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Einfluß der Symbolik und des Formalismus auf die Entwicklung des mathematischen Denkens
Author(s) -
Knobloch Eberhard
Publication year - 1980
Publication title -
berichte zur wissenschaftsgeschichte
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.109
H-Index - 8
eISSN - 1522-2365
pISSN - 0170-6233
DOI - 10.1002/bewi.19800030108
Subject(s) - philosophy of mathematics , formalism (music) , mathematics , philosophy , calculus (dental) , epistemology , literature , art , medicine , musical , dentistry
The object of this article is the study of possibilities and tendencies arising from the use of symbolic language including signs, characters, and symbols in mathematics. Five aspects are discussed: compactness and simultaneity, problem‐solving and generalizations, heuristics and progress, mechanisms and calculations, formalism. This is done primarily by looking at three disciplines, which at the same time are of fundamental importance to theoretical physics: classical algebra, calculus, and vector analysis. Mathematical achievements and statements by eminent mathematicians from antiquity to the present (Archimedes, Leibniz, Newton, Euler, Gauß, Hilbert) show the importance of adequate symbolism for the development of mathematics. The corresponding philosophical discussions (Hobbes, Condillac, Degérando, Apelt, Cassirer, among others) are controversial.