Related papers: Apology of Euclid
A variation of Dyck paths allows for down-steps of arbitrary length, not just one. Credits for this invention are given to Emeric Deutsch. Surprisingly, the enumeration of them is somewhat akin to the analysis of Motzkin-paths; the last…
The authors are not satisfied about the analysis.
French translation, by Henri Lombardi and Stefan Neuwirth, of the article "Did Euclid need the Euclidean algorithm to prove unique factorization?", American Mathematical Monthly 113 (2006), pages 196-205.
We provide a short and simple proof of a beautiful result of Kaczorowski and Perelli classifying the elements of degree one in the Selberg class.
Experimental contributors to the field of Superconducting Materials share their informal views on the subject.
The search of a rational explanation of eclipses pervades the beginnings of philosophical and scientific thought. Within this intellectual frame, the knowledge of the "saros cycle" (a cycle of 18 years, 10 or 11 days and 1/3 of a day that…
This text aims to explains briefly the formalism of quantum mechanics to mathematicians.
This is an attempt to look at the tropical geometry from topological point of view.
This paper is a short introduction to a special issue on philosophy of cosmology, published in the May 2014 issue of Studies in History and Philosophy of Modern Physics. I briefly introduce the philosophy of cosmology, and then provide a…
This is a concise foreword to, rather than a review of D-brane physics.
Dorpalen-Barry et al. proved Elser's conjecture about sign of Elser's number by interpreting them as certain sums of reduced Euler characteristics of an abstract simplicial complex known as $U$-nucleus complex. We prove a conjecture posed…
This is a short discussion of the definition of monad which was given by G.W. Leibniz in his "Monadology."
We give a concise exposition of Voevodsky's theory of motives.
This translation has been withdrawn due to certain imperfections and mistakes, which are corrected in the version uploaded at The Euler Archive (see E65 at http://www.eulerarchive.org/)
``When to the sessions of sweet silent thought I summon up re-membranes of things past, I sigh the lack of many a thing I sought''. (Apologies to William Shakespeare)
This article is a short survey of the history of functional analysis for topologists.
This paper is devoted to show the advantages of introducing a geometric viewpoint and a non extensive formulation in the description of apparently unrelated phenomena: combustion and earthquakes. Here, it is shown how the introduction of a…
Given two non-zero integers $a$ and $b$ there exist integers $m$ and $n$ for which $am-bn =(a,b)$. An increasing number of mathematicians have been calling this `B\'ezout's identity', some encouraged by finding "identit\'e de B\'ezout" in…
This is a brief account of the life and work of G\"oran Lindblad.
This paper has been withdrawn by the authors since it was discovered that most of its content was already known.