We trace the origins of trigonometry to the Old Babylonian era, between the 19th and 16th centuries B.C.E. This is well over a millennium before Hipparchus is said to have fathered the subject with his ‘table of chords’. The main piece of evidence comes from the most famous of Old Babylonian tablets: Plimpton 322, which we interpret in the context of the Old Babylonian approach to triangles and their preference for numerical accuracy. By examining the evidence with this mindset, and comparing Plimpton 322 with Madhava's table of sines, we demonstrate that Plimpton 322 is a powerful, exact ratio-based trigonometric table.
A number of scholars have recently maintained that a theorem in an unpublished treatise by Leibniz written in 1675 establishes a rigorous foundation for the infinitesimal calculus. I argue that this is a misinterpretation. Eine Reihe von Historikern haben vor kurzem behauptet, dass ein Satz in einer unveröffentlichten Abhandlung von Leibniz, die 1675 geschrieben wurde, eine strenge Grundlage für die Infinitesimalrechnung bildet. Ich behaupte, dass dies eine Fehlinterpretation ist.
Between 1947 and 1950, Laurent Schwartz (1915–2002) went from being almost unknown outside of France to being an international mathematical celebrity. This paper accounts for Schwartz's rapid ascent by focusing on the social, institutional, and mathematical contexts of his crucial trajectory from Nancy, via Copenhagen, to the world stage, culminating in his 1950 Fields Medal awarded in Cambridge, Massachusetts. We identify, based on new archival findings, the pivotal role of Danish mathematician Harald Bohr along this trajectory. Our analysis reveals the emerging dynamics of early postwar international mathematics, and explains how certain individuals and theories could rise to prominence in this period. Inconnu jusqu'alors hors de la France, Laurent Schwartz (1915–2002) est devenu entre 1947 et 1950 un mathématicien célèbre sur le plan international. Cet article présente l'ascension rapide de Schwartz en se concentrant sur les contextes sociaux, institutionnels et mathématique de sa trajectoire, depuis Nancy, via Copenhague, jusqu'à la scène mondiale, culminant avec sa médaille Fields, attribuée en 1950 à Cambridge, Massachusetts. Nous identifions, à partir de nouvelles découvertes dans les archives, le rôle central du mathématicien Danois Harald Bohr, le long de cette trajectoire. Notre analyse révèle certaines dynamiques émergentes des mathématiques internationales dans l'immédiate après-guerre, et explique comment certains individus et théories ont pu prendre une place proéminente pendant cette période.
Ada Lovelace is widely regarded as an early pioneer of computer science, due to an 1843 paper about Charles Babbage's Analytical Engine, which, had it been built, would have been a general-purpose computer. However, there has been considerable disagreement among scholars as to her mathematical proficiency. This paper presents the first account by historians of mathematics of the correspondence between Lovelace and the mathematician Augustus De Morgan from 1840–41. Detailed contextual analysis allows us to present a corrected ordering of the archive material, countering previous claims of Lovelace's mathematical inadequacies, and presenting a more nuanced assessment of her abilities. Ada Lovelace wird generell als frühe Pionierin der Informatik angesehen. Dies vor allem wegen des 1843 erschienenen Artikels über Charles Babbages ‘Analytical Engine’, die, wäre sie damals gebaut worden, einen Allzweckcomputer dargestellt hätte. Allerdings gibt es beträchtliche Meinungsverschiedenheiten unter Historikern hinsichtlich Lovelaces mathematischer Kenntnisse. Dieser Artikel präsentiert den ersten Bericht von Mathematikhistorikern über die Korrespondenz der Jahre 1840–41 zwischen Lovelace und dem Mathematiker Augustus De Morgan. Detaillierte Kontextanalyse erlaubt es uns, eine korrigierte Anordnung des Archivmaterials vorzulegen, die bisherigen Meinungen über die mathematischen Unzulänglichkeiten von Lovelace entgegenwirkt und die eine nuanciertere Bewertung ihrer Fähigkeiten erlaubt.
In 1917, as the air war raged in Europe, some of Britain's finest mathematicians, engineers and scientists engaged in their own battle to understand the fundamentals of aerodynamics and aircraft construction. In London, Wing Commander Alec Ogilvie led the Technical Section of the Admiralty Air Department, which included a number of individuals dedicated to addressing aircraft structural issues; amongst them were three women, Hilda Hudson, Letitia Chitty and Beatrice Cave-Browne-Cave. In this article I describe the aeronautical landscape in Britain during the second decade of the 1900s, the place of these women within it, and their contributions to the structural integrity of early, British military aircraft. Nel 1917, mentre in Europa infuriava la guerra aerea, alcuni tra i migliori matematici, ingegneri e scienziati britannici combattevano per carpire i pricipi dell'aerodinamica e della costruzione aeronautica. A Londra il Tenente Colonnello Alec Ogilvie dirigeva la Sezione Tecnica del Dipartimento aereo dell'Ammir-agliato, che includeva un gruppo di persone dedicate alle problematiche strutturali dei velivoli. Tra queste vi erano tre donne: Hilda Hudson, Letitia Chitty and Beatrice Cave-Browne-Cave. In questo articolo descrivo il panorama areonautico durante la seconda decade del 1900, il ruolo di queste donne all'interno in quell'epoca e il contributo che hanno apportato all'integritá strutturale della prima aeronautica militare britannica.
In this paper, we examine unpublished notes of a course on thermodynamics delivered by Eugenio Beltrami. This course is clearly influenced by Clausius's work and aims to present thermodynamics along the lines of rational mechanics, viewed as both a sound foundation and a methodological model, where use of mathematical tools can help to understand delicate points. The course contains also some lessons on the kinetic theory of gases where Beltrami never mentions probability explicitly.
We will study the historical emergence of or , from their origin as “imaginary” solutions of irrational equations, to their insertion in the context of study of the algebras of hypercomplex numbers. Analizzeremo l'evoluzione storica dei o numeri , dalla loro origine come soluzioni “immaginarie” di equazioni irrazionali, al loro inserimento nel contesto dello studio delle algebre di ipercomplessi.
In 1903, Epstein published his proof of meromorphic continuation and a functional equation for Dirichlet series associated with quadratic forms, now called Epstein zeta-functions. However, already in 1889 (or even earlier) Hurwitz was aware of these results as his mathematical diaries and some unpublished notes (in an almost final form) found in his estate at the ETH Zurich show. In this article we present and analyze Hurwitz's notes and compare his reasoning with Epstein's paper in detail.
In 1903, Epstein published his proof of meromorphic continuation and a functional equation for Dirichlet series associated with quadratic forms, now called Epstein zeta-functions. However, already in 1889 (or even earlier) Hurwitz was aware of these results as his mathematical diaries and some unpublished notes (in an almost final form) found in his estate at the ETH Zurich show. In this article we present and analyze Hurwitz's notes and compare his reasoning with Epstein's paper in detail. (C) 2017 Elsevier Inc. All rights reserved.
We will study the historical emergence of Tessarines or Bicomplex numbers, from their origin as "imaginary" solutions of irrational equations, to their insertion in the context of study of the algebras of hypercomplex numbers. (C) 2017 Elsevier Inc. All rights reserved.