Related papers: Ueber die Geometrie der alten Aegypter

During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to…

Both lectures focus on the first part of the so-called 'mathematical part' of Plato's Theaetetus. In this passage, the young Theaetetus briefly recounts the mathematical lesson given by the geometer Theodorus. The first lecture delves into…

Translated from the Latin original "Novae demonstrationes circa resolutionem numerorum in quadrata" (1774). E445 in the Enestrom index. See Chapter III, section XI of Weil's "Number theory: an approach through history". Also, a very clear…

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…

These are notes on Zhang's work and subsequent developments produced in preparation for 5 hours of talks for a general mathematical audience given in Cambridge, Edinburgh and Auckland over the last year. Being for colloquium-style talks,…

This paper aims to give a brief account of the mathematical work of the 7th-century Armenian polymath and natural philosopher Anania Shirakatsi. The three sections of Anania's ``Book of Arithmetic'' -- tables of arithmetic operations, a…

The current research conducts a comprehensive analysis of citation networks focusing on publications by authors affiliated with Egyptian institutions. Leveraging the Semantic Scholar platform and its API, a citation network and a…

This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…

Any rational number can be written as the sum of distinct unit fractions. In this survey paper we review some of the many interesting questions concerning such 'Egyptian fraction' decompositions, and recent progress concerning them.

This is an English translation of Moufang's notes "Grundlagen der Geometrie" at the University of Frankfurt in 1948, with added notes by the translator.

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…

This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…

A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.

This article focuses on evolvement of the history of mathematics as a science and development of its methodology from the 4th century B.C. to the age of Enlightenment.

This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries…

Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…

In 1512, on December 30, the first edition of Fray Juan de Ortega's Arithmetic was published in Lyon. The last chapter, titled "Rules of Geometry", deals with lower approximations of 14 square roots. In later editions of the Arithmetic on…

We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i.) to show how open questions in algebraic complexity theory are naturally posed as questions in geometry and representation theory, (ii.)…

This is an expanded version of the author's lecture at the Conference in Commutative Algebra and Algebraic Geometry in Messina Italy in June 1999. The purpose of the talk was to give a brief introduction to the subject of tight closure,…

Traditionally, mathematical knowledge is published in printed media such as books or journals. With the advent of the Internet, a new method of publication became available. To date, however, most online mathematical publications do not…