Related papers: Apology of Euclid

Short survey to be published at the Encyclopedia of Mathematical Physics.

This paper briefly discusses some questions with analytical and topological aspects, with hopefully some useful references on both sides.

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in…

A slight modification to one of Tarski's axioms of plane Euclidean geometry is proposed. This modification allows another of the axioms to be omitted from the set of axioms and proven as a theorem. This change to the system of axioms…

This is a preprint version of a chapter for Handbook of Algebra.

This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.

We investigate the space of simplices in Euclidean Space

This paper presents a gentle and informal introduction to the Skorokhod topologies. Focus is on motivating examples and concepts.

The exposition of the theory of structure species in Bourbaki's tractate takes only a few pages but still is quite difficult. However, in the exercises, Bourbaki outlines another approach that is based on the notion of structure type rather…

This paper has been withdrawn by the authors as requested by the journal.

We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.

A long-standing, unanswered question regarding Euclid's Elements concerns the absence of a theorem for the concurrence of the altitudes of a triangle, and the possible reasons for this omission. In the centuries following Euclid, a…

This is a philosophy paper rather than mathematical physics work. I will publish it in some other place.

A very short, bijective proof, of Touchard's Catalan identity is given, using Dyck paths.

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.

In introductions to the subject for a general audience of mathematicians or logicians, the univalence axiom is typically explained by handwaving. This gives rise to several misconceptions, which cannot be properly addressed in the absence…

Some typos corrected, slightly different abstract, same plots, results and conclusions.

This is a reply to a comment by P. Schlottmann and A.A. Zvyagin.

In this paper I respond to a critique of one of my papers previously published in the Royal Society Open Science entitled "Quantum correlations are weaved by the spinors of the Euclidean primitives." Without engaging with the geometrical…