Related papers: Euler's lute and Edwards' oud
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.
This essay delves into the ethical dilemmas encountered within the academic peer review process and investigates the prevailing deficiencies in this system. It highlights how established scholars often adhere to mainstream theories not out…
``In this paper we give the history of Leonhard Euler's work on the pentagonal number theorem, and his applications of the pentagonal number theorem to the divisor function, partition function and divergent series. We have attempted to give…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
We provide some historical context to the study of solid angles carried out by Euler in his memoir \emph{De mensura angulorum solidorum} (On the measure of solid angles). We extend our study to the general notion of angle (not only solid).…
The nineteenth century was an important period for both Oxford mathematics and algebra in general. While there is extensive documentation of mathematical research in Oxford at this time, the same cannot be said of the teaching. The content…
Engineering needs mathematics, but the converse is also increasingly evident. Indeed, mathematics is still recovering from the drawbacks of several "reforms". Encouraging is the revived interest in proofs indicated by various recent…
Einstein's blackboard is a well-known exhibit at the History of Science Museum at Oxford University. However, it is much less well known that the writing on the board provides a neat summary of a work of historic importance, Einstein's 1931…
Writing strong arguments can be challenging for learners. It requires to select and arrange multiple argumentative discourse units (ADUs) in a logical and coherent way as well as to decide which ADUs to leave implicit, so called enthymemes.…
We study a q-logarithm which was introduced by Euler and give some of its properties. This q-logarithm did not get much attention in the recent literature. We derive basic properties, some of which were already given by Euler in a…
The literature dealing with G\"{o}del's legacy is largely preoccupied with challenging his philosophical views, regarding them as outdated. We believe that such an approach prevents us from seeing G\"{o}del's views in the right light and…
The rate at which scholarly literature is being produced has been increasing at approximately 3.5 percent per year for decades. This means that during a typical 40 year career the amount of new literature produced each year increases by a…
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
A Thesis about Euler discussing the possibilities and limits of his method of work in Mathematics.
This paper was written in 2015, and published in the Journal of Humanistic Mathematics. This paper announces the first issue (2015) of Enchiridion: Mathematics User's Guides, a project to produce peer-reviewed User's Guides as companions to…
In many settings -- like market research and social choice -- people may be presented with unfamiliar options. Classical mechanisms may perform poorly because they fail to incentivize people to learn about these options, or worse, encourage…
This article proposes a reading of Book I of Euclid's Elements with an emphasis of the experiences of infinity supplied by it, as a preparatory study for a research on the embodied cognition of infinity and its material anchors. -- Cet…
This is an adapatation by U. Frisch of an English translation by Thomas E. Burton of Euler's memoir `Principes g\'en\'eraux du mouvement des fluides' (Euler, 1775b). Burton's translation appeared in Fluid Dynamics, 34} (1999) pp. 801-82,…
Generative large language models (LLMs) are incredibly useful, versatile, and promising tools. However, they will be of most use to political and social science researchers when they are used in a way that advances understanding about real…
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…