Abstracts Archive

During the first half of the nineteenth century, a debate took place amongst British mathematicians concerning the nature of the symbols used in algebra: did they necessarily stand for numbers, or could they simply be manipulated according to specified rules, with interpretation (if any) coming late...

As recognized by a growing body of literature, most conceptual and methodological shifts in early modern mathematics cannot be accounted for in terms of internal theoretical developments. On the contrary, this literature suggests, social and institutional contexts and the social practices of arithme...

In her Modern Introduction to Logic (1930), often considered the first textbook of analytic philosophy, British philosopher L. Susan Stebbing (1885–1943) presented a coherent long durée vision of the science of logic. Contrary to a caricature (popular then and now) that presents mathematical log...

The aim of this paper is to shed light on an understudied aspect of Giordano Bruno's intellectual biography, namely, his career as a mathematical practitioner. Early interpreters, especially, have criticized Bruno's mathematics for being “outdated” or too “concrete”. However, thanks to devel...

While historians of science rightly take the importance of quantification for granted, over the course of the modern period the sciences of mathematics and computation have generally become less focused on quantity. Numerical knowledge claims have continued to exert undeniable force in discourses fr...

Planetary automata, also called planetary clocks, were expensive and rare masterpieces of technical ingenuity designed to show the subtle motion of the heavenly bodies according to Ptolemaic theory. These automata may justly be considered mathematical instruments for a two-fold reason: they manifest...

In his manuscript of 1818 entitled “System of radical sympathies and antipathies,” Charles Fourier claimed to have devised “the art...of finding all those persons with whom one is in complete sympathy, and of surrounding oneself with them instantly and constantly.” Unfolding across 117 pages...

It is often claimed that analysis is grounded on the principle of contradiction alone and synthesis is grounded not only on the principle of contradiction but on pure intuition as well. This distinction is inaccurate. In my talk, I discuss the notion of analysis as something that can be grounded on ...

The sixteenth and seventeenth century have long been seen as fundamentally important to an understanding of the changing study of nature. The changes in this period have been variously categorized by historians as philosophical, methodological, or mathematical, among other explanations. A move to th...

In 1932, Professor Cassius Jackson Keyser called for “the disciplining of men, women, and children in the art of ‘postulate detection.’” An essential goal of education, he believed, was to teach Americans how to find the hidden assumptions that determine every system of thought, from politic...

This paper scrutinizes the revisions of mathematician Bernhard Riemann’s (1822-1862) 1854 habilitation lecture at the University of Göttingen. It argues that the lecture is a reflection of how mathematicians developed non-Euclidean geometries in the nineteenth century, breaking with long-standing...

Father Claude Richard (Ornans 1589 – Madrid 1664) was professor of mathematics at the Jesuit Imperial College in Madrid (1627-1767) from 1630 until his death. He published Euclides elementorum geometricorum libros tredecim Isidorum et Hypsidem et Recentiores de Corporibus Regularibus, et Procli pr...

Eighty years ago, in 1939, a radical collective of French mathematicians published the first installment of a monumental effort to rewrite the foundations of mathematics under the pseudonym Nicolas Bourbaki. The Elements de Mathematique, collectively planned, written, and revised, quickly became an ...

In the early 1960s, a semiautonomous Division of Computer Science existed within Stanford University’s Department of Mathematics. While the division had initially grown out of interest in numerical analysis within the mathematics department, members of the computer science division became increasi...

Around 1550 Antwerp was a vibrant port. Its many schools catered for the many companies, its Beurs was one of the first stock markets of the world, its printers published books on all subjects. Ships travelled to all parts of Europe, the Baltic, Italy, Scotland, the Azores with merchants dreaming of...

During the early modern period, the mathematical sciences dramatically upgraded its status. It went from having a secondary role and ancillary status in the mid 16th century, up to be considered the most powerful tool of scientific research by the turn of the 18th century. As recognized by a large h...

As is well known in the history of mathematics, the path to the invention of calculus in late seventeenth-century Europe passed through Buonaventura Cavalieri’s geometry of “indivisibles,” the infinitesimally small slices into which he proposed dividing geometric figures in order to compute th...

In the sixteenth and seventeenth centuries, mathematical sciences played an increasingly important role in Western societies. Most historical accounts try to understand how the study of nature came to use mathematical methods and how mathematical concepts and tool became the standard tool for schola...