Wolfram Mathematica

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Wolfram Mathematica
Mathematica Logo.svg
Mathematica logistic bifurcation.png
Mathematica 8.0.0 Linux frontend
Developer(s)Wolfram Research
Initial releaseJune 23, 1988; 32 years ago (1988-06-23)[1]
Stable release12.2 (December 16, 2020; 4 months ago (2020-12-16)) [±][2]
Written inWolfram Language,[3] C/C++, Java[4]
PlatformWindows (10),[5] macOS, Linux, Raspbian, online service.[6] All platforms support 64-bit implementations.[7] (list)
Available inEnglish, Chinese, Japanese
TypeComputer algebra, numerical computations, information visualization, statistics, user interface creation

Wolfram Mathematica (usually termed Mathematica) is a software system with built-in libraries for several areas of technical computing that allow symbolic computation, manipulating matrices, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois.[8][9] The Wolfram Language is the programming language used in Mathematica.[10]

Notebook interface[edit]

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 original front end, designed by Theodore Gray[11] in 1988, consists of a notebook interface and allows the creation and editing of notebook documents that can contain code, plaintext, images, and graphics.[12]Notebooks can be used to create slide decks.

Alternatives to the Mathematica front end include Wolfram Workbench—an Eclipse-based integrated development environment (IDE) that was introduced in 2006. It provides project-based code development tools for Mathematica, including revision management, debugging, profiling, and testing.[13]

There is also a plugin for IntelliJ IDEA-based IDEs to work with Wolfram Language code that in addition to syntax highlighting can analyze and auto-complete local variables and defined functions.[14] The Mathematica Kernel also includes a command line front end.[15]

Other interfaces include JMath,[16] based on GNU Readline and WolframScript[17] which runs self-contained Mathematica programs (with arguments) from the UNIX command line.

High-performance computing[edit]

Capabilities for high-performance computing were extended with the introduction of packed arrays in version 4 (1999)[18] and sparse matrices (version 5, 2003),[19] 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.[20] This release included CPU-specific optimized libraries.[21] In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed.[22]

In 2002, gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems[23] 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.[24]

In 2019, support was added for compiling Wolfram Language code to LLVM.[25]

Connections to other applications, programming languages, and services[edit]

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 provides a general interface between the kernel and other applications.[26]

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.,[27] a Java program that can ask Mathematica to perform computations. Similar functionality is achieved with .NET /Link,[28] but with .NET programs instead of Java programs.

Other languages that connect to Mathematica include Haskell,[29] AppleScript,[30] Racket,[31] Visual Basic,[32] Python,[33][34] and Clojure.[35]

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

Links are also available to many third party software packages, [36] and Mathematica can call a variety of cloud services.[37]

Mathematica can also capture real-time data from a variety of sources[38] and can read and write to public blockchains (Bitcoin, Ethereum, and ARK).[39]

It supports import and export of over 220 data, image, video, sound, computer-aided design (CAD), geographic information systems (GIS),[40] document, and biomedical formats

Computable data[edit]

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).[41]


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".[42]

See also[edit]


  1. ^ Wolfram, Stephen (23 Jun 2008), Mathematica Turns 20 Today, Wolfram, retrieved 16 May 2012
  2. ^ "Mathematica Quick Revision History". Retrieved 2020-12-16.
  3. ^ "Celebrating Mathematica's First Quarter Century". Retrieved 11 August 2015.
  4. ^ The Software Engineering of Mathematica—Wolfram Mathematica 9 Documentation. Reference.wolfram.com. Retrieved on 2015-03-23.
  5. ^ "Mathematica 12 System Requirements and Platform Availability". Retrieved 16 December 2020.
  6. ^ Raspberry Pi Includes Mathematica for Free The Verge
  7. ^ "Wolfram Mathematica". Retrieved 11 August 2015.
  8. ^ Stephen Wolfram: Simple Solutions; The iconoclastic physicist's Mathematica software nails complex puzzles, BusinessWeek, October 3, 2005.
  9. ^ "Contact Wolfram Research". Retrieved 11 August 2015.
  10. ^ "Stephen Wolfram's new programming language: Can he make the world computable?". Slate Magazine. Retrieved 11 August 2015.
  11. ^ Patent US8407580 Google Patent Search
  12. ^ Hayes, Brian (1990-01-01). "Thoughts on Mathematica" (PDF). Pixel.
  13. ^ "Wolfram intros Workbench IDE for Mathematica". Macworld. 21 June 2006. Retrieved 11 August 2015.
  14. ^ Mathematica plugin for IntelliJ IDEA
  15. ^ Using a Text-Based Interface documentation at wolfram.com
  16. ^ "JMath: A GNU Readline based frontend for Mathematica". Retrieved 11 August 2015.
  17. ^ "Directory listing". Retrieved 18 April 2019.
  18. ^ 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.
  19. ^ Mathematica 5.1: additional features make software well-suited for operations research professionals by ManMohan S. Sodhi, OR/MS Today, December 1, 2004.
  20. ^ The 21st annual Editors' Choice Awards, Macworld, February 1, 2006.
  21. ^ "Mathematica is tuned to take advantage of CPU features when available". Retrieved 13 April 2020.
  22. ^ "ClearSpeed Advance Accelerator Boards Certified by Wolfram Research; Math Coprocessors Enable Mathematica Users to Quadruple Performance". Retrieved 11 August 2015.
  23. ^ gridMathematica offers parallel computing solution by Dennis Sellers, MacWorld, November 20, 2002.
  24. ^ "CUDA and OpenCL support added in Mathematica 8". Retrieved 13 April 2020.
  25. ^ "Create LLVM code". Retrieved 13 April 2020.
  26. ^ Wolfram Symbolic Transfer Protocol (WSTP)
  27. ^ Mathematica 4.2 Archived 2007-11-21 at the Wayback Machine by Charles Seiter, Macworld, November 1, 2002.
  28. ^ .NET/Link: .NET/Link is a toolkit that integrates Mathematica and the Microsoft .NET Framework.
  29. ^ "mathlink: Write Mathematica packages in Haskell - Hackage". Retrieved 11 August 2015.
  30. ^ S.Kratky. "MathLink for AppleScript". Retrieved 11 August 2015.
  31. ^ "MrMathematica: Calling Mathematica from Scheme". Retrieved 11 August 2015.
  32. ^ "Mathematica for ActiveX - from Wolfram Library Archive". Retrieved 11 August 2015.
  33. ^ "erocarrera/pythonika". GitHub. Retrieved 11 August 2015.
  34. ^ "PYML (Python Mathematica interface) - from Wolfram Library Archive". Retrieved 11 August 2015.
  35. ^ "Clojuratica - Home". Clojuratica.weebly.com. Retrieved 2013-08-16.
  36. ^ "shadanan/HadoopLink". GitHub. Retrieved 11 August 2015.
  37. ^ Wolfram Language Documentation Yelp service Cconnection
  38. ^ Vernier and Mathematica
  39. ^ "Working with blockchains". Retrieved 15 April 2020.
  40. ^ Mathematica 6 Labs Review Cadalyst Feb 1, 2008
  41. ^ "Scientific and Technical Data", Mathematic Guide, Wolfram Research, archived from the original on 10 May 2012, retrieved 16 May 2012
  42. ^ "The BYTE Awards". BYTE. January 1989. p. 327.

External links[edit]