Related papers: Euler and the German Princess
Christian Ludwig Gerling's 1817 appointment as Professor for Mathematics, Physics and Astronomy resulted in the foundation of the Mathematical and Physical Institute of the Philipps University. In 1838, Gerling moved onto new premises in…
I recall my interactions with Julian Schwinger, first as a graduate student at Harvard, and then as a postdoc at UCLA, in the period 1968--81, and subsequently. Some aspects of his legacy to physics are discussed.
Since antiquity, from Euclid of Alexandria to Galileo Galilei to Immanuel Kant to Hermann Minkowksi to Albert Einstein, the question of the nature of space and time has occupied scientists and philosophers. In the four-dimensional…
For several decades a portrait of Johannes Kepler has been widely circulating among professional astronomers, scientific and academic institutions, and the general public. Despite its provenance and identification having been questioned in…
This is an annotated translation from Latin of 'Principia pro motu sanguinis per arterias determinando' in which Euler develops the first known work on the mechanics of flows in elastic tubes, intended to the first contest of the Dijon…
This article was written on the occasion of Hans Grauert receiving the Cantor Medallion of the Deutsche Mathematische Vereinigung. It is a brief overview of his mathematical contributions and attempts to convey the author's great respect…
There is an increasing recognition regarding of the importance of introducing modern Einsteinian concepts early in science education. This study investigates the efficacy of an innovative educational programme "Einstein-First", which…
Translation of the Latin original "Speculationes circa quasdam insignes proprietates numerorum" (1784). E564 in the Enestrom index. In this paper Euler talks about Farey sequences and proves some results about the phi function, the number…
In the late age of developing quantum mechanics, Lev Landau, one of the distinguished players, made great efforts to understand the nature of matter, even stellar matter, by applying the quantum theory. Ninety years ago, he published his…
We examine connections between the mathematics behind methods of drawing geographical maps due, on the one hand to Marinos and Ptolemy (1st-2nd c. CE) and on the other hand to Delisle and Euler (18th century). A recent work by the first two…
Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So,…
In correspondence with Goldbach, Euler began investigating series of the form $\sum_{k \geq 1} k^{-m}\left(1 + 2^{-n} + \cdots + k^{-n}\right)$, which are known today as Euler sums. For the case where $n=1$ and $m \geq 2$, Euler was able to…
We review and comment on some works of Euler and his followers on spherical geometry. We start by presenting some memoirs of Euler on spherical trigonometry. We comment on Euler's use of the methods of the calculus of variations in…
By using ideas on complexity and randomness originally suggested by the mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of algorithmic information is able to show that there can never be a "theory of everything" for…
The aim of this article has been to put together various aspects of the personality of the Italian mathematician Francesco Severi: the mathematical, the political, the institutional, academic and philosophical one. We tried in particular to…
In 1614 Johann Georg Locher, a student of the Jesuit astronomer Christoph Scheiner, proposed a physical mechanism to explain how the Earth could orbit the sun. An orbit, Locher said, is a perpetual fall. He proposed this despite the fact…
As in Greek mythology, the neutrino was born in the mind of Wolfgang Pauli to salvage a fundamental principle. Its existence met with universal skepticism by a scientific community used to infer particles from experiment. Its detection in…
Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information began by yielding new methods for achieving classical tasks such as factoring and key distribution…
From its very beginning, Quantum Theory developed contrary to the intentions of its creators. For Max Planck it marks the failure of a long-term research program, in which he tried to understand the 2nd law of thermodynamics…
Translation from the Latin original "Utrum hic numerus 1000009 sit primus necne inquiritur" (1778). E699 in the Enestrom index. The idea of this paper is that if some number is a sum of two squares in two ways, then some other smaller…