Why Mathematica? Compare Mathematica to Other Technical Computing Tools

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.

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Mathematica's advanced adaptive methods, feature detection, and automatic layout and styles yield visualizations that are both technically correct and visually appealing.

Automation in Computation

Advantages

In other systems...

Precision Control & Tracking

Just-in-Time Compilation

Algorithm Selection

Task Oriented Functions

Type Independent Functions

Reliable results without roundoff analysis

High performance in a high-level language�

Faster, better results, even for experts�

High-level, readable programs�

Easily apply existing code to new data�

Get unreliable results (or perform manual analysis)

Get slower results (or optimize manually)

Use poorly suited or generic algorithms

Programs obfuscated by algorithmic details

Memorize different functions for each data type

Automation in Visualization

Advantages

In other systems...

Style

Layout

Feature Detection

Adaptive Sampling

Interactivity

Composition

Publication-quality graphics at every stage�

Maximally informative diagrams and text�

Correctly visualize key features of functions

Efficiently resolve features on different scales�

Instant interactive plots and diagrams�

Compose text, images, tables, and controls

Manually specify colors, tick marks, etc.

Manually specify plot ranges, layouts, etc.

Incorrect plotting of discontinuities, branch cuts, etc.

Missed details (or wasted function evaluations)

Manually program interactive elements (or use none)

Generate only simple graphics (or use separate software)

Automation in Development

Advantages

In other systems...

Free-Form Linguistic Input

User Interface Construction

Cross-Platform Deployment

Memory Management

Parallelization

Translate free-form text into precise commands

Complete interfaces from minimal specification�

Intrinsically platform-independent applications

Optimized allocation, tracking, and deallocation

Zero-configuration parallelization

(No alternative)

Manually program all aspects of user interface

Limited deployment (or manually port to each platform)

Manually allocate and track memory

Manual parallelization (initialization, communication, etc.)

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.

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Mathematica immediately enables development across technical areas without costly add-ons.

Advantages

In other systems...

Smooth workflow from idea to deployment

Own a single technical platform

Learn a single technical platform

Explore ideas spanning different technical areas

Change tools and formats at each stage

Regularly need costly add-on toolboxes

Learn multiple specialized tools with limited scope

Creativity restricted by built-in functionality

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.

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Mathematica uses controlled high-precision numbers and symbolic analysis to solve problems that are intractable with traditional numerical methods and limited-precision numbers.

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In other systems...

Get exact, general results whenever possible

Track roundoff errors automatically�

Use hybrid methods that exploit the mathematical structure of the input�

Get only numerical results, often forfeiting insight

Get unreliable results (or manually track roundoff)

Only use less efficient generic methods

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.

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Mathematica lets you program in the style you prefer.

Advantages

In other systems...

Program the way you think

Use the best combination of techniques for the problem

Change your thinking to fit the platform

Operate within a single paradigm regardless of its suitability

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.

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Access standard data without any overhead, including Wolfram|Alpha, the world's largest collection of computable data.

Advantages

In other systems...

Readily computable data built in�

Automatically keep data up to date

Instantly access and use standard data

Incorporate standard data that would be hard to obtain

Manually import, validate, and restructure data

Regularly check source for updates and corrections

Interrupt workflow to obtain data

Restrict analyses to a more limited set of 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.

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