A history of mathematical impossibility
Many of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and compass, the solution of the quintic equation by radicals, Fermat’s last theorem, and the impossibility of proving the para...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Oxford
Oxford University Press
2022
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| Online Zugang: | zbMATH |
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Tag hinzufügen | Zusammenfassung: | Many of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and compass, the solution of the quintic equation by radicals, Fermat’s last theorem, and the impossibility of proving the parallel postulate from the other axioms of Euclidean geometry. This book tells the history of these and many other impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square. "Mathematical theorems stating that a problem cannot be solved using specific means are numerous. This book follows the history of such impossibility theorems from Greek antiquity through the early 20th century. It reveals that many impossibility statements started out as meta-statements but ended up as mathematical theorems that were proved by mathematical methods. Until the 19th century, impossibility theorems were often considered of secondary interest compared with positive results. This changed during the 19th century and today impossibility results are among the most famous and popular theorems of mathematics. The book will deal with some of the celebrated impossibility theorems in pure mathematics such as the quadrature of the circle, the duplication of the cube, the trisection of the angle, Fermat's last theorem, the impossibility of proving the parallel postulate and Gödel's theorem, as well as some theorems from applied mathematics such as Arrow's impossibility theorem. Although an impossibility may sound as a negative result, impossibilities have in fact acted as a creative force in the history of mathematics challenging mathematicians to circumvent the impossibility. The introduction of complex numbers is a case in point"-- |
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| Beschreibung: | Literaturverzeichnis: Seite 267-278 |
| Beschreibung: | xi, 284 Seiten Illustrationen 24 cm |
| ISBN: | 9780192867391 978-0-19-286739-1 |