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
Ferraro, Giovanni
Parsons, Charles D.
Goldstein, Catherine
Bullynck, Maarten
Haffner, Emmylou
Casolo, Carlo
Concepts
Mathematics
Philosophy of mathematics
Number theory; number concept
Geometry
Algebra
Sexagesimal system
Time Periods
19th century
18th century
20th century
17th century
Ancient
21st century
Places
United States
Germany
China
Mesopotamia
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