Related papers: Euler's lute and Edwards' oud
One of the greatest experimental mathematicians of all time was also one of the greatest mathematicians of all time, the great Leonhard Euler. Usually he had an uncanny intuition on how many "special cases" one needs before one can…
E30 in the Enestrom index. Translated from the Latin original "De formis radicum aequationum cuiusque ordinis coniectatio" (1733). For an equation of degree n, Euler wants to define a "resolvent equation" of degree n-1 whose roots are…
As an example of empirical metamathematics, we present a detailed study of the dependency structure of the 465 theorems in Euclid's Elements, finding empirical signatures of concepts such as the power of a theorem. We apply similar methods…
We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad…
The following notes are intended to make a small digression on the topics mentioned in the title of the same, since these were not addressed in the past tribute by the Institute of Physics of the UdeA. We believe more than platitude try to…
The ideals of the eighteenth century's Age of Enlightenment are the foundation of modern democracies. The era was characterized by thinkers who promoted progressive social reforms that opposed the long-established aristocracies and…
Understanding the notion of a model is not always easy in logic courses. Hence, tools such as Euler diagrams are frequently applied as informal illustrations of set-theoretical models. We formally investigate Euler diagrams as an…
In the 1770s, Euler wrote a series of papers (E563, E691 and E692) about finding the ellipse with minimal area or perimeter in the family of all ellipses passing through a fixed set of points. This is a translation of all three papers from…
The recently proposed Euclidean index offers a novel approach to measure the citation impact of academic authors, in particular as an alternative to the h-index. We test if the index provides new, robust information, not covered by existing…
This paper contains a number of letters exchanged between MM. Dollond, Short, and Euler in 1752 regarding the construction and use of various objective lenses. The final letters, authored by Euler, appear in translation for the first time.…
The book "A Course in Constructive Algebra" (1988) shows the way of understanding classical basic algebra in a constructive style similar to Bishop's Constructive Mathematics. Classical theorems are revisited, with a new flavour, and become…
When people mention the mathematical achievements of Euclid, his geometrical achievements always spring to mind. But, his Number-Theoretical achievements (See Books 7, 8 and 9 in his magnum opus \emph{Elements} [1]) are rarely spoken. The…
This small overview of the General Theory is the kind of summary I would have liked to have read, before embarking in a comprehensive study of the General Theory at the time I was a student. As shown here, the main ideas are quite simple…
We discuss the relevance of the recent Machine Learning (ML) literature for economics and econometrics. First we discuss the differences in goals, methods and settings between the ML literature and the traditional econometrics and…
E731 in the Enestrom index. Originally published as "Solutio problematis ob singularia calculi artificia memorabilis", Memoires de l'academie des sciences de St-Petersbourg 2 (1810), 3-9. For $z$ the distance from the origin, and $v$ a…
In this note we will present how Euler's investigations on various different subjects lead to certain properties of the Legendre polynomials. More precisely, we will show that the generating function and the difference equation for the…
Translated from the Latin original, "De numeris amicabilibus" (1747). E100 in the Enestroem index. Euler starts by saying that with the success of mathematical analysis, number theory has been neglected. He argues that number theory is…
The comments relate to the often overlooked, if not in fact intentionally disregarded depths of what the so called internal aspects of mathematical knowledge may involve, depths concerning among others issues such as its unreasonable…
Graduate courses can provide specialized knowledge for Ph.D. and Master's students and contribute to develop their hard and soft skills. At the same time, Systematic Literature Review (SLR) has been increasingly adopted in the computing…
This paper proposes and argues for a counterintuitive thesis: the truly valuable capabilities of large language models (LLMs) reside precisely in the part that cannot be fully captured by human-readable discrete rules. The core argument is…