Related papers: Exploring Felix Klein's contested modernism
Kolmogorov introduced an informal calculus of problems in an attempt to provide a classical semantics for intuitionistic logic. This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik…
Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces it has to be redesigned when applied to other…
The goal of this survey is to present intimate interactions between four branches of conformal dynamics: iterations of anti-rational maps, actions of Kleinian reflection groups, dynamics generated by Schwarz reflections in quadrature…
The dual character of invariance under transformations and definability by some operations has been used in classical work by for example Galois and Klein. Following Tarski, philosophers of logic have claimed that logical notions themselves…
We establish a new improvement of the classical $L^p$-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one dimensional Hardy inequality.…
Certain rearrangement inequalities of a type considered by Hardy, Riesz, and Brascamp-Lieb-Luttinger are studied. Subsets of the real line that extremize these inequalities are characterized. Our results apply only to special cases, and…
Karl Popper and Paul Feyerabend have been among the most influential philosophers of science of the twentieth century. Extensive studies have been dedicated to the development of their controversial relationship, which saw Feyerabend…
A Keller map is a counterexample to the Jacobian Conjecture. In dimension two every such map, if exists, leads to a complicated set of conditions on the map between the Picard groups of suitable compactifications of the affine plane. This…
We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides…
Mel Levy and Elliott Lieb are two of the most prominent researchers who have dedicated their efforts to the investigation of fundamental questions in many-electron theory. Their results have not only revolutionized the theoretical approach…
Counterfactual reasoning plays a crucial role in exploring hypothetical scenarios, by comparing some consequent under conditions identical except as results from a differing antecedent. David Lewis' well-known analysis evaluates…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and…
In their letter to PNAS and a comprehensive set of notes on arXiv [arXiv:0909.5673v2], Christian Robert, Kerrie Mengersen and Carla Chen (RMC) represent our approach to model criticism in situations when the likelihood cannot be computed as…
This essay offers an epistemological reinterpretation of the foundational divide between matrix mechanics and wave mechanics. Though formally equivalent, the two theories embody distinct modes of knowing: procedural construction and…
Two prominent conjectures by Herbert J. Ryser have been falsely attributed to a somewhat obscure conference proceedings that he wrote in German. Here we provide a translation of that paper and try to correct the historical record at least…
Recent advances in semiclassical gravity, both in our understanding of the gravitational path integral and the algebraic structure of a gravitating subregion, rely on the presence of an observer to obtain a nontrivial Hilbert space for…
The very early dismissal of Schwarzschild's original solution and manifold, and the rise, under Schwarzschild's name, of the inequivalent solution and manifold found instead by Hilbert, are scrutinised and commented upon, in the light of…
Abraham Robinson's philosophical stance has been the subject of several recent studies. Erhardt following Gaifman claims that Robinson was a finitist, and that there is a tension between his philosophical position and his actual…
I will talk about my recent work with Fernando Marques where we used Almgren-Pitts Min-max Theory to settle some open questions in Geometry: The Willmore conjecture, the Freedman-He-Wang conjecture for links (jointly with Ian Agol), and the…