Starting from version 3.0, all exceptions generated by the Commons Math code are unchecked (i.e. they inherit from the standard RuntimeException class). The main rationale supporting this design decision is that the exceptions generated in the library are not recoverable: They most of the time result from bad input parameters or some failure due to numerical problems. A thorough discussion of the pros and cons of checked and unchecked exceptions can be read in this post by Bruce Eckel.
The exceptions defined by Commons Math follow the Java standard hierarchies:
In all of the above exception hierarchies, several subclasses can exist, each conveying a specific underlying cause of the problem.
The detailed error messages (i.e. the string returned by the getLocalizedMessage method) can be localized. However, besides the American/English default, French is the only language for which a translation resource is available.
Every exception generated by Commons Math implements the ExceptionContextProvider interface. A call to the getContext method will return the ExceptionContext instance stored in the exception, which the user can further customize by adding messages and/or any object.