Related papers: Apology of Euclid

In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…

Exploring selected reductio ad absurdum proofs in Book 1 of the Elements, we show they include figures that are not constructed. It is squarely at odds with Hartshorne's claim that "in Euclid's geometry, only those geometrical figures exist…

This paper has been withdrawn by the authors due to a mistake in one of the proofs

In this report, I provide a brief summary of the literature in philosophy, psychology and cognitive science about Explanatory Virtues, and link these concepts to eXplainable AI.

We give a characterization of the Dynkin elements of a simple Lie algebra. Namely, we prove that one-half of a Dynkin element is the unique point of minimal length in its N-region. In type A_n this translates into a statement about the…

This is a short overview of the ekpyrotic/cyclic model of the universe, an alternative to the standard big bang inflationary paradigm.

Remarks on the life and work of Paul Erdos.

In this article we determine the implicational fragments of most of the known subintuitionistic logics.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

The purpose of this note is to correct an error in a paper of M. Cowling, G. Fendler and J.J.F. Fournier, and to give a counterexample to a conjecture of J.-L. Rubio de Francia.

This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.

We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…

This paper describes a formalism that subsumes Peterson's intermediate quantifier syllogistic system, and extends the ideas by van Eijck on Aristotle's logic. Syllogisms are expressed in a concise form making use of and extending the…

We give short elementary expositions of combinatorial proofs of some variants of Euler's partitition problem that were first addressed analytically by George Andrews, and later combinatorially by others. Our methods, based on ideas from a…

We reply to recent criticisms of the SIMPLE project by J.I. Collar [arxiv:1106.3559]

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

It is widely written and believed that Edwin Hubble introduced the terms `early' and `late types' to suggest an evolutionary sequence for galaxies. This is incorrect. Hubble took these terms from spectral classification of stars to signify…

This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season…