Why Mathematica?
Because principles matter.
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.
| 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.
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.
Mathematica uses controlled
high-precision numbers and symbolic analysis
to solve problems that are intractable with
traditional numerical methods and
limited-precision numbers.
| Advantages |
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, object-oriented, and
more.
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.
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.
Mathematica notebooks and
Computable Document Format (CDF) files
consolidate your calculations, interactive
visualizations, data, text, and more.
| Advantages |
In other systems... |
| Automatically
document as you work
Include interactivity in documents»
Easily re-target
documents for web, print, and
presentations and as applications |
Save data,
formulas, text, code, results, graphics,
and applications in separate files and
formats Lose intermediate steps
leading to difficulty reproducing
results
Graphics and other elements must be
static, not interactive
Start from scratch when
deploying to any new medium |
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