Related papers: Exploring Felix Klein's contested modernism

We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.

We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka…

In this paper, we discuss some subtle concepts, such as coordinate, measurement, simultaneity, Lorentz-FitzGerald contraction, singularity in fundamental physics. The explanations of these concepts in textbooks are usually incomplete and…

We connect two notions of tautological ring: one for the moduli space of curves (after Mumford, Faber, etc.), and the other for the Jacobian of a curve (after Beauville, Polishchuk, etc.). The motivic Lefschetz decomposition on the Jacobian…

Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first…

The Einstein-Maxwell equations on a smooth compact 4-manifold are reformulated as a purely Riemannian variational problem analogous to Calabi's variational problem for extremal Kahler metrics. Next, Seiberg-Witten theory is used to show…

The paper (in French) presents a survey of Hilbert's Epsilon operator focusing on the intensional aspects of its semantics. It comments on some epistemological problems, from Albert Lautman in the 1930s to John Bell, Grigori Mints, Barry…

Stephen Toulmin once observed that `it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate'. Might the application of Toulmin's layout of arguments to mathematics remedy this oversight?…

Weihrauch complexity is now an established and active part of mathematical logic. It can be seen as a computability-theoretic approach to classifying the uniform computational content of mathematical problems. This theory has become an…

We explore the different meanings of "quantum uncertainty" contained in Heisenberg's seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about "Anschaulichkeit",…

This article is a response to the recent Worrying Trends in Econophysics critique written by four respected theoretical economists. Two of the four have written books and papers that provide very useful critical analyses of the shortcomings…

We introduce a new Gentzen-style framework of grafted hypersequents that combines the formalism of nested sequents with that of hypersequents. To illustrate the potential of the framework, we present novel calculi for the modal logics…

The general aim of this article is to study the negation fragment of classical logic within the framework of contemporary (Abstract) Algebraic Logic. More precisely, we shall find the three classes of algebras that are canonically…

Crispin Wright in his 1982 paper argues for strict finitism, a constructive standpoint that is more restrictive than intuitionism. In its appendix, he proposes models of strict finitistic arithmetic. They are tree-like structures, formed in…

We critically revisit Einstein's 1905 heuristic argument for lightquanta, considering its internal coherence and the scope of its applicability. We argue that Einstein's reasoning, often celebrated for its originality, is ambiguous because…

We unravel a deep connection between limits of real numbers and limits in category theory. Using a new variant of the classical characterisation of the real numbers, we characterise the category of finite-dimensional Hilbert spaces and…

We critically analyze a recent paper by D. Mermin and we compare his statements with Bell's position on the problems he is discussing.

We continue to investigate various diagonalization properties for sequences of open covers of separable metrizable spaces introduced in Part I. These properties generalize classical ones of Rothberger, Menger, Hurewicz, and Gerlits-Nagy. In…

Bell derived the given inequalities on the basis of one rather forceful assumption that was supposed to hold in the hidden variable theory. However, this assumption has been so strong that it has corresponded only to the classical physics;…

This article is firstly a historic review of the theory of Riemann-Hilbert problems with particular emphasis placed on their original appearance in the context of Hilbert's 21st problem and Plemelj's work associated with it. The secondary…