Related papers: Euler and the German Princess
Euler had considered the problem of finding three integers whose sum, product, and also the sum of the products of the integers, taken two at a time, are all perfect squares. Euler's methods of solving the problem lead to parametric…
This is a pedagogical overview of neutrino physics from the invention of neutrino by Pauli in 1930 to the precise measurement of neutrino mass and mixing parameters via neutrino oscillation experiments in recent years. I have tried to pitch…
In this article, we investigate how Euler might have been led to conjecture the Prime Number Theorem, based on what he knew. We also speculate on why he did not do so.
The Bohr--Einstein debate is one of the more remarkable protracted intellectual exchanges in the history of physics. Its influence has been lasting: One of the few clear patterns in a 2013 survey about quantum foundations was that the…
Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, Lehmer's generalized Euler numbers are studied to give certain…
We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian…
Schroedinger's great discovery of wave mechanics in 1926 - his annus mirabilis - is discussed in detail. Beside the six most important papers that appeared during the first half of 1926, letters between Schroedinger and leading physicists…
I study the sequences of Euler and Springer numbers from the point of view of the classical moment problem.
This is an English translation of Euler's 1750 paper "De numeris amicabilibus" (E152), the most substantial of his three works with this name. In it, he expounds at great length the ad hoc methods he has developed to search for pairs of…
Starting with Einstein's famous papers of 1905, we review some of the ensuing developments and their impact on present-day physics. We attempt to cover topics that are of interest to historians and philosophers of science as well as to…
In 1763, Euler published "Dilucidationes de resistentia fluidorum" (Explanations on the resistance of fluids), a memoir that challenges the fluid resistance theories proposed by Isaac Newton and d'Alembert. Euler's work explores the…
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 following translation of Leonhard Euler's "Examination of an Artifice for Propelling a Ship by the Principle of Internal Motion," originally published in 1750, offers a glimpse into a fascinating historical debate in the field of…
I recall my "first hour" events following on my meeting in Fall 1968 in the classroom with my academic teacher and thesis mentor Prof. Dr. Dr. h.c. multiple Walter Greiner. My comments focus on the creation of the new "strong fields" domain…
In his interviews with Eckermann in the 1820s, Goethe referred to his Theory of Colors as his greatest and ultimate achievement. Its reception following publication in 1810 and subsequent reviews throughout the history of physical science…
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…
The contributions of Emmy Noether to particle physics fall into two categories. One is given under the rubric of Noether's theorem, and the other may be described as her important contributions to modern mathematics. These are discussed…
We review Euler's work on spherical geometry. After an introduction concerning the general place that trigonometric formulae occupy in geometry, we start by the two memoirs of Euler on spherical trigonometry, in which he establishes the…
Newton's Principia, when it appeared in 1687, was received with the greatest admiration, not only by the foremost mathematicians and astronomers in Europe, but also by philosophers like Voltaire and Locke and by members of the educated…
Particular families of special functions, conceived as purely mathematical devices between the end of XVIII and the beginning of XIX centuries, have played a crucial role in the development of many aspects of modern Physics. This is indeed…