Historically Speaking– Debatable or Erroneous Statements Relating to the History of Mathematics

1968 ◽  
Vol 61 (1) ◽  
pp. 75-79
Author(s):  
Cecil B. Read

The student or teacher who consults several references to obtain information about some historical point in the development of mathematics may, at first, be shocked to find definite discrepancies. Further study may reveal that while in certain cases the reference seems to be definitely in error, in other cases the point may be debatable. Sometimes the error seems clearly to be typographical; in other situations the author has been careless in drawing too-general conclusions; in still others the situation is simply one in which even competent research has not yet produced clear-cut evidence. Unfortunately, in some cases, reading of the references indicates an error caused by repeating an unchecked statement made by some previous author.

2019 ◽  
Vol 56 (3) ◽  
pp. 169-185
Author(s):  
Vladislav A. Shaposhnikov ◽  

The paper deals with some conceptual trends in the philosophy of science of the 1980‒90s, which being evolved simultaneously with the computer revolution, make room for treating it as a revolution in mathematics. The immense and widespread popularity of Thomas Kuhn’s theory of scientific revolutions had made a demand for overcoming this theory, at least in some aspects, just inevitable. Two of such aspects are brought into focus in this paper. Firstly, it is the shift from theoretical to instrumental revolutions which are sometimes called “Galisonian revolutions” after Peter Galison. Secondly, it is the shift from local (“little”) to global (“big”) scientific revolutions now connected with the name of Ian Hacking; such global, transdisciplinary revolutions are at times called “Hacking-type revolutions”. The computer revolution provides a typical example of both global and instrumental revolutions. That change of accents in the post-Kuhnian perspective on scientific revolutions was closely correlated with the general tendency to treat science as far more pluralistic and transdisciplinary. That tendency is primarily associated with the so-called Stanford School; Peter Galison and Ian Hacking are often seen as its representatives. In particular, that new image of science gave no support to a clear-cut separation of mathematics from other sciences. Moreover, it has formed prerequisites for the recognition of material and technical revolutions in the history of mathematics. Especially, the computer revolution can be considered in the new framework as a revolution in mathematics par excellence.


2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.


Author(s):  
Jed Z. Buchwald ◽  
Mordechai Feingold

Isaac Newton’s Chronology of Ancient Kingdoms Amended, published in 1728, one year after the great man’s death, unleashed a storm of controversy. And for good reason. The book presents a drastically revised timeline for ancient civilizations, contracting Greek history by five hundred years and Egypt’s by a millennium. This book tells the story of how one of the most celebrated figures in the history of mathematics, optics, and mechanics came to apply his unique ways of thinking to problems of history, theology, and mythology, and of how his radical ideas produced an uproar that reverberated in Europe’s learned circles throughout the eighteenth century and beyond. The book reveals the manner in which Newton strove for nearly half a century to rectify universal history by reading ancient texts through the lens of astronomy, and to create a tight theoretical system for interpreting the evolution of civilization on the basis of population dynamics. It was during Newton’s earliest years at Cambridge that he developed the core of his singular method for generating and working with trustworthy knowledge, which he applied to his study of the past with the same rigor he brought to his work in physics and mathematics. Drawing extensively on Newton’s unpublished papers and a host of other primary sources, the book reconciles Isaac Newton the rational scientist with Newton the natural philosopher, alchemist, theologian, and chronologist of ancient history.


1985 ◽  
Vol 19 (1) ◽  
pp. 9-33 ◽  
Author(s):  
J. L. Berggren

In Recent Years, many discoveries in the history of Islamic mathematics have not been reported outside the specialist literature, even though they raise issues of interest to a larger audience. Thus, our aim in writing this survey is to provide to scholars of Islamic culture an account of the major themes and discoveries of the last decade of research on the history of mathematics in the Islamic world. However, the subject of mathematics comprised much more than what a modern mathematician might think of as belonging to mathematics, so our survey is an overview of what may best be called the “mathematical sciences” in Islam; that is, in addition to such topics as arithmetic, algebra, and geometry we will also be interested in mechanics, optics, and mathematical instruments.


Sign in / Sign up

Export Citation Format

Share Document