相关论文: Mathematical conquerors, Unguru polarity, and the …

We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leibniz, Euler, Cauchy and other giants of infinitesimal…

Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Klein. Some of Mehrtens' conclusions have been picked up by…

This paper contains a case study of the work and self-definition of two important mathematicians during the rise of modern mathematics: Felx Hausdorff (1868--1942) and Hermann Weyl (1885--1955). The two had strongly diverging positions with…

In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that…

We describe a mainstream "universalist" approach to the understanding of mathematics. We then conduct a systematic (but not exhaustive) review of the academic literature on the decolonisation of mathematics and identify how this challenges…

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…

This paper is devoted to show that the last quarter of the past century can be considered as the golden age of the Mathematical Finance. In this period the collaboration of great economists and the best generation of probabilists, most of…

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).…

This book covers the history of probability up to Kolmogorov with essential additional coverage of statistics up to Fisher. Based on my work of ca. 50 years, it is the only suchlike book. Gorrochurn (2016) is similar but his study of events…

The studies of Bonaventura Cavalieri's indivisibles by Giusti, Andersen, Mancosu and others provide a comprehensive picture of Cavalieri's mathematics, as well as of the mathematical objections to it as formulated by Paul Guldin and other…

University level mathematics in a number of countries is under pressure to `decolonise the curriculum'. This paper considers, as a test case, a possible `decolonisation' of linear algebra. This is a representative case, since linear algebra…

The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…

I briefly consider the Kuhnian notion of "paradigm shifts" applied to the history of mathematics and argue that the succession and intergenerational continuity of mathematical thought was undeservedly neglected in the historical studies. To…

We consider the mathematical theory of geographical maps, with an emphasis on the eighteenth century works of Euler, Lagrange and Delisle. This period is characterized by the frequent use of maps that are no more obtained by the…

Historically, probability theory has been studied for a long time, and Kolmogorov, Levy Ito Kiyoshi, and others have mathematically developed modern probability in conjunction with measurement theory. On the other hand, commutative algebra…

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of…

During a first St. Petersburg period Leonhard Euler, in his early twenties, became interested in the Basel problem: summing the series of inverse squares (posed by Pietro Mengoli in mid 17th century). In the words of Andre Weil (1989) "as…

Three thinkers of the 19th century revolutionized the science of logic, mathematics, and philosophy. Edmund Husserl (1859-1938), mathematician and a disciple of Karl Weierstrass, made an immense contribution to the theory of human thought.…

We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…

The received Hilbert-style axiomatic foundations of mathematics has been designed by Hilbert and his followers as a tool for meta-theoretical research. Foundations of mathematics of this type fail to satisfactory perform more basic and more…