Noise, Oscillators and Algebraic Randomness
Volume 550 of the series Lecture Notes in Physics pp 667
Mathemagics
 Pierre CartierAffiliated withCNRS, Ecole Normale Supérieure de ParisInstitut des Hautes Etudes Scientifiques, Le Bois Marie
Abstract
The implicit philosophical belief of the working mathematician is today the HilbertBourbaki formalism. Ideally, one works within a closed system: the basic principles are clearly enunciated once for all, including (that is an addition of twentieth century science) the formal rules of logical reasoning clothed in mathematical form. The basic principles include precise definitions of all mathematical objects, and the coherence between the various branches of mathematical sciences is achieved through reduction to basic models in the universe of sets. A very important feature of the system is its noncontradiction ; after Gödel, we have lost the initial hopes to establish this noncontradiction by a formal reasoning, but one can live with a corresponding belief in noncontradiction. The whole structure is certainly very appealing, but the illusion is that it is eternal, that it will function for ever according to the same principles. What history of mathematics teaches us is that the principles of mathematical deduction, and not simply the mathematical theories, have evolved over the centuries. In modern times, theories like General Topology or Lebesgue’s Integration Theory represent an almost perfect model of precision, flexibility and harmony, and their applications, for instance to probability theory, have been very successful.
My thesis is: there is another way of doing mathematics, equally successful, and the two methods should supplement each other and not fight.
 Title
 Mathemagics
 Book Title
 Noise, Oscillators and Algebraic Randomness
 Book Subtitle
 From Noise in Communication Systems of Number Theory Lectures of a School Held in Chapelle des Bois, France, April 5–10, 1999
 Pages
 pp 667
 Copyright
 2000
 DOI
 10.1007/3540454632_2
 Print ISBN
 9783540675723
 Online ISBN
 9783540454632
 Series Title
 Lecture Notes in Physics
 Series Volume
 550
 Series ISSN
 00758450
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
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 Industry Sectors
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 Editors

 Michel Planat ^{(14)}
 Editor Affiliations

 14. Laboratoire de Physique et Merologie, des Oscillateurs du CNRS
 Authors

 Pierre Cartier ^{(15)} ^{(16)}
 Author Affiliations

 15. CNRS, Ecole Normale Supérieure de Paris, 45 rue d’Ulm, 75230, Paris Cedex 05
 16. Institut des Hautes Etudes Scientifiques, Le Bois Marie, 35 Route de Chartres, 91440, BuressurYvette, France
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