Mathematica

What Is Mathematica?

Almost any workflow involves computing results, and that's what Mathematica does—from building a hedge-fund trading website or publishing interactive engineering textbooks, to developing embedded image-recognition algorithms or teaching calculus.

Mathematica is renowned as the world's ultimate application for computations. But it's much more—it's the only development platform fully integrating computation into complete workflows, moving you seamlessly from initial ideas all the way to deployed individual or enterprise solutions.
 
Industry Solutions   Education
     
  • Data Science
  • Finance
  • Modeling
  • Software
  • Development
  • Engineering
  • Biotechnology
  • Medicine
 
  • Higher Education
  • Community College
  • Primary & Secondary
  • Students
 

Over 20 Years of Experience—Millions of Users

 
With more than 20 years of experience and millions of users from Fortune 500 companies to government departments to thousands of universities worldwide, Mathematica technology lies behind many of the world's most impressive projects, processes, and organizations—and your future innovation? Discover the key advantages that set Mathematica apart.
 

What's new in Mathematica 11

Representing a major milestone in an unprecedented 30-year journey, Mathematica 11 significantly extends the reach of Mathematica and introduces many innovations that give all Mathematica users new levels of power and effectiveness.

With its bold long-term vision of integrating and automating all areas of computation and knowledge, each new version of Mathematica makes new domains accessible as a routine part of any user's workflow. Want to find the solution to a partial differential equation and then 3D print it? Mathematica 11 provides integrated tools that yet again vastly expand the scope of cross-domain projects that can routinely be done by users at all levels.

Mathematica 11 builds on Wolfram's recent R&D breakthroughs in a host of areas—including neural network computation, audio integration, and linguistic computing. Existing Mathematica users will also find a wide range of convenient enhancements in interface, language, and algorithm depth and efficiency.
Neural Networks

Version 11 introduces a high-performance neural network framework with both CPU and GPU training support. A full complement of vision-oriented layers is included, as well as encoders and decoders to make trained networks interoperate seamlessly with the rest of the language. Constructing and training networks often requires only a few lines of code, putting deep learning in the hands of even non-expert users.

Improved Machine Learning

The new version extends and improves its machine learning capabilities. New functions allow users to extract features, reduce dimension, cluster data, optimize hyperparameters, and obtain interpretable models. The feature extraction functionality can be used to visualize datasets or to create semantic distances for search systems. Computer vision is substantially improved: ImageIdentify can recognize more than 10,000 objects, and performances of Classify on images are enhanced. Additionally, machine learning functions accept a wider range of data types.

3D Printing

Mathematica provides fully integrated capabilities to directly 3D print geometric models, using either an online printing service or your own printer. Algorithmically generate geometric models or import 3D models from files and immediately output physical 3D objects—all highly automated for easy use unlike anything ever seen before.

Core Geometry

It adds numerous extensions and improvements to the already strong capabilities in geometric computing. It is now possible to construct regions from arrays and images or to immediately access them from curated collections. A full integration into the Wolfram Language makes it easy to analyze, solve over, visualize, and 3D print regions. Performance improvements are available across the board.

Computational Audio

Version 11 introduces fully integrated support for audio processing. An audio signal can be stored in-memory for fast computations or linked to a local or remote file. File-based audio representation allows for handling of very large audio files or very large collections of audio files. New capabilities covering audio synthesis, processing, and analysis combined with comprehensive support for signal processing, statistical analysis, and machine learning enable easy prototyping of applications in various fields, including music, speech, communication, and broadcasting.

Computational Photography

It adds new functionality specifically designed for performing tasks in the domain of computational photography. The new additions, combined with the previously developed set of image processing capabilities, allow for immediate enhancement of photographs, including removal of unwanted feature such as noise and color cast, as well as adding photography effects to photographs or even combining images of different focus and exposure. In addition, the comprehensive support for import and export of image metadata allows for a wide range of analysis performed on large collections of images.

Image and Signal Processing

This new version continues to add powerful image and signal processing functions. Several functions are introduced to process and analyze sequences of images captured at different times, with different exposures, or with different focuses. Efficient viewing of very large images, fast conversions of images to mesh regions, sequence alignment and similarity analysis, and a lot more improve the workflow of applications in research and development, computational photography, microscopy, and more.

Partial Differential Equations

The upgrade adds extensive support for symbolic solutions of boundary value problems related to classical and modern PDEs. Numerical PDE-solving capabilities have been enhanced to include events, sensitivity computation, new types of boundary conditions, and better complex-valued PDE solutions. These developments provide powerful and flexible tools for modeling problems in physics, engineering, and other fields.

Differential Eigensystems

Mathematica 11 extends its symbolic and numerical differential equation-solving capabilities to include finding eigenvalues and eigenfunctions over regions. Given a possibly coupled partial differential equation (PDE), a region specification, and, optionally, boundary conditions, the eigensolvers find corresponding eigenvalues and eigenfunctions of the PDE operator over the given domain. This functionality will enable you to gain a deeper understanding of your physics and engineering designs.

Symbolic & Numeric Calculus

This version builds on its industry-leading capabilities in calculus, with new symbolic and numeric features that enhance each other. Integral transforms are extended with the Mellin transform, along with related convolution and function simplification operations. The cutting-edge symbolic differential equation solver has been extended to support multiple types of integral and integro-differential equations. A new back end has been added to the numerical optimization engine for faster and more accurate solutions for large systems. Small tweaks include a new function for computing difference quotients and extending volume computations to understand non-Cartesian coordinates. Taken together, these enhancements make calculus faster, easier, and better at all levels of sophistication.

Algebra and Number Theory

Enhancements include enumeration of new classes of natural integers, manipulation of number digits, representation of complex numbers, coordinate conversions, matrix operations, combinatorial optimization, and parametrized enumeration of points, vectors, and paths.

Visualization: Labels, Scales, Exclusions

Version 11 energizes the core visualization functions by adding powerful features that make plots easier to read and use. It is now easy to add labels to individual points or entire datasets, using positions that are automatically computed or explicitly given. Callouts extend this with a rich language for controlling the appearance of the label, leader lines, and overall appearance. Use logarithmic scaling functions to make it easier to view plots that span wide ranges of values, or reverse the axes to turn a plot on its head. The exclusions engine has been extended to detect and remove artifacts around singularities, including poles and essential singularities, for a wider set of functions.

New Visualization Domains

From anatomy to audio to automata, this version adds specialized visualization functions for a wide range of topics. Date and time visualization has been expanded to include timelines for showing what happened when and histograms for seeing the frequency of events. The distribution of geographic locations can also be visualized as histograms, and there are interactive maps that can be panned and zoomed. New functions for language and text visualization make it easy to visualize themes using word clouds and to see the grammatical structure of sentences.

Volume Visualization

The Wolfram Language adds new classes of functions for 4D visualization. Density plots combine colors and opacity to represent the values of formulas and vectors over a 3D region. Slice plots show contours, densities, and vector fields on surfaces passing through a volume. The slice surfaces are quite flexible, supporting any combination of built-in planes, equations, and arbitrary regions.

Graphs and Networks

This release adds numerous extensions and improvements to its already very strong capabilities in graphs and networks. These include additional graph constructors, new graph properties for curated data, and new domain-specific networks. Performance improvements are available across the board.

Random Matrices

Mathematica 11 also introduces support for random matrices. The efficient generation of matrix variates, estimation of their properties, and computations of their limiting distributions are tightly integrated with the existing probability & statistics framework. Random matrices have uses in a surprising variety of fields, including statistics, physics, pure mathematics, biology, and finance, among others.

Extended Probability & Statistics

On the statistics side, there are numerous improvements and extensions throughout the probability and statistics functionality. From descriptive statistics and random variables to time series and random processes, the whole framework is stronger, faster, and easier to use.

Enhanced Geo Visualization

Version 11 brings even more flexibility and power to geographic visualization. The new outlines of continents and countries, satellite imagery, and support for independent sources of geo tiles make it easy to create custom appearances for maps. More than a hundred new projections have been added to the system, highlighting specialized features and preserving geometric properties. New primitives make it easy to draw common geographic regions. View the distribution of geographic locations by grouping them into larger regions. Easily adjust maps by changing the background or projection, or even combine multiple maps. Interactive maps allow panning and zooming to see the big picture or fine details.

Geo Computation

This new release improves and extends the functionality for geo computation and geophysics. There are new functions to compute geodetic lengths and areas, new functions to compute travel instructions and estimations of their length and duration, and new functions to compute properties of the Earth's gravitational and magnetic fields. There is also a large collection of new cartographic projections, as well as new datums for the Earth. All together, the new geo functions provide very large computational power in general problems of geodesy and geophysics.

Geo Data

The Wolfram Geo framework continues expanding its knowledge base of geo-related information, including new types of entities, new types of map backgrounds, geophysics data, new geo projections, and much more. All this, together with the extended functionality for geo visualization, makes exploring all kinds of interesting data about society, the world, and other planets even easier.

Text & Language Processing

Mathematica also enhances the string, text, and natural language processing framework, providing new and more powerful functionality for symbolic manipulation and analysis of texts. New functions are available to identify and extract structured data from unstructured text, explore historical word frequency data, and parse natural language input.

Multilingual Functionality

This new release adds a new set of improvements and features to the multilingual functionality through the entity-property framework. There are now 150+ alphabets and new functions to work efficiently with them—from sorting letters to advanced text manipulation tools. These new functions provide a deeper understanding of the relations between alphabets, languages, and writing scripts.

Time Series Processing

Improvements were added to time series processing throughout the framework. Direct arithmetic and function applications just work; applying a function over windows now allows natural specifications such as monthly duration, as well as precise control over where the resulting value is placed in time. Generally, date and quantity support is more complete and natural. Time series are now produced and accepted by many functions in the system.

Quantities in Probability & Statistics

Version 11 supports quantities across the probability and statistics functionality, fully automating conversion, propagation, and transformations—from data to models to correct interpretation.

Units & Dates

This release also expands on the extensive collection of different units and date functions, creating an expressive and intuitive system for working with physical quantities and dates. Enhancements include efficient array storage of quantities, new date forms and formats, and new date visualization functions to examine temporal relations.

Core Language

Mathematica 11 extends the functionality of the core language. Enhancements include fine-tuned manipulation of associations with new predicates and association pattern matchings, extraction and comparison of sequences of expressions, manipulation and creation of coordinate arrays, easy tuning and debugging with visualization of intermediate steps of a computation, new built-in capabilities for the study of computational systems, broader possibilities for functional iterations, and updated formatting of dataset structure.

Systems-Level Functionality

The new release adds several system-level functions in areas like network programming, file processing, cryptography, and command shell automation. Network functionality ranges from basic ping times to advanced socket programming and cookie manipulation. The brand-new command line script interpreter can process data and run scripts using local or cloud-based kernels.

User Interface Enhancements

The notebook environment, a concept invented and developed by Wolfram Research, continues to see improvements to its leading interface in Version 11. Real-time spellchecking is augmented with dictionaries for technical terms and proper names, as well as support for some 25 languages. The coding environment is more modern with a lighter font, more functional with drill-down from error messages, and more helpful with contextual autocompletions everywhere.

External Services

The connections have been extended and improved with a set of external services. Connect to social media, storage, health & fitness, business, research, and other external services and APIs. Authentication and data exchanges are managed by the Wolfram Language, providing a seamless experience and integrating natural language and knowledge base capabilities.

Knowledgebase Expansion

Enhancements include a number of improvements to the already extensive Wolfram Knowledgebase. Additions include several new entity types such as anatomy and food, as well as richer ways of filtering and aggregating entities. Better data alignment across different entity types enables cross-domain queries, and optimized results allow immediate further computation.

Richer Knowledgebase Access

This release improves speed and adds flexible ways of accessing a large variety of socioeconomic, geographic, scientific, and mathematical datasets in the entity-property framework. A major enhancement to the knowledge representation is support for user-defined entities and properties, thus allowing arbitrary datasets to be seamlessly integrated.

Cloud & Web Interfaces

Version 11 expands the functionality to generate rich, dynamic, cloud-backed websites. More flexible form-based input and gallery-based output make it easy to generate compelling web interfaces. Automatic form-based user interactions, automatic mail processing, and automatic report generation provide the tools for a whole new level of efficiency in the development and operation of dynamic websites.

Cloud Storage & Operations

Expanded capabilities were added for storing, manipulating, and sharing data in the cloud. The Wolfram Data Drop gives multiple ways of incrementally storing data values. The Wolfram Data Repository provides storage for datasets. Cloud expressions allow storage and direct manipulation of any expression in the cloud. Permissions keys give fine-grained control over shared access to all cloud resources.

Channel Framework

This new release of Mathematica adds experimental support for publish-subscribe communication, brokered in the Wolfram Cloud through channelbroker.wolframcloud.com. Sending and receiving messages through a "channel" (rather than pairing specific senders and receivers) allows for a more abstract and scalable communication system that facilitates asynchronous communication between sessions, in the cloud or on the desktop, as well as external systems, with data provided in a JSON format.

Why Mathematica?

Because principles matter.

Over 20 years of building on bold design principles make Mathematica the world's ultimate computation platform.
 
Automation
Automation is the key to productive computing. Unlike other systems, Mathematica applies intelligent automation in every part of the system, from algorithm selection to plot layout and user interface design. You get reliable, high-quality results without needing algorithm expertise—and even if you're an expert, you get results faster.

Mathematica's advanced adaptive methods, feature detection, and automatic layout and styles yield visualizations that are both technically correct and visually appealing.
 
Integrated All-in-One Platform
Specialized software and add-on toolboxes discourage the creative exploration of new ideas and areas—an even greater cost than their purchase price. Mathematica requires no add-ons. It has built-in specialized functionality for many technical areas, from computational biology to wavelet analysis, all tightly integrated with the rest of the system.

Mathematica immediately enables development across technical areas without costly add-ons.
 
Hybrid Symbolic-Numeric Methodology
Symbolic and numerical computation are traditionally thought of as separate, to the detriment of users. In Mathematica, they are seamlessly integrated, enabling unique hybrid methods for many problems and ensuring consistent results whenever quantities of any precision are combined.

Mathematica uses controlled high-precision numbers and symbolic analysis to solve problems that are intractable with traditional numerical methods and limited-precision numbers.
 
Multiparadigm Language
No one programming style is ideally suited to every problem. Mathematica stands out from traditional computer languages by simultaneously supporting many programming paradigms, such as procedural, functional, rule-based, pattern-based, and more.

Mathematica lets you program in the style you prefer.
 
Built-in Knowledge
Searching and updating standard datasets shouldn't interrupt your workflow. Mathematica is unique among technical computing platforms because it includes a vast collection of carefully curated data of all kinds, continuously updated and expanded.

Access standard data without any overhead, including Wolfram|Alpha, the world's largest collection of computable data.
 
Document-Based Workflow
You shouldn't need one program to process your data, another to visualize it, and a third to interactively present it. Mathematica does everything in a single workflow, keeping all elements of a project—calculations, visualizations, data, documentation, and even interactive applications—together, in uniquely flexible documents.

Mathematica notebooks and Computable Document Format (CDF) files consolidate your calculations, interactive visualizations, data, text, and more.
 

Mathematica Features

 

Compute

 
Numerics of any precision, symbolics, or visualization—Mathematica is the ultimate computational tool, with systemwide technology to ensure reliability, ease of use, and performance. Use Mathematica computation directly, as the engine in an infrastructure, or integrated into a standalone application.    
    Core Algorithms   Numerical Computing
    The world's largest integrated web of mathematical capabilities and algorithms   Industrial-strength numerics, from instant computations to heavy number crunching
         
   
Application Areas   Data Sources & Analysis   Graphics & Visualization
Fully integrated, specialist technical functionality   One-stop solution for data acquisition, processing, analysis, and visualization   Uniquely integrated graphics and powerful visualization
 

Develop

 
Develop tools, applications, documents, or infrastructure components using Mathematica's seamless workflow, unique symbolic language, and advanced code editing environment, achieving fast turnaround on small projects and record times on large systems.    
    Programming & Development   Interactivity & Interface Design
    The uniquely powerful symbolic language that is the foundation for Mathematica   Dynamic interactive computing and instant interface building
 

Deploy

 
Whether your deliverables are interactive documents, presentations, applications, or enterprise systems, Mathematica can deploy your results in a wide range of formats locally or across a network. With many ways to connect to and work with external systems, Mathematica is designed to maximize your productivity.    
    Deployment & Connectivity   Productivity & Usability
    Immediate deployment for all scales   Streamlined workflow, from concept to results
 

Customer Stories

   
         
Courseware of the Future—Today: Developing Interactive Textbooks with CDF (2:52)

Eric Schulz, Co-author of Calculus, by Briggs and Cochran
  Geared for Success: Optimizing Face Gear Surfaces in Mathematica (3:11)
Steve Bush, Mechanical Engineer, The Procter & Gamble Company
  Empowering Data-Driven Decisions: Data Mining and Analysis with Mathematica (2:25)
Ariel Sepúlveda, Founder, Pronto Analytics
         
 


Landing a Solid Model: Mathematica's Role in Flight Operational Safety Analysis
Mike Ulrey, Advanced Air Traffic Management, Boeing
Play (3:22)
 

At the Heart of Future Treatment: Mathematica's Role in Blood Pressure Research
Tim Shine, Anesthesiologist, Mayo Clinic
Play (3:10)
     


A Comprehensive Solution: Developing an Enterprise-Wide Platform with Mathematica
Philip Zecher, Chief Risk Officer, EQA Partners, LP
Play (3:50)
 

The Ultimate Tool for Biomedical Research: Developing Light Microscopy Techniques with Mathematica
Daniel Zicha, Head of Light Microscopy, Cancer Research UK
Play (3:26)
     


Exploring the Science of Cooking: Mathematica's Role in Modernist Cuisine
Nathan Myhrvold, Author of Modernist Cuisine and former CTO, Microsoft
Play (4:24)
 

Dynamics of Change: Modeling the Economic Effects of Global Warming with Mathematica
Stuart Nettleton, Senior Lecturer, University of Technology, Sydney
Play (3:45)
     


An Immersive Environment: Teaching Real-World Problems with Mathematica
Paul Abbott, School of Physics, The University of Western Australia
Play (2:46)
 

Financial Data on Demand: Building an Interactive Web Service with Mathematica
Alan Savoy, Technical Manager and Architect, nGenera Corporation
Play (2:52)
     


Breaking Down Biofuels: Eco-friendly Solutions with Mathematica
Andrew Hull, Consulting Scientist
Play (2:27)
 

Teaching the Bigger Picture: Exploring Mathematics with Mathematica
Debra Woods, Founder, Mathematics Professor, University of Illinois at Urbana-Champaign (UIUC)
Play (3:04)
     


Striking a Virtual Chord: Mathematica Hits High Note with Music Producer
John Kiehl, Co-owner, Soundtrack Recording Studios
Play (1:56)
 

Prescription for Savings: Mathematica Powers Efficiency in Drug Trials
David DeBrota, Senior Clinical Research Physician
Play (3:22)
     


Modeling the Aftermath: Mathematica's Role in Hurricane Insurance Research
Seth Chandler, University of Houston Law Center
Play (2:58)
 

A Natural Choice: Mathematica's Role in Natural Resource Studies
Yu-Feng Lin, Hydrogeologist, Illinois State Water Survey
Play (3:34)
     


An Edge in Education: Advancing Math Courses with Mathematica
Dana Vazzana, Associate Professor of Mathematics, Truman State University
Play (2:49)
 

A Measure of Success: Designing Hearing Aid Parts with Mathematica
Daniel Warren, Director of Research, Knowles Electronics
Play (2:23)
     


Modern Quality Control: Measuring True Performance with Mathematica
George Woodrow III, Research Specialist, Quest Diagnostics
Play (2:39)
 

Inside the Interface: Optimizing Search with Mathematica
Joel Drouillard, BondDesk Group LLC
Play (3:23)
     


Finding the Missing Link: Building an Integrated System in Mathematica
Frank Scherbaum, Geophysics Professor, University of Potsdam
Play (2:48)
 

A Game Changer for Mathematics: Mathematica in the College Classroom
Bruce Torrence, Chair, Department of Mathematics, Randolph-Macon College
Play (2:42)
     
 

Mathematica Resources

 

Learn at Your Own Pace

 
 
Mathematica Learning Center   Mathematica Documentation Center
Access videos, "How tos", tutorials, and hundreds more options to help you get started with Mathematica   Find help inside the complete and up-to-date documentation of Mathematica's functions and capabilities.
     
Mathematica Books   Solutions in Your Field
Browse our broad selection of Mathematica books and references written by leading experts.   Discover solutions in science, engineering, biotechnology, finance, art, education, and more.
 

Interact with Demonstrations

 

Wolfram Demonstrations Project

Choose from thousands of fully functional, interactive Demonstrations and their full source code on subjects ranging from math and science to geography and music.
 

Learn from the Experts

 
 
Free Virtual Events   Live and On-Demand Courses
Be the first to see new Wolfram technologies in action and talk with our experts from the convenience of your own desk.   Get started quickly with live and on-demand courses, for both new and experienced users, that introduce how Mathematica is used in different application areas.
     
 

Get Involved

 
Wolfram Community   Wolfram Partnerships Group   Wolfram Insider
Mingle online with other Mathematica users like you. Share ideas, collaborate on problems, make new friends, and have fun!   If you're a developer, author, or publisher, join a program to get better results and exposure for your work.   Stay up to date and get all the latest Wolfram news delivered to your inbox.
   

Follow Us

Stay connected with Wolfram via Facebook, Twitter, YouTube, and more.

 

Get Help

 
Wolfram Support Center   Premier Service
Have a problem? Find the answer among the wide range of self-help options, or contact our expert customer service and technical support teams.   Subscribe to our comprehensive program of exclusive services and discounts that will help you save time and money and boost your productivity.
     

How to Buy Mathematica

 
For Industry & Individuals   For Government   For Education
   
         
 

Mathematica 11.1 | March 2017

Version 11.1 extends Mathematica and the Wolfram Language's state-of-the-art capabilities in machine learning, neural nets, audio processing, robust statistics and much more.

• Over 130 new functions across a wide range of application areas
• 20 new neural net layer types, and seamless support for recurrent nets and variable-length sequences
NetModel to access a growing repository of complete trained and untrained neural nets

FeatureSpacePlot for machine-learning-based visualization of spaces of data, images, text, etc.

• New machine learning functions, including SequencePredict, ActiveClassification and ActivePrediction



• Record audio directly in notebooks using AudioCapture, readying it for immediate processing and analysis • Do arithmetic (with *, -, etc.) directly on 2D and 3D images
• Extended support for computational photography and computational microscopy
ImageGraphics to find vector graphic approximations to bitmaps

• Space-filling and fractal region constructors such as HilbertCurve and SierpinskiMesh
• New robust and spatial statistics, including WinsorizedMean and SpatialMedian

GeoBubbleChart, as well as extended support for Callout, ScalingFunctions, etc.
• Support for derivatives with symbolic orders
• Higher-resolution geo elevation data
• Seamlessly integrated external services for web search, web image search and text translation
• Broad PersistentValue system for storing values between sessions locally, in the cloud, etc.
AutoCopy for seamless distribution of separately editable notebooks in the cloud
• Creation of WolframScript .wls files with a notebook-based script editor
• Self-executing Wolfram Language scripts extended to Windows
• New, responsive design for all documentation and online examples