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.
...More
Article
Catherine Goldstein;
(2016)
«Découvrir des principes en classant» : la classification des formes quadratiques selon Charles Hermite
(/isis/citation/CBB947622345/)
Book
Bussotti, Paolo;
(2006)
From Fermat to Gauss: Indefinite Descent and Methods of Reduction in Number Theory
(/isis/citation/CBB000772063/)
Article
Bullynck, Maarten;
(2010)
Factor Tables 1657--1817, with Notes on the Birth of Number Theory
(/isis/citation/CBB001033636/)
Article
Jöran Friberg;
(2019)
Three Thousand Years of Sexagesimal Numbers in Mesopotamian Mathematical Texts
(/isis/citation/CBB634644866/)
Book
Goldstein, Catherine;
Schappacher, Norbert;
Schwermer, Joachim;
(2007)
The Shaping of Arithmetic after C. F. Gauss's Disquisitiones Arithmeticae
(/isis/citation/CBB001035076/)
Article
Jan R. Magnus;
(2022)
Gauss on least-squares and maximum-likelihood estimation
(/isis/citation/CBB054933541/)
Book
Richard Dedekind;
Heinrich Weber;
(2019)
Theorie Des Fonctions Algebriques d'Une Variable
(/isis/citation/CBB160173996/)
Article
Bullynck, Maarten;
(2009)
Reading Gauss in the Computer Age: On the U.S. Reception of Gauss's Number Theoretical Work (1938--1989)
(/isis/citation/CBB000932086/)
Book
Kurt Godel;
Solomon Feferman;
John W. Dawson;
Warren Goldfarb;
Charles Parsons;
Wilfried Sieg;
(2013)
Kurt Gödel: Collected Works: Volume IV
(/isis/citation/CBB660754544/)
Article
Bartha, Paul;
(2004)
Countable Additivity and the de Finetti Lottery
(/isis/citation/CBB000410760/)
Book
Pellatt, Valerie;
(2007)
Numbers and Numeracy in Chinese Culture, Language and Education: The Social Substratum of the Development of Mathematical Thinking
(/isis/citation/CBB001023835/)
Article
Paolo Rossini;
(2020)
Changing conceptions of mathematics and infinity in Giordano Bruno’s vernacular and Latin works
(/isis/citation/CBB044626758/)
Article
Glasberg, Ronald;
(2003)
Mathematics and Spiritual Interpretation: A Bridge to Genuine Interdisciplinarity
(/isis/citation/CBB000411132/)
Article
Martínez Finkelshtein, Andrei;
(2003)
El Análisis Numérico en los últimos 25 años
(/isis/citation/CBB000530007/)
Article
Lavers, Gregory;
(2013)
Frege, Carnap, and Explication: “Our Concern Here Is to Arrive at a Concept of Number Usable for the Purpose of Science”
(/isis/citation/CBB001212885/)
Article
Robin E. Rider;
(2020)
Equations as Unruly Objects
(/isis/citation/CBB581466291/)
Article
Sugimoto, Toshio;
(1986)
Berichtigungen der Zahlenrechnungen, die in den Gauss'schen Werken enthalten sind
(/isis/citation/CBB000056171/)
Book
Pieper, H.;
(1978)
Variationen über ein zahlentheoretisches Thema von C. F. Gauss
(/isis/citation/CBB000027943/)
Article
Neumann, Olaf;
(1979)
Zur Genesis der algebraischen Zahlentheorie: Bemerkungen aus heutiger Sicht über Gauss' Beiträge zu Zahlentheorie, Algebra und Funktionentheorie
(/isis/citation/CBB000028531/)
Book
Gauss, Carl Friedrich;
(1995)
Disquisitiones arithmeticae. Traducción al español hecho por Barrantes Campos, Hugo, Michael Josephy, Angel Ruiz Zúñiga
(/isis/citation/CBB000068690/)
Be the first to comment!