Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow

machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

symbolic computation In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions ...

, data manipulation, network analysis, time series analysis, NLP,

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

, plotting functions and various types of data, implementation of

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

s, creation of

user interface In the industrial design field of human–computer interaction, a user interface (UI) is the space where interactions between humans and machines occur. The goal of this interaction is to allow effective operation and control of the machine f ...

s, and interfacing with programs written in other

programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...

s. It was conceived by

Stephen Wolfram Stephen Wolfram (; born 29 August 1959) is a British-American computer scientist, physicist, and businessman. He is known for his work in computer science, mathematics, and theoretical physics. In 2012, he was named a fellow of the American Ma ...

, and is developed by

Wolfram Research Wolfram Research, Inc. ( ) is an American multinational company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988. Other products include Wo ...

of Champaign, Illinois. The

Wolfram Language The Wolfram Language ( ) is a general multi-paradigm programming language developed by Wolfram Research. It emphasizes symbolic computation, functional programming, and rule-based programming and can employ arbitrary structures and data. It is ...

is the programming language used in ''Mathematica''. Mathematica 1.0 was released on June 23, 1988 in

Champaign, Illinois Champaign ( ) is a city in Champaign County, Illinois, United States. The population was 88,302 at the 2020 census. It is the tenth-most populous municipality in Illinois and the fourth most populous city in Illinois outside the Chicago metropo ...

and

Santa Clara, California Santa Clara (; Spanish for " Saint Clare") is a city in Santa Clara County, California. The city's population was 127,647 at the 2020 census, making it the eighth-most populous city in the Bay Area. Located in the southern Bay Area, the cit ...

. __TOC__

Notebook interface

Wolfram Mathematica (called ''Mathematica'' by some of its users) 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 Theodore W. "Theo" Gray is a co-founder of Wolfram Research, science author, and co-founder of app developer Touch Press. Education Theodore Gray was educated at the University of Illinois Laboratory High School. He would later graduate wit ...

in 1988, consists of a

notebook interface A notebook interface (also called a computational notebook) is a virtual notebook environment used for literate programming, a method of writing computer programs. Some notebooks are WYSIWYG environments including executable calculations embedded i ...

and allows the creation and editing of notebook documents that can contain code, plaintext, images, and graphics. Alternatives to the Mathematica front end include Wolfram Workbench—an

Eclipse An eclipse is an astronomical event that occurs when an astronomical object or spacecraft is temporarily obscured, by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three ce ...

-based

integrated development environment An integrated development environment (IDE) is a software application that provides comprehensive facilities to computer programmers for software development. An IDE normally consists of at least a source code editor, build automation tools a ...

(IDE) that was introduced in 2006. It provides project-based code development tools for Mathematica, including revision management, debugging, profiling, and testing. There is also a plugin for

IntelliJ IDEA IntelliJ IDEA is an integrated development environment (IDE) written in Java (programming language), Java for developing computer software written in Java, Kotlin (programming language), Kotlin, Groovy (programming language), Groovy, and other ...

-based IDEs to work with Wolfram Language code that in addition to

syntax highlighting Syntax highlighting is a feature of text editors that are used for programming, scripting, or markup languages, such as HTML. The feature displays text, especially source code, in different colours and fonts according to the category of terms ...

can analyze and auto-complete local variables and defined functions. The Mathematica Kernel also includes a command line front end. Other interfaces include JMath, based on GNU Readline and WolframScript which runs self-contained Mathematica programs (with arguments) from the UNIX command line. The file extension for Mathematica files is .nb and .m for configuration files. Mathematica is designed to be fully stable and backwards compatible with previous versions.

High-performance computing

Capabilities for

high-performance computing High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems. Overview HPC integrates systems administration (including network and security knowledge) and parallel programming into a mult ...

were extended with the introduction of

packed array Data structure alignment is the way data is arranged and accessed in computer memory. It consists of three separate but related issues: data alignment, data structure padding, and packing. The CPU in modern computer hardware performs reads and ...

s in version 4 (1999) and

sparse matrices In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse b ...

(version 5, 2003), and by adopting the

GNU Multi-Precision Library GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There are no practical limits to the precision except the ones imp ...

to evaluate high-precision arithmetic. Version 5.2 (2005) added automatic multi-threading when computations are performed on

multi-core A multi-core processor is a microprocessor on a single integrated circuit with two or more separate processing units, called cores, each of which reads and executes program instructions. The instructions are ordinary CPU instructions (such a ...

computers. This release included CPU-specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as

ClearSpeed ClearSpeed Technology Ltd was a semiconductor company, formed in 2002 to develop enhanced SIMD processors for use in high-performance computing and embedded systems. Based in Bristol, UK, the company has been selling its processors since 2005. ...

. In 2002,

gridMathematica gridMathematica is a software product sold by Wolfram Research which extends the parallel processing capabilities of its main product Mathematica. Features gridMathematica increases the number of parallel processes that Mathematica can run at o ...

was introduced to allow user level

parallel programming Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different for ...

on heterogeneous clusters and multiprocessor systems and in 2008 parallel computing technology was included in all Mathematica licenses including support for grid technology such as

Windows HPC Server 2008 Windows HPC Server 2008, released by Microsoft on 22 September 2008, is the successor product to Windows Compute Cluster Server 2003. Like WCCS, Windows HPC Server 2008 is designed for high-end applications that require high performance computing ...

, Microsoft Compute Cluster Server and

Sun Grid Sun Cloud was an on-demand Cloud computing service operated by Sun Microsystems prior to its acquisition by Oracle Corporation. The Sun Cloud Compute Utility provided access to a substantial computing resource over the Internet for US$1 per CPU- ...

. Support for

CUDA CUDA (or Compute Unified Device Architecture) is a parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for general purpose processing, an approach ca ...

and

OpenCL OpenCL (Open Computing Language) is a framework for writing programs that execute across heterogeneous platforms consisting of central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), field-progra ...

GPU A graphics processing unit (GPU) is a specialized electronic circuit designed to manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display device. GPUs are used in embedded systems, mobi ...

hardware was added in 2010.

Extensions

As of Version 13, there are 6,051 built-in functions and symbols in the Wolfram Language. 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. At the time of Stephen Wolfram's release announcement for Mathematica 13, there were 2,259 functions contributed as Resource Functions. 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. Wolfram Mathematica is the basis of the Combinatorica package, which adds discrete mathematics functionality in combinatorics and graph theory to the program.

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 provides a general interface between the kernel and other applications. 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.,Mathematica 4.2
by Charles Seiter, ''Macworld'', November 1, 2002. a

Java Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's List ...

program that can ask Mathematica to perform computations. Similar functionality is achieved with .NET /Link, but with .NET programs instead of Java programs. Other languages that connect to Mathematica include

Haskell Haskell () is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research and industrial applications, Haskell has pioneered a number of programming lan ...

AppleScript AppleScript is a scripting language created by Apple Inc. that facilitates automated control over scriptable Mac applications. First introduced in System 7, it is currently included in all versions of macOS as part of a package of system automa ...

, Racket,

Visual Basic Visual Basic is a name for a family of programming languages from Microsoft. It may refer to: * Visual Basic .NET (now simply referred to as "Visual Basic"), the current version of Visual Basic launched in 2002 which runs on .NET * Visual Basic (cl ...

Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pro ...

, and

Clojure Clojure (, like ''closure'') is a dynamic and functional dialect of the Lisp programming language on the Java platform. Like other Lisp dialects, Clojure treats code as data and has a Lisp macro system. The current development process is comm ...

. Mathematica supports the generation and execution of

Modelica Modelica is an object-oriented, declarative, multi-domain modeling language for component-oriented modeling of complex systems, e.g., systems containing mechanical, electrical, electronic, hydraulic, thermal, control, electric power or process-o ...

models for

systems modeling Systems modeling or system modeling is the interdisciplinary study of the use of models to conceptualize and construct systems in business and IT development.Wolfram System Modeler. Links are also available to many third-party software packages and APIs. Mathematica can also capture real-time data from a variety of sources and can read and write to public blockchains (

Bitcoin Bitcoin ( abbreviation: BTC; sign: ₿) is a decentralized digital currency that can be transferred on the peer-to-peer bitcoin network. Bitcoin transactions are verified by network nodes through cryptography and recorded in a public distr ...

Ethereum Ethereum is a decentralized, open-source blockchain with smart contract functionality. Ether (Abbreviation: ETH; sign: Ξ) is the native cryptocurrency of the platform. Among cryptocurrencies, ether is second only to bitcoin in market capita ...

, and ARK). It supports import and export of over 220 data, image, video, sound,

computer-aided design Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve c ...

(CAD),

geographic information system A geographic information system (GIS) is a type of database containing Geographic data and information, geographic data (that is, descriptions of phenomena for which location is relevant), combined with Geographic information system software, sof ...

s (GIS), document, and biomedical formats. In 2019, support was added for compiling Wolfram Language code to

LLVM LLVM is a set of compiler and toolchain technologies that can be used to develop a front end for any programming language and a back end for any instruction set architecture. LLVM is designed around a language-independent intermediate represen ...

. Version 12.3 of the Wolfram Language added support for

Arduino Arduino () is an open-source hardware and software company, project, and user community that designs and manufactures single-board microcontrollers and microcontroller kits for building digital devices. Its hardware products are licensed unde ...

Computable data

Mathematica is also integrated with

Wolfram Alpha WolframAlpha ( ) is an answer engine developed by Wolfram Research. It answers factual queries by computing answers from externally sourced data. WolframAlpha was released on May 18, 2009 and is based on Wolfram's earlier product Wolfram Mathe ...

, an online

answer engine Question answering (QA) is a computer science discipline within the fields of information retrieval and natural language processing (NLP), which is concerned with building systems that automatically answer questions posed by humans in a natural ...

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).

Reception

BYTE The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...

'' 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". Mathematica has been criticized for being closed source. Wolfram Research claims keeping Mathematica closed source is central to its business model and the continuity of the software.

References

External links

*
Mathematica Documentation Center
documenting the growth of code base and number of functions over time {{authority control 1988 software Astronomical databases Notebook interface Computer algebra system software for Linux Computer algebra system software for macOS Computer algebra system software for Windows Computer algebra systems Cross-platform software Data mining and machine learning software Earth sciences graphics software Econometrics software Formula editors Interactive geometry software Mathematical optimization software Mathematical software Numerical analysis software for Linux Numerical analysis software for macOS Numerical analysis software for Windows Numerical programming languages Numerical software Physics software Pi-related software Plotting software Proprietary commercial software for Linux Proprietary cross-platform software Proprietary software that uses Qt Regression and curve fitting software Simulation programming languages Software that uses Qt Statistical programming languages Theorem proving software systems Time series software Wolfram Research Graph drawing software