My goal was for this book to be light and bubbly like champagne, to show that math and science are fun. Read it and tell me if you think I succeeded!
Reading through this material myself, I sense three key themes. The first two themes are paradoxes: Even though math is the most rational discipline, mathematical creation involves passion, intuition, imagination and inspiration, just as artistic creation does. And my work, like that of Gödel and Turing, limits the power of individual formal axiomatic theories, but itself illustrates how mathematics advances in spite of these pessimistic results by continually inventing revolutionary new fields and concepts. The third theme is Poincaré and insight versus Hilbert and formalization as a key thread of 20th century thought, as discussed in Tasic, Mathematics and the Roots of Postmodern Thought.
Let me put this on the table right away: I am more and more aware of the limitations of the ideas discussed here, but I hope that they may help to open the door to future developments. As for the personal references, they prove that mathematicians are only human.
Many thanks are in order!
First of all, I thank Cristian Calude for publishing my three previous Springer books in his DMTCS (Discrete Mathematics and Theoretical Computer Science) series, and for suggesting that this book should also be published by Springer.
A big ``thank you'' to John Casti for explaining my ideas so well in his many books and publications, most recently in his essay ``Formally speaking'' in Nature (31 May 2001).
It is my pleasure and my duty to thank Françoise Chaitin-Chatelin and F. Walter Meyerstein for many, many stimulating discussions of philosophical issues.
I thank Charles Steele at UMass-Lowell, Hans-Christian Reichel at the University of Vienna, and Ilya Prigogine at the Free University of Brussels, for inviting me to give the lectures collected in this book, and the very responsive audiences that came to my talks. I also thank all of the interviewers for their stimulating questions and for their lively interest in my ideas.
Thanks to Maria F. de Mello, Vitória Mendonça de Barros and Américo Sommerman for inviting me to visit their Center for Transdisciplinary Education at the University of São Paulo, which led to the Globo News TV interview at the end of this book.
Last but not least, I'm extremely grateful to my management here at IBM Research, Paul Horn, Alfred Spector, Daniel Yellin, and Mark Wegman, for their support.
G. J. Chaitin, June 2001