How Mathematicians Think. Using Ambiguity, Contradiction, and Paradox to Create Mathematics
A lot has been said and written about the philosophy of mathematics, yet not enough. There are too many unanswered questions. For example, is mathematics discovered or created? There still seems to be room for a good book in this field, and this one is wonderful, a must-read for everyone interested in mathematics, philosophy and/or history. One of the most pervasive myths about mathematics is that it is a dull technocratic discipline carried out by grim computer-like minds that have no feelings and who work without intuition, ambiguity or doubt and produce strictly formal algorithms and theorems free of contradictions, conflicts and paradoxes. Such myths, unfortunately still rather common among ‘outsiders’, call for such a book.
The author, a great mathematician and philosopher, and also a practitioner of Zen-Buddhism, shows how essential non-logical qualities are in mathematical research and creativity and that the secret of successful mathematics is not in its logical structure, or at least not only there. Excellent discussions are presented about ambiguity, contradiction, paradox and their central role in the world of mathematical discovery.