Related papers: Hilbert's Error?

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

In this note, we prove a concrete variant of the twistor theorem of Hitchin--Karlhede--Lindstr\"om--Ro\v{c}ek which applies when one already has the real manifold on which one wishes to construct a hyper-K\"ahler structure, and so one does…

Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing,…

For a singular integral equation on an interval of the real line, we study the behavior of the error of a delta-delta discretization. We show that the convergence is non-uniform, between order $O(h^{2})$ in the interior of the interval and…

We study the iteration that replaces a planar hexagon by the hexagon formed by joining the midpoints of consecutive edges. While this iteration quickly drives any polygon toward a point and their shapes asymptotically regularize, we show a…

Euclid's reasoning is essentially constructive. Tarski's elegant and concise first-order theory of Euclidean geometry, on the other hand, is essentially non-constructive, even if we restrict attention (as we do here) to the theory with…

We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off lines.

We give a new proof the arithmetic Hilbert-Samuel theorem by using classical reductions in the theory of coherent sheaves, a direct proof in the case of the projective space and the conservation of some numerical invariants, called…

We prove a functional identity between the Hilbert metric and the visual angle metric in the unit disk. The proof utilizes the Poincar\'e hyperbolic metric in terms of which both metrics can be expressed. This identity then yields sharp…

We give an expression for the Smith-Thom deficiency of the Hilbert square $X^{[2]}$ of a smooth real algebraic variety $X$ in terms of the rank of a suitable Mayer-Vietoris mapping in several situations. As a consequence, we establish a…

M\"uger proved in 2003 that the center of a spherical fusion category C of non-zero dimension over an algebraically closed field is a modular fusion category whose dimension is the square of that of C. We generalize this theorem to a…

We prove that two dimensional convex subsets of spherical buildings are either buildings or have a center.

We present a version of a proof by Andy Chermak of the existence and uniqueness of centric linking systems associated to arbitrary saturated fusion systems. This proof differs from the one by Chermak in that it is based on the computation…

We develop a theory of universal central extensions of Hom-Lie algebras. Classical results of universal central extensions of Lie algebras cannot be completely extended to Hom-Lie algebras setting, because of the composition of two central…

We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The proof uses a doubling argument with the goal of converting…

Constructive properties of uniform convexity, strict convexity, near convexity, and metric convexity in real normed linear spaces are considered. Examples show that certain classical theorems, such as the existence of points of osculation,…

I review several proofs for non-existence of orthogonal complex structures on the six-sphere, most notably by G. Bor and L. Hernandez-Lamoneda, but also by K. Sekigawa and L. Vanhecke that we generalize for metrics close to the round one.…

This paper is devoted to demonstrate Kakeya's geometric proof of his theorem (1912), independently established earlier by Enestr\"om (1893). By calculating centers and radii of the interlacing circles of Kakeya's method, we prove Kakeya's…

The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively. If we are using compass and ruler the way we construct new points is by first…

We demonstrate the homogeneity of the Hilbert Cube. In particular, we construct explicit self-homeomorphisms of the Hilbert cube so that given any two points, a homeomorphism moving one to the other may be realized.