Related papers: Apology of Euclid

We present two proofs each, all shorter than the original proofs, of two elegant combinatorial identities that came up in the beautiful article arXiv:2010.00077 .

Explanations are a fundamental element of how people make sense of the political world. Citizens routinely ask and answer questions about why events happen, who is responsible, and what could or should be done differently. Yet despite their…

Creating a new Ontology: a Modular Approach

These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.

This is the written version of the Bourbaki seminar given in January 2013 and published in 2014 (modulo an additional early reference added subsequently). It describes the first construction of infinite, finitely generated amenable simple…

This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].

This is a short tribute to Alexandr Alexandrov (1912--1999).

A few final comments on arXiv:1210.7548 are given to confute incorrect arguments claimed there.

In this talk I make some remarks about the search for the origin of the electroweak scale.

Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.

The article is an historical overview of some of the major contributions from different areas of Science with which, for centuries, it has been built up a scientific, sound and consistent vision of the atom. Some experiments that led us to…

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…

An interpretation of selected parts of Newton's Principia, with modern notation and methods. Keplers Laws are derived from an inverse square law using Newton's methods.

While the contents of Euclid's Elements are well-known these days, some characters of the original text have been overlooked due to interpretation by modern mathematical languages. The lens of modern mathematics once anachronistically…

We appended an errata to the original submission. The purpose of this errata is to point out two errors in [2] and give a weakened version of those statements made.

We contemplate a higher-level bipolar abstract argumentation for non-elementary arguments such as: X argues against Ys sincerity with the fact that Y has presented his argument to draw a conclusion C, by omitting other facts which would not…

In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.

This article is a very short introduction to pcf theory for topologists.

The paper approaches to the reader to topology with a curious example of topological classification by homeomorphisms applied to the letters of the alphabet viewed as subsets of Euclidean plane.

The modern usage of the words astronomy and astrology is traced back to distinctions, largely ignored in recent scholarship. Three interpretations of celestial phenomena (in a geometric, a substantialist and a prognostic versions) coexisted…