Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others. The system is used in many technical, scientific, engineering, mathematical, and computing fields. It was conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois.[7][8] The Wolfram Language is the programming language used in Mathematica.[9]

The Notebook interface

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

The front end, designed by Theodore Gray[10] in 1988, provides a graphical user interface (GUI), which allows the creation and editing of Notebook documents[11] containing program code with Syntax highlighting, formatted text together with results including typeset mathematics, graphics, GUI components, tables, and sounds. All content and formatting can be generated algorithmically or edited interactively. Standard word processing capabilities are supported, including real-time multi-lingual spell-checking.

Documents can be structured using a hierarchy of cells, which allow for outlining and sectioning of a document and support automatic numbering index creation. Documents can be presented in a slideshow environment for presentations. Notebooks and their contents are represented as Mathematica expressions that can be created, modified or analyzed by Mathematica programs or converted to other formats.

Presenter tools support the creation of slide-show style presentations that support interactive elements and code execution during the presentation.

Among the alternative front ends is the Wolfram Workbench, an Eclipse based integrated development environment (IDE), introduced in 2006. It provides project-based code development tools for Mathematica, including revision management, debugging, profiling, and testing.[12] There is a plugin for IntelliJ IDEA based IDEs to work with Wolfram Language code which in addition to syntax highlighting can analyse and auto-complete local variables and defined functions.[13] The Mathematica Kernel also includes a command line front end.[14] Other interfaces include JMath,[15] based on GNU readline and WolframScript[16] 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 arrays in version 4 (1999)[17] and sparse matrices (version 5, 2003),[18] and by adopting the GNU Multi-Precision Library to evaluate high-precision arithmetic.

Version 5.2 (2005) added automatic multi-threading when computations are performed on multi-core computers.[19] This release included CPU-specific optimized libraries.[20] In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed.[21]

In 2002, gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems[22] and in 2008 parallel computing technology was included in all Mathematica licenses including support for grid technology such as Windows HPC Server 2008, Microsoft Compute Cluster Server and Sun Grid.

Support for CUDA and OpenCL GPU hardware was added in 2010.[23] Also, since version 8 it can generate C code, which is automatically compiled by a system C compiler, such as GCC or Microsoft Visual Studio.

In 2019 support was added for compiling Wolfram Language code to LLVM.[24]

Features

Features of Wolfram Mathematica include:[25]

Libraries of mathematical elementary functions and special functions including Number theory function and combinatoric functions

Support for complex number, arbitrary precision arithmetic, interval arithmetic, numbers with uncertainty censored data, temporal data, time series, and unit based data, and symbolic computation

Matrix and data manipulation tools including support for sparse arrays and associative arrays

2D and 3D data, function and geo visualization and animation tools

Solvers for systems of equations, diophantine equations, ordinary differential equations (ODEs), non-linear partial differential equations (PDEs), differential algebraic equations (DAEs), delay differential equations (DDEs), stochastic differential equations (SDEs), and recurrence relations

Finite element analysis including 2D and 3D adaptive mesh generation

Numeric and symbolic tools for discrete and continuous calculus including continuous and discrete integral transforms

Constrained and unconstrained local and global optimization

Multivariate statistics libraries including fitting, hypothesis testing, and probability and expectation calculations on over 160 distributions.

Calculations and simulations on random processes and queues

Supervised and unsupervised machine learning tools for data, images and sounds including artificial neural networks

Tools for text mining including regular expressions, semantic analysis, sentiment analysis and fact extraction

Data mining tools such as cluster analysis, sequence alignment and pattern matching

Computational geometry in 2D, 3D and higher dimensions and Euclid-style 2D geometry

Libraries for signal processing including wavelet analysis on sounds, images and data

Audio processing filters and measures including audio recognition

Tools for 2D and 3D image processing[26] and morphological image processing including image recognition

Tools for visualizing and analysing directed and undirected graphs

Tools for cryptography including symmetric and asymmetric keys, hashing and elliptic curve cryptography

Tools for financial calculations including bonds, annuities, derivatives, options etc.

Group theory and symbolic tensor functions

Tools for Automated theorem proving

Linear and non-linear control system libraries

Microcontroller kit for giving symbolic specifications from which it automatically generates and deploys code to run autonomously in microcontrollers.

Tools for computational chemistry including bond length and angle calculations and databases of chemical properties

Programming language supporting procedural, functional, object-oriented constructs and parallel programming

Toolkit for adding user interfaces to calculations and applications

Tools for creating and deploying cloud based computational applications and services

Tools to connect to dynamic-link library (DLL), Java, .NET, C++, Fortran, CUDA, OpenCL, and Hypertext Transfer Protocol (HTTP) based systems

Using both "free-form linguistic input" (a natural language user interface)[27][28] and Wolfram Language in notebook when connected to the Internet

Deployment

This list is incomplete; you can help by expanding it.

There are several ways to deploy applications written in Wolfram Mathematica:

Mathematica Player Pro is a runtime version of Mathematica that will run any Mathematica application but does not allow editing or creation of the code.[29]

A free-of-charge version, Wolfram CDF Player, is provided for running Mathematica programs that have been saved in the Computable Document Format (CDF).[30] It can also view standard Mathematica files, but not run them. It includes plugins for common web browsers on Windows and Macintosh.

webMathematica allows a web browser to act as a front end to a remote Mathematica server. It is designed to allow a user-written application to be remotely accessed via a browser on any platform. It may not be used to give full access to Mathematica. Due to bandwidth limitations interactive 3D graphics is not fully supported within a web browser.

Wolfram Language code can be converted to C code or to an automatically generated DLL.

Wolfram Language code can be run on a Wolfram cloud service as a web-app or as an API either on Wolfram-hosted servers or in a private installation of the Wolfram Enterprise Private Cloud.

Connections to other applications, programming languages, and services

Communication with other applications occurs through a protocol called Wolfram Symbolic Transfer Protocol (WSTP). It allows communication between the Wolfram Mathematica kernel and front-end, and also provides a general interface between the kernel and other applications.[31] Wolfram Research freely distributes a developer kit for linking applications written in the programming language C to the Mathematica kernel through WSTP. Using J/Link.,[32] a Java program can ask Mathematica to perform computations; likewise, a Mathematica program can load Java classes, manipulate Java objects, and perform method calls. Similar functionality is achieved with .NET /Link,[33] but with .NET programs instead of Java programs. Other languages that connect to Mathematica include Haskell,[34] AppleScript,[35] Racket,[36] Visual Basic,[37] Python,[38][39] and Clojure.[40]

Mathematica supports the generation and execution of Modelica models for Systems modeling and connects with Wolfram System Modeler.

Links are available to many third party software packages including OpenOffice.org Calc,[41] Microsoft Excel,[42] MATLAB,[43][44][45] R,[46] SageMath (which can also pull up Mathematica),[47][48][49][50] Singular,[51] Wolfram SystemModeler, and Origin.[52] It also links to the Unity game engine and the OpenAI Gym. Mathematical equations can be exchanged with other computational or typesetting software via MathML.

Mathematica includes interfaces to SQL databases (via Java Database Connectivity JDBC),[53] MongoDB, and it can access RDF graph databases via SPARQL. Mathematica can also install web services from a Web Services Description Language (WSDL) description.[54][55] It can access HDFS data via Hadoop.[56].

Mathematica can call a variety of cloud services to retrieve or send data including arXiv, Bing, ChemSpider, CrossRef, Dropbox, Facebook, Federal Reserve, Fitbit, Flickr, Google (Analytics, Calendar, Contacts, Custom search, Plus, search, translate), Instagram, LinkedIn, MailChimp, Microsoft Translator, Mixpanel, OpenLibrary, OpenPHACTS, PubChem, PubMed, Reddit, RunKeeper, SeatGeek, SurveyMonkey, Twilio, Twitter, Wikipedia, and Yelp.[57]

Mathematica can capture real-time data via a link to LabVIEW,[58] from financial data feeds,[59] and directly from hardware devices via GPIB (IEEE 488),[60] USB,[61] and serial interfaces.[62] It automatically detects and reads from devices following the HID USB protocol. It can read directly from a range of Vernier sensors that are Go!Link-compatible.[63]

Mathematica can read and write to public blockchains (Bitcoin, Ethereum, and ARK).[64]

It supports import and export of over 220 data, image, video, sound, computer-aided design (CAD), geographic information systems (GIS),[65] document, and biomedical formats

Computable data

A stream plot of live weather data

Wolfram Mathematica includes collections of curated data provided for use in computations. Mathematica is also integrated with Wolfram Alpha, an online computational knowledge answer engine which provides additional data, some of which is kept updated in real time. Some of the data sets include astronomical, chemical, geopolitical, language, biomedical and weather data, in addition to mathematical data (such as knots and polyhedra).[66]

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".[67]

Version history

Mathematica version history

Wolfram Mathematica built on the ideas in Cole and Wolfram's earlier Symbolic Manipulation Program (SMP).[68][69] The name of the program "Mathematica" was suggested to Stephen Wolfram by Apple cofounder Steve Jobs although Wolfram had thought about it earlier and rejected it.[70]

Wolfram Research has released the following versions of Mathematica:[71]

1.0 – June 23, 1988[72][73][74][75]

1.1 – October 31, 1988

1.2 – August 1, 1989[75][76]

2.0 – January 15, 1991[75][77]

2.1 – June 15, 1992[75]

2.2 – June 1, 1993[75][78]

3.0 – September 3, 1996[79]

4.0 – May 19, 1999[75][80]

4.1 – November 2, 2000[75]

4.2 – November 1, 2002[75]

5.0 – June 12, 2003[75][81]

5.1 – October 25, 2004[75][82]

5.2 – June 20, 2005[75][83]

6.0 – May 1, 2007[84][85]

7.0 – November 18, 2008[86]

8.0 – November 15, 2010[87]

9.0 – November 28, 2012[88]

10.0 – July 9, 2014[89]

10.1 – March 30, 2015[90]

10.2 – July 14, 2015[91]

10.3 – October 15, 2015

10.4 – March 2, 2016

11.0.0 – August 8, 2016[92]

11.0.1 – September 28, 2016

11.1 – March 16, 2017[93]

11.1.1 – April 25, 2017

11.2 – September 14, 2017[94]

11.3 – March 8, 2018[95]

12.0 – April 16, 2019[96]

12.1 - March 18, 2020[97]

12.1.1 – June 17, 2020[98]

See also

Comparison of multi-paradigm programming languages

Comparison of numerical analysis software

Comparison of programming languages

Comparison of regular expression engines

Computational X

Dynamic programming language

Fourth-generation programming language

Functional programming

List of computer algebra systems

List of computer simulation software

List of graphing software

Literate programming

Mathematical markup language

Mathematical software

Wolfram Alpha, a web answer engine

Wolfram Language

Wolfram SystemModeler, a physical modeling and simulation tool which integrates with Mathematica

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Raspberry Pi Includes Mathematica for Free The Verge

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Wolfram Symbolic Transfer Protocol (WSTP)

Mathematica 4.2 Archived 2007-11-21 at the Wayback Machine by Charles Seiter, Macworld, November 1, 2002.

.NET/Link: .NET/Link is a toolkit that integrates Mathematica and the Microsoft .NET Framework.

"mathlink: Write Mathematica packages in Haskell - Hackage". Retrieved 11 August 2015.

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"Clojuratica - Home". Clojuratica.weebly.com. Retrieved 2013-08-16.

CalcLink Lauschke Consulting

"Mathematica Link for Excel: Bringing the Power of Mathematica to Excel". Retrieved 11 August 2015.

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"MaMa: Calling MATLAB from Mathematica with MathLink - from Wolfram Library Archive". Retrieved 11 August 2015.

RLink Mathematica Documentation

Gourgoulhon, Eric; Bejger, Michal; Mancini, Marco (21 Dec 2014). "Tensor calculus with open-source software: the SageManifolds project". Journal of Physics: Conference Series. 600: 012002. arXiv:1412.4765. Bibcode:2015JPhCS.600a2002G. doi:10.1088/1742-6596/600/1/012002.

"Interface to Mathematica - Sage Reference Manual v7.4: Interpreter Interfaces". doc.sagemath.org. Retrieved 2017-01-08.

"Using Mathematica within Sagemath | LSUMath". www.math.lsu.edu. Retrieved 2017-01-08.

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"shadanan/HadoopLink". GitHub. Retrieved 11 August 2015.

Wolfram Language Documentation Yelp service Cconnection

Mathematica Link to Labview BetterView Consulting

DDFLink Lauschke Consulting

GITM SourceForge. Note that the GITM project currently (as of 2014-08-03) has no downloadable artefacts and appears to be inactive so GPIB support for Mathematica may not actually exist.

BTopTools A commercial interface to USB devices

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Vernier and Mathematica

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Mathematica 5.0 Adds Up: Exactly 15 years after Mathematica's initial release, Wolfram Research has released Mathematica, PC Magazine, September 3, 2003.

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External links

Official website

Mathematica Documentation Center

Wolfram Open Cloud limited free access to Mathematica via a browser

Image identification website powered by Mathematica

Wolfram Demonstrations Project Mathematica based demonstrations

A little bit of Mathematica history documenting the growth of code base and number of functions over time

Wolfram Screencast & Video Gallery: Hands-on Start to Mathematica

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

Hellenica World - Scientific Library

Retrieved from "http://en.wikipedia.org/"

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