Good math books to discover stuff by programming

The following quote is the starting point of chapter I in

• Mathematics by Experiment, Plausible Reasoning in the 21st Century by J. Borwein and D. Bailey

  ''The computer has in turn changed the very nature of mathematical experience, suggesting for the first time that mathematics, like physics, may yet become an empirical discipline, a place where things are discovered because they are seen.''

  From: David Berlinski, ''Ground Zero: A Review of the The Pleasures of Counting, by T.W. Koerner,'' 1997

Both authors are well known for their highly creative usage of computational power in mathematical problems.

• From the preface of the book:

  Our goal in these books is to pesent a variety of accessible examples of modern mathematics where intelligent computing plays a significant role (along with a few examples showing the limitations of computing). We have concentrated primarily on examples from analysis and number theory, as this is where we have the most experience but there are numerous excursions into other areas of mathematics as well.

Here the authors also address the follow-up book: Experimentation in Mathematics - Computational Paths to Discovery.

Hint: You might also want to take a look at experimentalmath.info.

Ilan Vardi, Computational Recreations in Mathematica.

A = B by Marko Petkovsek, Herbert S Wilf, & Doron Zeilberger