mathematicaplugin.halirutan.de/| title = Mathematica plugin for IntelliJ IDEA}}</ref> Atom, [[Vim (text editor)|Vim]], [[Visual Studio Code]] and [[Git]]. The Mathematica Kernel also includes a command line front end.<ref>[http://reference.wolfram.com/mathematica/tutorial/UsingATextBasedInterface.html Using a Text-Based Interface] {{Webarchive|url=https://web.archive.org/web/20131029192506/http://reference.wolfram.com/mathematica/tutorial/UsingATextBasedInterface.html |date=2013-10-29 }} documentation at wolfram.com</ref>

Other interfaces include JMath,<ref>{{cite web|url=http://robotics.caltech.edu/~radford/jmath/|title=JMath: A GNU Readline based frontend for Mathematica|access-date=11 August 2015}}</ref> based on [[GNU Readline]] and WolframScript<ref>{{cite web|url=https://reference.wolfram.com/language/ref/program/wolframscript.html|title=Directory listing|access-date=18 April 2019}}</ref> which runs self-contained Mathematica programs (with arguments) from the UNIX command line.

== High-performance computing ==

Capabilities for [[high-performance computing]] were extended with the introduction of [[packed array]]s in version 4 (1999)<ref>[http://goliath.ecnext.com/premium/0199/0199-1526706.html Math software packs new power; new programs automate such tedious processes as solving nonlinear differential equations and converting units] by Agnes Shanley, ''Chemical Engineering'', March 1, 2002.</ref> and [[sparse matrix|sparse matrices]] (version 5, 2003),<ref>[http://www.accessmylibrary.com/coms2/summary_0286-9587712_ITM Mathematica 5.1: additional features make software well-suited for operations research professionals] {{Webarchive|url=https://web.archive.org/web/20080925041741/http://www.accessmylibrary.com/coms2/summary_0286-9587712_ITM |date=2008-09-25 }} by ManMohan S. Sodhi, ''OR/MS Today'', December 1, 2004.</ref> and by adopting the [[GNU Multiple Precision Arithmetic Library]] to evaluate high-precision arithmetic.

Version 5.2 (2005) added automatic [[Thread (computer science)|multi-threading]] when computations are performed on [[multi-core]] computers.<ref>[http://www.accessmylibrary.com/coms2/summary_0286-12336000_ITM The 21st annual Editors' Choice Awards] {{Webarchive|url=https://web.archive.org/web/20090112073949/http://www.accessmylibrary.com/coms2/summary_0286-12336000_ITM |date=2009-01-12 }}, ''Macworld'', February 1, 2006.</ref> This release included CPU-specific optimized libraries.<ref>{{cite web|url=https://support.wolfram.com/39353|title=Mathematica is tuned to take advantage of CPU features when available|access-date=13 April 2020}}</ref> In addition Mathematica is supported by third party specialist acceleration hardware such as [[ClearSpeed]].<ref>{{cite web|url=http://www.thefreelibrary.com/ClearSpeed+Advance(TM)+Accelerator+Boards+Certified+by+Wolfram...-a0147498410|title=ClearSpeed Advance Accelerator Boards Certified by Wolfram Research; Math Coprocessors Enable Mathematica Users to Quadruple Performance.|access-date=11 August 2015|archive-date=25 January 2016|archive-url=https://web.archive.org/web/20160125141511/http://www.thefreelibrary.com/ClearSpeed+Advance(TM)+Accelerator+Boards+Certified+by+Wolfram...-a0147498410|url-status=dead}}</ref>

In 2002, [[gridMathematica]] was introduced to allow user level [[Parallel computing|parallel programming]] on heterogeneous clusters and multiprocessor systems<ref>[http://www.macworld.com/news/2002/11/20/mathematica/index.php gridMathematica offers parallel computing solution] {{Webarchive|url=https://web.archive.org/web/20051202160438/http://www.macworld.com/news/2002/11/20/mathematica/index.php |date=2005-12-02 }} by Dennis Sellers, ''MacWorld'', November 20, 2002.</ref> and in 2008 parallel computing technology was included in all Mathematica licenses including support for grid technology such as [[Windows HPC Server 2008]], [[Windows Server 2003|Microsoft Compute Cluster Server]] and [[Sun Grid]].

Support for [[CUDA]] and [[OpenCL]] [[GPU]] hardware was added in 2010.<ref>{{cite web|url=https://www.wolfram.com/mathematica/new-in-8/cuda-and-opencl-support/|title=CUDA and OpenCL support added in Mathematica 8|access-date=13 April 2020}}</ref>

== Extensions ==
As of Version 14, there are 6,602 built-in functions and symbols in the Wolfram Language.<ref>{{Cite web |title=The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica |url=https://writings.stephenwolfram.com/2024/01/the-story-continues-announcing-version-14-of-wolfram-language-and-mathematica/ |access-date=2024-06-25 |website=writings.stephenwolfram.com |date=9 January 2024 |language=en}}</ref> 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.<ref>{{Cite web |title=The Wolfram Function Repository: Launching an Open Platform for Extending the Wolfram Language—Stephen Wolfram Writings |url=https://writings.stephenwolfram.com/2019/06/the-wolfram-function-repository-launching-an-open-platform-for-extending-the-wolfram-language/ |access-date=2022-05-16 |website=writings.stephenwolfram.com |date=11 June 2019 |language=en}}</ref> There are currently more than 3000 functions contributed as Resource Functions.<ref>{{Cite web |title=Alphabetic listing of Wolfram Resource Functions |url=https://resources.wolframcloud.com/FunctionRepository/all |access-date=2025-08-20|date=20 August 2025 |language=en}}</ref> 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.<ref>{{Cite web |title=Launching the Wolfram Data Repository: Data Publishing that Really Works—Stephen Wolfram Writings |url=https://writings.stephenwolfram.com/2017/04/launching-the-wolfram-data-repository-data-publishing-that-really-works/blog.wolfram.com/2017/04/20/launching-the-wolfram-data-repository-data-publishing-that-really-works/ |access-date=2022-05-16 |website=writings.stephenwolfram.com |date=20 April 2017 |language=en}}</ref>

Wolfram Mathematica is the basis of the Combinatorica package, which adds discrete mathematics functionality in combinatorics and graph theory to the program.<ref>{{Cite book |last=Skiena |first=Steven |title=Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica |publisher=Cambridge University Press |year=2003}}</ref>

== Connections to other applications, programming languages, and services==
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.<ref>{{cite web| url = https://www.wolfram.com/wstp/| title = Wolfram Symbolic Transfer Protocol (WSTP)}}</ref>

Wolfram Research freely distributes a developer kit for linking applications written in the programming language [[C (programming language)|C]] to the Mathematica kernel through WSTP using J/Link.,<ref name="macworld.com">[http://www.macworld.com/2002/11/reviews/mathematica/ Mathematica 4.2] {{webarchive|url=https://web.archive.org/web/20071121151440/http://www.macworld.com/2002/11/reviews/mathematica/ |date=2007-11-21 }} by Charles Seiter, ''Macworld'', November 1, 2002.</ref> a [[Java (programming language)|Java]] program that can ask Mathematica to perform computations. Similar functionality is achieved with .NET /Link,<ref>[http://www.wolfram.com/solutions/mathlink/netlink/ .NET/Link] {{Webarchive|url=https://web.archive.org/web/20100909043100/http://www.wolfram.com/solutions/mathlink/netlink/ |date=2010-09-09 }}: .NET/Link is a toolkit that integrates Mathematica and the Microsoft .NET Framework.</ref> but with [[.NET Framework|.NET]] programs instead of Java programs.

Other languages that connect to Mathematica include [[Haskell]],<ref>{{cite web|url=http://hackage.haskell.org/package/mathlink|title=mathlink: Write Mathematica packages in Haskell - Hackage|access-date=11 August 2015}}</ref> [[AppleScript]],<ref>{{cite web|url=http://www.unisoftwareplus.com/products/mathlinkosax/|title=MathLink for AppleScript|author=S.Kratky|access-date=11 August 2015|archive-date=17 July 2011|archive-url=https://web.archive.org/web/20110717163309/http://www.unisoftwareplus.com/products/mathlinkosax/|url-status=dead}}</ref> [[Racket (programming language)|Racket]],<ref>{{cite web|url=http://www.cs.utah.edu/~czhu/SchemeLink/mrmma.html|title=MrMathematica: Calling Mathematica from Scheme|access-date=11 August 2015}}</ref> [[Visual Basic]],<ref>{{cite web|url=http://library.wolfram.com/infocenter/TechNotes/4710/|title=Mathematica for ActiveX - from Wolfram Library Archive|access-date=11 August 2015}}</ref> [[Python (programming language)|Python]],<ref>{{cite web|url=https://code.google.com/p/pythonika/|title=erocarrera/pythonika|work=GitHub|access-date=11 August 2015}}</ref><ref>{{cite web|url=http://library.wolfram.com/infocenter/MathSource/585/|title=PYML (Python Mathematica interface) - from Wolfram Library Archive|access-date=11 August 2015}}</ref> and [[Clojure]].<ref>{{cite web|url=http://clojuratica.weebly.com/ |title=Clojuratica - Home |publisher=Clojuratica.weebly.com |access-date=2013-08-16}}</ref>

Mathematica supports the generation and execution of [[Modelica]] models for [[systems modeling]] and connects with [[Wolfram SystemModeler|Wolfram System Modeler]].

Links are also available to many third-party software packages and APIs.<ref>{{cite web|url=https://reference.wolfram.com/language/ref/ServiceConnect.html|title=Wolfram Documentation: ServiceConnect|access-date=4 August 2021}}</ref>

Mathematica can also capture real-time data from a variety of sources<ref>{{cite web| url = https://www.vernier.com/news/2017/08/25/vernier-and-mathematica/| title = Vernier and Mathematica| access-date = 2017-09-12| archive-date = 2019-05-29| archive-url = https://web.archive.org/web/20190529010854/https://www.vernier.com/news/2017/08/25/vernier-and-mathematica/| url-status = dead}}</ref> and can read and write to public blockchains ([[Bitcoin]], [[Ethereum]], and ARK).<ref>{{cite web|url=https://reference.wolfram.com/language/guide/Blockchain.html|title=Working with blockchains|access-date=15 April 2020}}</ref>

It supports import and export of over 220 data, image, video, sound, [[computer-aided design]] (CAD), [[geographic information system]]s (GIS),<ref>[http://www.cadalyst.com/general-software/mathematica-6-cadalyst-labs-review-6299 Mathematica 6 Labs Review] {{Webarchive|url=https://web.archive.org/web/20220325053439/http://www.cadalyst.com/general-software/mathematica-6-cadalyst-labs-review-6299 |date=2022-03-25 }} ''Cadalyst'' Feb 1, 2008</ref> document, and biomedical formats.

In 2019, support was added for compiling Wolfram Language code to [[LLVM]].<ref>{{cite web|url=https://www.wolfram.com/language/12/code-compilation/create-llvm-code.html|title=Create LLVM code|access-date=13 April 2020}}</ref>

Version 12.3 of the Wolfram Language added support for [[Arduino]].<ref>{{Cite web|title=Launching Version 12.3 of Wolfram Language & Mathematica—Stephen Wolfram Writings|url=https://writings.stephenwolfram.com/2021/05/launching-version-12-3-of-wolfram-language-mathematica/|access-date=2022-01-29|website=writings.stephenwolfram.com|date=20 May 2021 |language=en}}</ref>

== Computable data ==
Mathematica is also integrated with [[Wolfram Alpha]], an online [[answer 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).<ref>{{citation|chapter=Scientific and Technical Data|title=Mathematic Guide|chapter-url=http://reference.wolfram.com/mathematica/guide/ScientificAndTechnicalData.html|publisher=Wolfram Research|access-date=16 May 2012|url-status=dead|archive-url=https://web.archive.org/web/20120510202912/http://reference.wolfram.com/mathematica/guide/ScientificAndTechnicalData.html|archive-date=10 May 2012}}</ref>

== Reception ==
''[[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".<ref name="byte198901">{{Cite magazine |date=January 1989 |title=The BYTE Awards |url=https://archive.org/stream/byte-magazine-1989-01/1989_01_BYTE_14-01_PC_Communications_and_Annual_Awards_and_Digitizing_Tablets#page/n371/mode/2up |magazine=BYTE |page=327}}</ref>

Mathematica has been criticized for being closed source.<ref>{{Cite web|title=Paul Romer|url=https://paulromer.net/jupyter-mathematica-and-the-future-of-the-research-paper/|access-date=2021-08-05|website=paulromer.net}}</ref> Wolfram Research claims keeping Mathematica closed source is central to its business model and the continuity of the software.<ref>{{Cite web|title=Why Wolfram Tech Isn't Open Source—A Dozen Reasons—Wolfram Blog|url=https://blog.wolfram.com/2019/04/02/why-wolfram-tech-isnt-open-source-a-dozen-reasons/|access-date=2021-08-05|website=blog.wolfram.com|date=2 April 2019 |language=en}}</ref><ref>{{Cite web |title=Six Reasons Why the Wolfram Language Is (Like) Open Source—Wolfram Blog |url=https://blog.wolfram.com/2021/11/30/six-reasons-why-the-wolfram-language-is-like-open-source/ |access-date=2022-05-16 |website=blog.wolfram.com |date=30 November 2021 |language=en}}</ref>

== See also ==
{{Div col|colwidth=22em}}
* [[Comparison of multi-paradigm programming languages]]
* [[Comparison of numerical-analysis software]]
* [[Comparison of programming languages]]
* [[Comparison of regular expression engines]]
* [[Dynamic programming language]]
* [[Fourth-generation programming language]]
* [[Functional programming]]
* [[List of computer algebra systems]]
* [[List of computer simulation software]]
* [[List of information graphics software]]
* [[Literate programming]]
* [[Mathematical markup language]]
* [[Mathematical software]]
* [[SageMath]]
* [[Wolfram Language]]
* [[Wolfram SystemModeler]], a physical modeling and simulation tool which integrates with Mathematica
* [[WolframAlpha]], a web answer engine
{{Div col end}}

== References ==
{{Reflist}}

== External links ==
{{sisterlinks|d=y|n=no|s=no|commons=Category:Mathematica (software)|voy=no|m=no|mw=no|species=no|q=no|wikt=no|v=no}}
*{{Official website|https://www.wolfram.com/mathematica/}}
*[https://reference.wolfram.com/language/ Mathematica Documentation Center]
*[https://www.12000.org/my_notes/compare_mathematica/index.htm A little bit of Mathematica history] documenting the growth of code base and number of functions over time

{{Computer algebra systems}}
{{Numerical analysis software}}
{{Statistical software}}
{{Mathematical optimization software}}
{{Fractal software}}
{{Image Processing Software}}
{{Graph Analysis Software}}
{{Deep Learning Software}}
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