Discrete Thoughts

Essays on Mathematics, Science and Philosophy
Nachdruck of the 1992 2. Auflage 2008
ISBN: 978-0-8176-4774-2
Verlag: Birkhäuser Boston

Buch, Englisch, 266 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 435 g

Reihe: Modern Birkhäuser Classics

as anywhere today, it is becoming more d- ficult to tell the truth. To be sure, our store of accurate facts is more plentiful now than it has ever been, and the minutest details of history are being thoroughly recorded. Scientists, - men and scholars vie with each other in publishing excruciatingly definitive accounts of all that happens on the natural, political and historical scenes. Unfortunately, telling the truth is not quite the same thing as reciting a rosary of facts. Jos6 Ortega y Gasset, in an adm- able lesson summarized by Antonio Machado's three-line poem, prophetically warned us that the reason people so often lie is that they lack imagination: they don't realize that the truth, too, is a matter of invention. Sometime, in a future that is knocking at our door, we shall have to retrain ourselves or our children to properly tell the truth. The exercise will be particularly painful in mathematics. The enrapturing discoveries of our field systematically conceal, like footprints erased in the sand, the analogical train of thought that is the authentic life of mathematics. Shocking as it may be to a conservative logician, the day will come when currently MATHEMATICS, IN vague concepts such as motivation and purpose will be made formal and accepted as constituents of a revamped logic, where they will at last be allotted the equal status they deserve, si- by-side with axioms and theorems.

Zielgruppe

Research

Autoren/Hrsg.

Kac, Mark

Schwartz, Jacob T.

Rota, Gian-Carlo

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Wissenschaften: Theorie, Epistemologie, Methodik

Inhaltsverzeichnis

Discrete Thoughts.- Discrete Thoughts.- I.- Mathematics: Tensions.- The Pernicious Influence of Mathematics on Science.- Statistics.- Statistics and Its History.- Combinatorics.- Computer Science.- Mathematics: Trends.- The Future of Computer Science.- Economics, Mathematical and Empirical.- II.- Complicating Mathematics.- Mathematics and Its History.- Academic Responsibility.- Husserl and the Reform of Logic.- Husserl.- Artificial Intelligence.- Computing and Its History.- Will Computers Replace Humans?.- Computer-Aided Instruction.- Misreading the History of Mathematics.- The Wonderful World of Uncle Stan.- Ulam.- Kant.- Heidegger.- Doing Away with Science.- More Discrete Thoughts.