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