In the 1870s, Carl Neumann proposed the so-called method of the arithmetic mean for solving the Dirichlet problem on convex domains. Neumann’s approach was considered at the time to be a reliable existence proof, following Weierstrass’s criticism of the Dirichlet principle. However, in 1937 H. Lebesgue pointed out a serious gap in Neumann’s proof. Curiously, the erroneous argument once again involved confusion between the notions of infimum and minimum. The objective of this paper is to show that Lebesgue’s sharp criticism of Neumann’s proof was only partially justified.
...MoreSimilar Citations
Thesis
Villeneuve, Jean-Philippe;
(2008)
Types de generalisations et epistemologie des mathematiques: De l'integrale de Cauchy a l'integrale de Lebesgue
(/isis/citation/CBB001562844/)
Article
Enrico Rogora;
(2021)
A Priority Claim of Henri Lebesgue against Leonida Tonelli
(/isis/citation/CBB674062575/)
Article
Jemma Lorenat;
(2022)
An Okapi Hypothesis: Non-Euclidean Geometry and the Professional Expert in American Mathematics
(/isis/citation/CBB066890396/)
Article
Moore, Gregory H.;
(2008)
The Emergence of Open Sets, Closed Sets, and Limit Points in Analysis and Topology
(/isis/citation/CBB000950203/)
Article
Chademan, Arsalan;
(2006)
Lebesgue's Famous Article on Integral
(/isis/citation/CBB001510458/)
Book
Gray, Jeremy;
(2008)
Plato's Ghost: The Modernist Transformation of Mathematics
(/isis/citation/CBB000950298/)
Book
Colyvan, Mark;
(2001)
Indispensability of Mathematics
(/isis/citation/CBB000102198/)
Chapter
JEAN PAUL VAN BENDEGEM;
(2016)
Contingency in Mathematics: Two Case Studies
(/isis/citation/CBB062227235/)
Article
Vincenzo De Risi;
(2021)
Euclid’s Common Notions and the Theory of Equivalence
(/isis/citation/CBB348431913/)
Book
Goldenbaum, Ursula;
Jesseph, Douglas;
(2008)
Infinitesimal Differences: Controversies between Leibniz and His Contemporaries
(/isis/citation/CBB000950297/)
Chapter
IAN HACKING;
(2016)
On the Contingency of What Counts as “Mathematics”
(/isis/citation/CBB236243675/)
Book
de Ceglia, Francesco Paolo;
(1999)
De Natantibus: Una Disputa ai Confini tra Filosofia e Matematica nella Toscana Medicea (1611-1615)
(/isis/citation/CBB000100280/)
Article
Rusnock, Paul;
(2013)
On Bolzano's Concept of a Sum
(/isis/citation/CBB001212145/)
Chapter
Carlo Casolo;
(2018)
La Biblioteca Universale
(/isis/citation/CBB604701261/)
Book
Richard Dedekind;
Heinrich Weber;
(2019)
Theorie Des Fonctions Algebriques d'Une Variable
(/isis/citation/CBB160173996/)
Article
Ferraro, Giovanni;
Panza, Marco;
(2012)
Lagrange's Theory of Analytical Functions and His Ideal of Purity of Method
(/isis/citation/CBB001220403/)
Book
Ricketts, Tom;
Potter, Michael D.;
(2010)
The Cambridge Companion to Frege
(/isis/citation/CBB001211647/)
Article
Yap, Audrey;
(2011)
Gauss' Quadratic Reciprocity Theorem and Mathematical Fruitfulness
(/isis/citation/CBB001024184/)
Article
Lizhen Ji;
Chang Wang;
(2020)
Poincaré’s stated motivations for topology
(/isis/citation/CBB272091949/)
Article
Francesca Biagioli;
(2020)
Ernst Cassirer's transcendental account of mathematical reasoning
(/isis/citation/CBB961648354/)
Be the first to comment!