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The Paths of Creation

Creativity in Science and Art

Series:

Sixto J. Castro and Alfredo Marcos

Edited By Sixto J. Castro and Alfredo Marcos

The Paths of Creation explores the idea of creativity both in science and in art. The editors have collected papers from different philosophers working on philosophy of science and aesthetics to show that the creative processes of science and art share identical procedures: metaphor, ruled method, analogy, abduction, similarity. They are both surrounded by emotions, contain inspirations, proceed through revolutions that maintain some kind of continuity, and have a long common history in which no one worried about whether something was science or art. The purpose of this volume is to show that there are no different rationalities applied to science and art, but the same human reason developing in different forms to create not just different disciplines, but different worlds as well.

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Part II. Thematic Spheres of Creativity

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Creativity and Mathematical Inspiration1 JAVIER DE LORENZO 1. Establishing the Topic At the International Congress of Mathematicians in Madrid in 2006, the Fields Medal was awarded to Terence Tao, a mathematician born in Adelaide on July 17, 1975. On 13 February 2007, Terence Tao posted an essay on the Internet entitled “What is Good Mathematics?”2, which was subsequently published in the October issue of the Bulletin of the AMS. Tao assumes that any mathematical creator – not a teacher or anyone who merely applies mathematics to the sciences – intends “to produce good mathematics”. Thus, if such a thing as “good” mathematics exists, that means that in contrast, there also exists “bad”. The mere formulation of this question, and the supposition upon which it rests, clearly indicate Tao’s stance regarding mathematical undertaking: the question is not whether the mathematician must produce true mathematics, nor is it an ontological question concerning the existence of mathematical entities. The groundwork laid down by a mathematical creator such as Tao is axiological, and within it lies the aes- thetic: the goal of the mathematician is to produce “good” mathematics and not just true mathematics. Hence, it becomes reasonable to ask whether it is also beautiful or ugly, elegant or tasteless, useful or not... Some questions to which Tao sees multiple possible responses relate to the many aspects of mathematical quality. A real 21st century mathematician, Terence Tao, asked such questions in 2007. These questions would have been nonsense a few years ago, when the influence...

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