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Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing. It was originally conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois.[2][3]

A plot and manipulation dialog created with Mathematica

Features of Mathematica include:[4]

* Elementary mathematical function library
* Special mathematical function library
* Matrix and data manipulation tools including support for sparse arrays
* Support for complex number, arbitrary precision, interval arithmetic and symbolic computation
* 2D and 3D data and function visualization and animation tools
* Solvers for systems of equations, diophantine equations, ODEs, PDEs, DAEs, DDEs and recurrence relations
* Numeric and symbolic tools for discrete and continuous calculus
* Multivariate statistics libraries
* Constrained and unconstrained local and global optimization
* Programming language supporting procedural, functional and object oriented constructs
* Toolkit for adding user interfaces to calculations and applications
* Tools for image processing [5] and morphological image processing
* Tools for visualizing and analysing graphs
* Tools for combinatoric problems
* Data mining tools such as cluster analysis, sequence alignment and pattern matching
* Number theory function library
* Continuous and discrete integral transforms
* Import and export filters for data, images, video, sound, CAD, GIS[6], document and biomedical formats
* Database collection for mathematical, scientific, and socio-economic information
* Notebook interface for review and re-use of previous inputs and outputs including graphics and text annotations
* Technical word processing including formula editing and automated report generating
* Tools for connecting to SQL, Java, .NET, C++, FORTRAN and http based systems
* Tools for parallel programing


Mathematica is split into two parts, the "kernel" and the front end. The kernel interprets expressions (Mathematica code) and returns result expressions.

The front end, designed by Theodore Gray, provides a GUI, which allows the creation and editing of Notebook documents containing program code with prettyprinting, formatted text together with results including typeset mathematics, graphics, GUI components, tables, and sounds. All contents and formatting can be generated algorithmically or interactively edited. One level of "undo" is supported, along with most standard word processing capabilities.

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 analysed by Mathematica programs. This allows conversion to other formats such as TeX or XML.

The front end includes development tools such as a debugger, input completion and automatic syntax coloring.

The kernel and the front end communicate via the MathLink protocol. It is possible to use the kernel on one computer and the front end on another.

The standard front end is used by default, but alternative front ends are available. They include the Wolfram Workbench, an Eclipse based IDE, introduced in 2006. It provides project-based code development tools for Mathematica, including revision management, debugging, profiling, and testing.[7] Mathematica also includes a command line front end.

High-performance computing

In recent years, the capabilities for high-performance computing have been extended with the introduction of packed arrays (version 4, 1999) [8], sparse matrices (version 5, 2003)[9], 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.[10] This release included CPU specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed.[11]

In 2002, gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems [12] 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.

Planned support for CUDA hardware was announced in 2008 but is still only provided by a third party add-on.


Several solutions are available for deploying applications written in 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.[13]
* Mathematica Player is a free interactive player is provided for running Mathematica programs that have been digitally signed for non-commercial use via a Wolfram Research web service, or published on the Wolfram Demonstrations Project website. It can also view unsigned Mathematica files, but not run them.
* 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.

Connections with other applications

Communication with other applications occurs through a protocol called MathLink. It allows communication between the Mathematica kernel and front-end, and also provides a general interface between the kernel and other applications.

Although Mathematica has a large array of functionality, a number of interfaces to other software have been developed, for use where other programs have functionality that Mathematica does not provide, to enhance those applications, or to access legacy code.


* Wolfram Research freely distributes a developer kit for linking applications written in the C programming language to the Mathematica kernel through MathLink.[14]
* Using .NET/Link.[15] , a .NET program can ask Mathematica to perform computations; likewise, a Mathematica program can load .NET classes, manipulate .NET objects and perform method calls. This makes it possible to build .NET graphical user interfaces from within Mathematica.
* Similar functionality is achieved with J/Link.[16], but with Java programs instead of .NET programs.
* GUIKit allows the construction of custom interfaces to Mathematica using the Java Swing libraries.
* Communication with SQL databases is achieved through built-in support for JDBC.[17]
* Mathematica can also install web services from a WSDL description.[18][19]
* Other languages that connect to Mathematica include Haskell[20], AppleScript[21], PLT Scheme[22], Visual Basic[23], Python[24] and Clojure[25].


* Bi-directional linkage between Mathematica and OpenOffice.org Calc spreadsheets is supported with a commercial package CalcLink[26].
* Microsoft Excel can call Mathematica via a commercial add-on [27]

Specialized mathematical software

* MATLAB can be called from Mathematica, using freeware software written by Wolfram Research[28].
* R can be called from within Mathematica using a commercial interface [29] [30] .
* Sage can be called from within Mathematica[31][32].
* SINGULAR can be called from within Mathematica. [33]
* MathModelica integrates with Mathematica
* Mathematica can be called from Origin [34]
* Mathematical equations can be exchanged with other computational or typesetting software as MathML.
* Mathematica content can be converted into Maple content with the Mma Translator Package[35]

Data acquisition

* Mathematica can link to LabView[36].
* Real-time streaming financial data can be provided with a commercial package DDFLink[37].
* GPIB (IEEE 488) devices can be accessed via a free package [38]
* USB devices can be connected to Mathematica by use of a commercial add-on [39]
* A free package [40] written for Mathematica 5.2 connects Mathematica to serial, parallel and USB devices.
* Mathematica automatically detects and reads from HID devices.

Alternative Interfaces

* JMath is a third-party front end based on GNU readline that runs on UNIX-like operating systems.[41]
* MASH runs self contained Mathematica programs (with arguments) from the UNIX command line.[42]

[edit] Computable data
A stream plot of live weather data

Mathematica includes collections of curated data in a consistent framework for immediate computation. Data can be accessed programmatically to inform or test models and is updated automatically from a data server at Wolfram Research[43]. Some data such as share prices and weather are delivered in real-time. Data sets currently include:

* Astronomical data: 99 properties of 155,000 astronomical bodies
* Chemical data: 111 properties of 34,000 chemical compounds, 86 properties of 118 chemical elements and 35 properties of 1000 subatomic particles
* Geopolitical data: 225 properties of 237 countries and 14 properties of 160,000 cities around the world
* Financial data: 71 historical and real-time properties of 186,000 shares and financial instruments
* Mathematical data: 89 properties of 187 polyhedra, 258 properties of 3000 graphs, 63 properties of 6 knots, 37 properties of 21 lattice structures, 32 properties of 52 geodesic schemes
* Language data: 37 properties of 149,000 English words. 26 additional language dictionaries
* Biomedical data: 41 properties of all 40,000 human genes, 30 properties of 27,000 proteins
* Weather data: live and historical measurements of 43 properties of 17,000 weather stations around the world


Mathematica is proprietary software restricted by both trade secret and copyright law.[44]

A regular single-user license for Mathematica used in a commercial environment costs $2495. It includes four additional kernels for parallel computations and one year of service that includes updates, technical support, a home use license, a webMathematica Amateur license[45], a Wolfram Workbench license and three Mathematica Player Pro licenses. Discounts are available for government, charity, educational, pre-college, school, student, home use[46] and retiree use and depend on geographical region. Student licenses cost $140. Educational site licenses allow use by students at home. A license manager similar to FLEXnet is available to provide sharing of licenses within a group.

Platform availability

Mathematica 7 is supported on various versions of Linux, Apple's Mac OS X, NT-based Microsoft Windows, and Sun's Solaris platforms. All platforms are supported with 64-bit implementations.[47] Earlier versions of Mathematica up to 6.0.3 supported other operating systems, including AIX, Convex, HP-UX, IRIX, MS-DOS, NeXTSTEP, OS/2, Ultrix and Windows Me[48].

The Mathematica Home Edition is a 32-bit application on Microsoft Windows, Linux and Mac OS X (Intel).


Support via email is available to registered users by emailing support@wolfram.com.

There is no official public support forum for professional users, although there is an official support forum for students.[49] Posts are reviewed by a Wolfram Research moderator before they appear on the student forum.

MathGroup is a moderated email list and internet newsgroup * comp.soft-sys.math.mathematica. It has more than 100,000 posts [50] and is the dominant public forum although it is not controlled by Wolfram Research. The moderator is Steve Christensen. Wolfram Research staff regularly answer questions on Mathgroup. The posts are archived by Wolfram Research.

There are several other unofficial support forums, which are unmoderated, so posts appear without delay. These include the newsgroup sci.math.symbolic and http://www.mathematica-users.org, but none have the popularity of the dominant Mathgroup.


There are a large number of books written about Mathematica. While some are general introductions, others cover specific areas such as graphics, numerics, symbolic computation, programming etc.

The 408 page book Mathematica programming: An advanced Introduction written by Leonid Shifrin, released under the Creative Commons License may be read online or downloaded as a PDF file for no charge.

Version history

Mathematica built on the ideas in Cole and Wolfram's earlier Symbolic Manipulation Program (SMP).[51][52]

Wolfram Research has released the following versions of Mathematica[53]:

* Mathematica 1.0 (1988)[54]
* Mathematica 1.1 (1989)[55]
* Mathematica 1.2 (1989)[56]
* Mathematica 2.0 (1991)[57]
* Mathematica 2.1 (1992)[14]
* Mathematica 2.2 (1993)[58]
* Mathematica 3.0 (1996)[59]
* Mathematica 4.0 (1999)[60]
* Mathematica 4.1 (2000)
* Mathematica 4.2 (2002)[16]
* Mathematica 5.0 (2003)[61]
* Mathematica 5.1 (2004)[62]
* Mathematica 5.2 (2005)[63]
* Mathematica 6.0 (2007)[64]
* Mathematica 6.0.1 (2007)
* Mathematica 6.0.2 (2008)
* Mathematica 6.0.3 (2008)
* Mathematica 7.0 (2008)[65]
* Mathematica 7.0.1 (2009)

See also

* Publicon, a technical software publication marketed by Wolfram Research
* Wolfram Alpha
* IMTEK Mathematica Supplement, an open source Mathematica add-on for Finite Element Simulation
* List of computer simulation software
* List of graphing software
* Mathematical software


1. ^ http://blog.wolfram.com/2008/06/23/mathematica-turns-20-today/
2. ^ Stephen Wolfram: Simple Solutions; The iconoclastic physicist's Mathematica software nails complex puzzles, BusinessWeek, October 3, 2005.
3. ^ Wolfram Research Contact Info
4. ^ Mathematica documentation
5. ^ Review: Mathematica 7. Technical computing powerhouse gets more oomph Macworld, Jan 2009
6. ^ Mathematica 6 Labs Review Cadalyst Feb 1, 2008
7. ^ MacWorld review of Wolfram Workbench
8. ^ 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.
9. ^ Mathematica 5.1: additional features make software well-suited for operations research professionals by ManMohan S. Sodhi, OR/MS Today, December 1, 2004.
10. ^ The 21st annual Editors' Choice Awards, Macworld, February 1, 2006.
11. ^ ClearSpeed Advance(TM) Accelerator Boards Certified by Wolfram Research; Math Coprocessors Enable Mathematica Users to Quadruple Performance.
12. ^ gridMathematica offers parallel computing solution by Dennis Sellers, MacWorld, November 20, 2002.
13. ^ Mathematica Player Pro - new Application Delivery System for Mathematica www.gizmag.com
14. ^ a b New Mathematica: faster, leaner, linkable and QuickTime-compatible: MathLink kit allows ties to other apps. (Wolfram Research Inc. ships Mathematica 2.1, new QuickTime-compatible version of Mathematica software) by Daniel Todd, MacWeek, June 15, 1992.
15. ^ .NET/Link: .NET/Link is a toolkit that integrates Mathematica and the Microsoft .NET Framework.
16. ^ a b Mathematica 4.2: [[Feature-rich Feature-Rich Math Program Integrates with the Web, Adds Full Java Support] by Charles Seiter, Macworld, November 1, 2002.
17. ^ Mathematica 5.1 Available , Database Journal, Jan 3, 2005.
18. ^ Mathematical Web Services: W3C Note 1 August 2003
19. ^ Introduction to Web Services, Mathematica Web Services Tutorial
20. ^ Haskell pakages
21. ^ Unisoftware plus
22. ^ MrMathematica website
23. ^ [http://library.wolfram.com/infocenter/TechNotes/4710/ Mathematica for ActivX
24. ^ Pythonika MathLink module for Python
25. ^ [1]
26. ^ CalcLink Lauschke Consulting
27. ^ [2] Mathematica Link for Excel
28. ^ Mathsource item #618 for calling MATLAB from Mathematica Roger Germundsson from Wolfram Research
29. ^ R-Link Calling R from within Mathematica
30. ^ Using R's functionality with Mathematica Wolfram Technology Conference in 2006
31. ^ http://facstaff.unca.edu/mcmcclur/Mathematica/Sage/ Calling Sage from Mathematica
32. ^ http://facstaff.unca.edu/mcmcclur/Mathematica/Sage/UsingSage.nb A Mathematica notebook to call Sage from Mathematica.
33. ^ [3] Manuel Kauers and Viktor Levandovskyy of the Johannes Kepler University in Austria
34. ^ * Interface Links Origin And Mathematica Software Electronic Design
35. ^ [4]
36. ^ Mathematica Link to Labview BetterView Consulting
37. ^ DDFLink Lauschke Consulting
38. ^ GITM SourceForge
39. ^ BTopTools A commercial interface to USB devices
40. ^ [http://library.wolfram.com/infocenter/MathSource/6380/ Interfacing Hardware with Mathematica]
41. ^ JMath website
42. ^ MASH website
43. ^ http://reference.wolfram.com/mathematica/guide/ScientificAndTechnicalData.html
44. ^ Wolfram Mathematica License Agreement
45. ^ webMathematica terms
46. ^ Mathematica Home Edition Released Macworld, Feb 2009
47. ^ Supported platforms list
48. ^ Mathematica 6 Platform Availability
49. ^ Official support forum for students
50. ^ Mathgroup
51. ^ Math, the universe, and Stephen: the author of Mathematica created a whirlwind of scientific controversy this year when, after more than 10 years of research, he published his treatise on the ability of simple structures to create unpredictable complex patterns. (2002 Scientist Of The Year).(Stephen Wolfram) by Tim Studt, R&D, November 1 , 2002.
52. ^ A Top Scientist's Latest: Math Software by Andrew Pollack, The New York Times, June 24, 19988.
53. ^ Quick Revision History of Mathematica
54. ^ Supercomputer Pictures Solve the Once Insoluble, John Markoff, October 30, 1988.
55. ^ Mathematica 1.1. Biotechnology Software. Vogel, W. K. (1989)
56. ^ Mathematica 1.2 adds new graphics options: upgrade also promises concurrent operations by Elinor Craig, MacWeek, July 25, 1989.
57. ^ Mathematica + 283 functions = Mathematica 2.0 by Raines Cohen, MacWeek, January 15, 1991.
58. ^ New version of Mathematica, Mechanical Engineering, June 1, 1993.
59. ^ New Mathematica by Stephen H. Wildstrom, BusinessWeek, June 15, 1997.
60. ^ Mathematica 4.0 by Charles Seiters, Macworld, October 1, 1999.
61. ^ Mathematica 5.0 Adds Up: Exactly 15 years after Mathematica's initial release, Wolfram Research has released Mathematica , PC Magazine, September 3, 2003.
62. ^ Mathematica 5.1's Web Services Add Up; Mathematica 5.1 delivers improvements over Version 5.0 that are vastly out of proportion for a .1 upgrade. by Peter Coffee, eWeek, December 6, 2004.
63. ^ Mathematica hits 64-bit, MacWorld UK, July 13, 2005.
64. ^ Mathematica 6: Felix Grant finds that version 6 of Wolfram Research's symbolic mathematical software really does live up to its expectations. Scientific Computing, 2007.
65. ^ Mathematica 7: Released Wolfram Blog, 2008.

External links

* Official website
* Wolfram Research
* Mathematica Documentation Center
* Google Directories entry containing a wide variety of useful links and tutorials
* Mathematica Photo Gallery, examples of art using Mathematica
* Will it rot my students' brains if they use Mathematica? by Theodore W. Gray and Jerry Glynn, excerpted from The Beginner's Guide to Mathematica V4, published by Cambridge University Press.
* "Levels Of A Mathematica Expression" by Enrique Zeleny, Wolfram Demonstrations Project.
* A little bit of Mathematica history documenting the growth of code base and number of functions over time.
* Comparison of mathematical programs for data analysis ScientificWeb

* Mathematica by example

Mathematics Software

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