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Jonathan M. Borwein, David H. Bailey.
Mathematics by Experiment: plausible reasoning in the 21st century.
A K Peters. 2004

Mathematicians have always used experiments and visualization to explore new ideas and ways to prove them.

Using examples that truly represent the experimental methodology, this book provides the historical context of, and rationale behind, experimental mathematics. It shows how today, the use of advanced computing technology provides mathematicians with an amazing, previously unimaginable “laboratory,” in which examples can be analyzed, new ideas tested, and patterns discovered.

David H. Bailey, Jonathan M. Borwein, Neil J. Calkin, Roland Girgensohn, D. Russell Luke, Victor H. Moll.
Experimental Mathematics in Action.
A K Peters. 2007

The last twenty years have been witness to a fundamental shift in the way mathematics is practiced. With the continued advance of computing power and accessibility, the view that “ real mathematicians don’t compute” no longer has any traction for a newer generation of mathematicians that can really take advantage of computer-aided research, especially given the scope and availability of modern computational packages such as Maple, Mathematica, and MATLAB. The authors provide a coherent variety of accessible examples of modern mathematics subjects in which intelligent computing plays a significant role.