Mathematica seamlessly integrates a numeric and symbolic computational engine, graphics system, programming language, documentation system, and advanced connectivity to other applications. It is this range of capabilities - many world-leading in their own right - that makes Mathematica uniquely capable as a 'one-stop shop'? for you or your organization's technical work.

Features:
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.

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.

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.

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.

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.

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.

What’s New in Mathematica 10
• 700+ new functions—and that's just the beginning
• Mathematica celebrated its 25th anniversary in 2013, and is stronger than ever. Leveraging its core principles of automation and unification, it's advancing at an ever-increasing rate.
• Mathematica 10 introduces a host of new areas—such as machine learning, computational geometry, geographic computation, and device connectivity—as well as deepening capabilities and coverage across the algorithmic world.
• Mathematica 10 is the first version of Mathematica based on the complete Wolfram Language.

What new in Mathematica 10.0.1
- Image processing updates and enhancements, including new image effects, Image3D options for WatershedComponents, and built-in color support for Nearest and FindClusters
- Simplified SendMail syntax for easier usability
- New operators and compositions of operators enabled for associations functions such as Dataset and Query
- RLink compatibility update for R 3.1.
- New Interpreter types such as Beach, CountryClass, OilField, and Reef
- New optimizations, supported inputs, and path types for geographic computation and regions
- Machine learning functions Classify and Predict now support NeuralNetwork as a built-in classification method
- Stability and performance improvements for smoother user interface experience on all platforms
- Improved coverage of supported types in SemanticImport and optimizations for handling anonymous columns, empty fields, headerless data, and import of files with long file names
- Updates and improvements to a wide range of areas including weather data, associations, symbolic integration, and measure computations over implicit regions
- Stability and performance updates for select plot and chart types and for numerical solvers including NDSolve, ParametricNDSolve, SparseArray, and MatrixExp
- Compatibility update for InterpolatingFunction saved with Version 9 and earlier