The Java programming language and the math extensions in commons-lang provide implementations for only the most basic mathematical algorithms. Routine development tasks such as computing basic statistics or solving a system of linear equations require components not available in java or commons-lang.

Most basic mathematical or statistical algorithms are available in open source implementations, but to assemble a simple set of capabilities one has to use multiple libraries, many of which have more restrictive licensing terms than the ASF. In addition, many of the best open source implementations (e.g. the R statistical package) are either not available in Java or require large support libraries and/or external dependencies to work.

Commons-Math is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang. The guiding principles for commons-math are:

1. Real-world application use cases determine priority
2. Emphasis on small, easily integrated components rather than large libraries with complex dependencies
3. All algorithms are fully documented and follow generally accepted best practices
4. In situations where multiple standard algorithms exist, use the Strategy pattern to support multiple implementations
5. Limited dependencies. No external dependencies beyond Commons components and the JDK