Article ID: CBB001024184

Gauss' Quadratic Reciprocity Theorem and Mathematical Fruitfulness (2011)

unapi

This paper presents an account of the fruitfulness of new mathematical calculi in terms of their relationship to existing mathematical methods which is suggested by Carl Friedrich Gauss. This is done by considering some remarks that Gauss made explaining the fruitfulness of new calculi. These can be clarified in the context of his own (very fruitful) theory of congruences, which is considered as a case study for this alternative account. Such an account has the benefit of not being dependent on a particular metaphysical view in the philosophy of mathematics.

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Authors & Contributors
Bullynck, Maarten
Goldstein, Catherine
Bartha, Paul
Bussotti, Paolo
Dawson, John W., Jr.
Dedekind, Richard
Journals
Archive for History of Exact Sciences
British Journal for the Philosophy of Science
Historia Scientiarum: International Journal of the History of Science Society of Japan
History and Philosophy of Logic
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
NTM: Zeitschrift für Geschichte der Naturwissenschaften, Technik und Medizin
Publishers
Academia Colombiana de Ciencias Exactas, Físicas y Naturales
Birkhäuser
E. Rauner Verlag
Edwin Mellen Press
Oxford University Press
Springer
Concepts
Number theory; number concept
Mathematics
Philosophy of mathematics
Algebra
Number notation; mathematical notation
Translations
People
Gauss, Carl Friedrich
Euler, Leonhard
Bruno, Giordano
Carnap, Rudolf
Dedekind, Richard
Frege, Gottlob
Time Periods
19th century
18th century
20th century
17th century
16th century
20th century, late
Places
Great Britain
Mesopotamia
China
France
Italy
United States
Institutions
Académie des Sciences, Paris
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