In his writings about hypergeometric functions Gauss succeeded in moving beyond the restricted domain of eighteenth-century functions by changing several basic notions of analysis. He rejected formal methodology and the traditional notions of functions, complex numbers, infinite numbers, integration, and the sum of a series. Indeed, he thought that analysis derived from a few, intuitively given notions by means of other well-defined concepts which were reducible to intuitive ones. Gauss considered functions to be relations between continuous variable quantities while he regarded integration and summation as appropriate operations with limits. He also regarded infinite and infinitesimal numbers as a façon de parler and used inequalities in order to prove the existence of certain limits. He took complex numbers to have the same legitimacy as real quantities. However, Gauss's continuum was linked to a revised form of the eighteenth-century notion of continuous quantity: it was not reducible to a set of numbers but was immediately given.
...More
Article
Craik, Alex D. D.;
(2013)
Polylogarithms, Functional Equations and More: The Elusive Essays of William Spence (1777--1815)
(/isis/citation/CBB001213656/)
Article
Bullynck, Maarten;
(2010)
Factor Tables 1657--1817, with Notes on the Birth of Number Theory
(/isis/citation/CBB001033636/)
Article
Yap, Audrey;
(2011)
Gauss' Quadratic Reciprocity Theorem and Mathematical Fruitfulness
(/isis/citation/CBB001024184/)
Book
Mittler, Elmar;
Glitsch, Silke;
(2005)
“Wie der Blitz einschlägt, hat sich das Räthsel gelöst”: Carl Friedrich Gauß in Göttingen
(/isis/citation/CBB001232255/)
Article
Ferraro, Giovanni;
(2007)
Convergence and Formal Manipulation in the Theory of Series from 1730 to 1815
(/isis/citation/CBB000771368/)
Book
Bussotti, Paolo;
(2006)
From Fermat to Gauss: Indefinite Descent and Methods of Reduction in Number Theory
(/isis/citation/CBB000772063/)
Article
Sørensen, Henrik Kragh;
(2013)
What's Abelian about Abelian Groups?
(/isis/citation/CBB001212298/)
Article
Ponce-Campuzano, Juan Carlos;
Maldonado-Aguilar, Miguel Ángel;
(2015)
Vito Volterra's Construction of a Nonconstant Function with a Bounded, Non-Riemann Integrable Derivative
(/isis/citation/CBB001552093/)
Article
Tazzioli, Rossana;
(2001)
Green's Function in Some Contributions of 19th Century Mathematicians
(/isis/citation/CBB000100594/)
Article
Coates, John;
(2008)
Euler's Work on Zeta and L-Functions and Their Special Values
(/isis/citation/CBB000931916/)
Article
Ferraro, Giovanni;
(2004)
Differentials and Differential Coefficients in the Eulerian Foundations of the Calculus
(/isis/citation/CBB000410838/)
Article
Nicola M. R. Oswald;
(2017)
On a Relation Between Modular Functions and Dirichlet Series: Found in the Estate of Adolf Hurwitz
(/isis/citation/CBB449429999/)
Article
Rusnock, Paul;
Kerr-Lawson, Angus;
(2005)
Bolzano and Uniform Continuity
(/isis/citation/CBB000771353/)
Article
Bråting, Kajsa;
(2007)
A New Look at E.G. Björling and the Cauchy Sum Theorem
(/isis/citation/CBB000720350/)
Article
Sørensen, Henrik Kragh;
(2005)
Exceptions and Counterexamples: Understanding Abel's Comment on Cauchy's Theorem
(/isis/citation/CBB000771350/)
Article
Adelmann, Clemens;
Gerbracht, Eberhard H.-A.;
(2009)
Letters From William Burnside to Robert Fricke: Automorphic Functions, and the Emergence of the Burnside Problem
(/isis/citation/CBB000932072/)
Article
González Redondo, Francisco A.;
(2002)
Daviet de Foncenex y Lazare Carnot: ¿Las raíces dimensionales de Fourier? Algunos comentarios a Martins, Grattan-Guinnes y Gillespie
(/isis/citation/CBB000300774/)
Article
Grcar, Joseph F.;
(2011)
How Ordinary Elimination Became Gaussian Elimination
(/isis/citation/CBB001036217/)
Article
Roussanova, Elena;
(2009)
Leonhard Euler and Carl Friedrich Gauss: A Precious Discovery in the Archive of the Academy of Sciences in St. Petersburg
(/isis/citation/CBB155889812/)
Article
Bullynck, Maarten;
(2009)
Modular Arithmetic before C. F. Gauss: Systematizations and Discussions on Remainder Problems in 18th-Century Germany
(/isis/citation/CBB000953002/)
Be the first to comment!