Market Background: Mathematica

Mathematica: Product Background

Mathematica is the leading software system for numerical, symbolic, and graphical computation, used internationally by professionals in almost every area of scientific and technical computing. Mathematica lets users solve, visualize, and harness the power of mathematics without the pencil-and-paper, calculator, or complex custom software approaches that were previously necessary. Mathematica handles the mechanics of mathematics, so that people can concentrate instead on the content and implications of their work. The combination of fast new internal algorithms, increased capabilities for importing and exporting, and new document processing features make Mathematica 4 ideal for final simulations as well as prototyping--a complete ideas-to-results computing environment. Mathematica can be used as an interactive calculation tool and as a high-level programming language. Some general uses include the following:

as an interactive numerical and symbolic calculator
as a visualization and sound generation system for functions and data
as a high-level programming language in which you can create programs, large and small
as a modeling, simulation, and data analysis environment
as a system for representing knowledge in mathematical and technical fields
as a control language for external programs and processes
as a high-level shell for file, text, and data manipulation
as a tool for creating interactive documents mixing text, animated graphics, and active formulas
as a technical publishing tool for both traditional print and on the web

Defining a New Market for Technical Computing

Hundreds of thousands of technical professionals and students use Mathematica on a regular basis. Currently, Mathematica users can be broken down into the following categories:

Engineering 32%

Physical Sciences 21%

Mathematical Sciences 16%

Computer Sciences 13%

Business/Social Sciences 6%

Life Sciences 5%

Other 7%

Half of our registered Mathematica users are in commercial or government organizations and half are in academic institutions. Mathematica is used today in all Fortune 50 companies and in each of the fifteen major departments of the U.S. government. In the academic world, all of the 50 largest universities granting Ph.D. degrees in the physical sciences and mathematics use Mathematica. College campuses across the world also use Mathematica or Mathematica-based courseware in undergraduate education. Academic publishers are using Mathematica technology to create online versions of traditional texts--a popular calculus textbook recently has been converted to a completely interactive electronic version with Mathematica. Currently, over half of Wolfram Research's sales are international. Wolfram offices in Europe and Japan support international sales and marketing, and Wolfram Research has started to create localized (language-specific) software kits. The Mathematica Japanese Language Kit is a completely translated version of Mathematica, with the entire interface--including menus, palettes, dialog boxes, error and warning messages, and over a thousand pages of online help--all in Japanese. Japan is now the second largest market for Mathematica after the United States. Although Mathematica has already sold well in the technical professional markets, there remains an extraordinary potential for growth. There are an estimated 4.2 million technical professionals in the United States, according to the U.S. Department of Labor. Nearly two million of these are engineers; only about 800,000 are mathematicians. And while Mathematica has become the de facto standard in fields such as mathematics and physics research, other fields including engineering, natural sciences, financial analysis, and the social sciences are filled with potential customers for Wolfram Research's products. Mathematica was first released on June 23, 1988, and was immediately lauded by the scientific and technical community, as well as the media, as a dramatic advance in technical computing. In 1991, Wolfram Research introduced Mathematica Version 2, which included an enhanced programming language, a compiler, and sound-sampling capabilities. Version 3, released in 1996, presented Mathematica with a new, easy-to-use interface which included a programmable user interface with buttons and palettes. Mathematica Version 4 offers dramatically faster numeric calculations, expanded interaction with other software programs, and a host of enhancements to the user interface that ease programming and technical publishing--making Mathematica a comprehensive ideas-to-results technical computing environment.

Achieving Strong Platform Independence

Wolfram Research has always made Mathematica available on the operating systems in widest use by technical professionals. Mathematica currently runs on the following hardware platforms:

Windows 95/98/NT/2000 (PC)
Mac OS (Power Macintosh)
Linux (PC)
SunOS/Solaris
HP-UX
IRIX
AIX
Digital Unix/Compaq Tru64 Unix

Some Users of Mathematica

The versatility of Mathematica is amply demonstrated by the breadth of its uses throughout industry. The following examples illustrate just a small number of ways all kinds of people use Mathematica in their work.

Engineering/Manufacturing

An engineer for an interplanetary probe launch mission uses Mathematica to perform risk assessment by investigating all combinations of launch accidents that could potentially release hazardous materials into the environment. A separate risk assessment team then uses Mathematica's mapping features to map the possible paths the hazardous particles could take should a launch accident occur at various times in the first few minutes of the mission.

A research director at a heavy equipment manufacturer uses Mathematica to build symbolic models of complex armatures for earth-moving machinery. Mathematica's symbolic and graphical capabilities allow his entire department to calculate optimal specifications without manual trial-and-error numeric calculations, saving ten months of work on one project alone.

A design engineer rebuilding a paper-making machine uses Mathematica to calculate system transfer functions and conduct stability analysis. Forty drive circuits and six tension-regulating circuits yield highly complex algebra problems with many variables. Using Mathematica saves him months of time by allowing him to solve for the correct bandwidth symbolically, instead of crunching numbers manually.

Finance/Economics

A financial analyst for a large international banking firm uses Mathematica for modeling options pricing, where he can incorporate symbolic as well as numerical values; improved models provide a competitive edge.

Three professors team up with a researcher from the Justice Department to create Mathematica-based software that simulates the effects of horizontal mergers. Anti-trust enforcement agencies, economics students, and attorneys use the software to predict post-merger prices and demand.

Life Sciences

An East Coast physician who works as a statistician for clinical cancer trials uses Mathematica to analyze therapies and to create new survival models. Mathematica is particularly useful for setting up the theoretical side of these complicated models.

Another physician uses Mathematica to create mathematical models of the spread of infectious diseases, where the software's graphing capabilities are especially appreciated.

A researcher uses Mathematica to model the foraging habits of bees. Mathematica allows him to combine data on bee behavior with formulas that predict their movements to create graphics that illustrate the bees' pollen-harvesting habits.

Education

A student takes a traditional calculus course supplemented with Mathematica. With Mathematica shouldering most of the calculational burden, she is able to explore a greater quantity and variety of examples and graphs than with pencil and paper or a graphing calculator. Using Mathematica, she learns concepts instead of strategies for calculation.

Two students at a small, rural high school take a Mathematica-based calculus class over the internet from the University of Illinois. The students get college credit and a head start on their undergraduate studies by taking a class otherwise unavailable at their school.

Mathematics

A 17-year-old uses Mathematica to explore cryptography, and has created a new algorithm that could revolutionize the way computers communicate secure information. Her algorithm makes data encryption 30% faster than the current industry standard. Mathematica's interactivity and ability to handle large numbers with no loss in accuracy foster exhaustive exploration of mathematical concepts and ideas.

Graphics/Animation

A graphic artist in Southern California uses Mathematica to create sculptures of his mathematical data, writing programs for generating three-dimensional surfaces.

A movie animator uses Mathematica to design snowflakes for a snowstorm scene. Mathematica allows him to create new types of motion images that blend art and a heightened sense of reality.

A physicist creates textile designs based on the patterns of stochastic processes, using Mathematica to create the patterns. His designs appear on wallpaper, gift wrap, car interiors, and fashion fabrics.

Computer Science

A computer game developer uses Mathematica to program and maintain a web site database for game players. He has programmed Mathematica to automatically extract information, generate JPEG images, and create HTML files from user-submitted game scenarios. Mathematica's programming flexibility allows the developer to streamline the daily updates of the database while still processing large amounts of data and graphics.

Web Technology

Engineers, high level researchers, and high school students around the world come to The Integrator to solve tough integrals. The Integrator is a web interface to Mathematica's built-in Integrate function and provides typeset solutions to definite and indefinite integrals.

The primary contractor for the U.S. Patent Office uses Mathematica to create both printed and electronic forms of mathematical formulas for patents. A custom-designed user interface gives the contractor efficient and accurate formula entry for the 3500--4000 patents processed each week, dramatically reduces the training time of production floor workers, and automatically creates multiple electronic files for each formula, including EPS, TIFF, notebook (.nb document standard), and MathML.

A software developer uses Mathematica's HTMLSave function to produce online documentation for a scientific software application. He now creates, edits, and converts software manuals for web site publication from a single Mathematica notebook.