History of Mathematics

El sólido hiperbólico agudo

by Rosa María Herrera

Published in Pensamiento Matemático (2012)

The English Renaissance Stage: Geometry, Poetics, and the Practical Spatial Arts, 1580–1630

by Elizabeth Spiller

Rev. of Henry S. Turner, “The English Renaissance Stage: Geometry, Poetics, and the Practical Spatial Arts 1580-1630.” Renaissance Quarterly 59.3 (2006): 965-67.

On some theorems to elementary number theory by kamal al-din farisi

by Sonja Brentjes

Vito Volterra: The Extent of Pathological Functions

by Brent Perreault

A Math History Paper for my Mathematics Senior Seminar Course, Spring 2012.

La notion husserlienne de multiplicité : au-delà de Cantor et Riemann

by Carlo Ierna

in Methodos 12, April 2012

The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his... more The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of space. Husserl’s Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and context of Husserl’s own development.

Blindness and Enlightenment: An Essay: With a New Translation of Diderot's' Letter on the Blind'and La Mothe Le Vayer's' Of a Man Born Blind'

by Kate Tunstall

Review. R. Rashed, AL-KHWARIZMI, Le commencement de I'algebre, ed. and trans, (into French)

by Sonja Brentjes

Reading Mittag-Leffler’s biography of Abel as an act of mathematical self-fashioning

by Henrik Kragh Sørensen

Published in "The History of the History of Mathematics. Case Studies for the Seventeenth, Eighteenth and Nineteenth Centuries". Ed. by Benjamin Wardhaugh. Oxford et al.: Peter Lang, 2012, pp. 115–144.

Otakar Boruvka (1899-1995) and the Minimum Spanning Tree

by Helena Durnova

On the nature of the table Plimpton 322

by Christine Proust

in: R. Tobies and D. Tournès (Eds) Mini-Workshop: History of Numerical and Graphical Tables, February 27th - March 5th, 2011, Mathematisches Forschungsinstitut Oberwolfach Report Vol. 12/2011 (2011)

The cuneiform tablet Plimpton 322 (P322 in the following) is generally understood to be a table providing 15... more The cuneiform tablet Plimpton 322 (P322 in the following) is generally understood to be a table providing 15 Pythagorean triples. This document is the best known and the most controversial of the cuneiform mathematical texts. Various interpretations of the text were offered by many scholars. The various interpretations rely on different assumptions about the very nature of the text. What kind of table is P322?

La multiplication babylonienne: la part non écrite du calcul

by Christine Proust

published in 'Revue d'Histoire des Mathématiques', 6, pp. 1001-1011 (2000)

Certain kinds of calculation errors found in Babylonian texts, dating either from the Old Babylonian period or the... more Certain kinds of calculation errors found in Babylonian texts, dating either from the Old Babylonian period or the more recent Seleucid period, recur and are characteristic in the use of numbers with more than five sexagesimal positions. These errors might give clues about the multiplication process of such numbers. Numbers of a large size would have been cut into two pieces, each of which was then multiplied separately, and the pieces recombined by addition. This method brings to light a limitation to five digits in the multiplication process, which might have been induced by the use of some kind of a counting instrument. The instrument possibly depended on the five fingers of the hand, either in its origin, concept or operation. The persistent and often enigmatic occurrence of the word ``hand'' in the Sumerian vocabulary for numeration are worth looking into in order to substantiate this hypothesis.

Al-Khwārizmī, Le commencement de l'algèbre, ed. and trans, (into French) R. Rashed. (Collection Sciences dans l'Histoire.) Paris: Librairie scientifique et technique Albert Blanchard, 2007.

by Sonja Brentjes

Al-Khwārizmī, Le commencement de l'algèbre, ed. and trans, (into French) R. Rashed. (Collection Sciences dans l'Histoire.) Paris: Librairie scientifique et technique Albert Blanchard, 2007. Paper. Pp. viii, 386; many black-and-white figures and 1 table. €45.

Sonja Brentjes (2009)
Speculum, , Volume 84, Issue 03 , July 2009 pp 737-739
http://journals.cambridge.org/abstract_S0038713400209834

Yupana, tabla de contar inca

by Viviana Moscovich

Yupana, tabla de contar inca: Estructura interna

by Viviana Moscovich

Puig, L. (2011). Historias de al-Khwārizmī (6ª entrega). El cálculo con la cosa. Suma, 67, pp. 101-110.

by Luis Puig

Narrative in Greek Mathematics? 2012

by Markus Asper

Published version of my Inaugural lecture (delivered May 2011, in German)

(in cooperation with S.S. Demidov, A.N. Parshin, I.P. Shafarevich, S.S. Petrova, G.S. Smirnova, V.M. Tikhomirov) “In Memoriam Isabella Grigoryevna Bashmakova (1921-2005),

by Ioannis Vandoulakis

Archives Internationale d’histoire des Sciences 56 (2006) 1-2, 179-183

Summary of Dedekind's Supplement XI

by Ansten Klev

We give a summary of some key sections in Dedekind's Supplement XI to the 4th edition of Dirichlet's Lectures on... more We give a summary of some key sections in Dedekind's Supplement XI to the 4th edition of Dirichlet's Lectures on Number Theory.

Freedom and Mathematical Science: The problem of freedom in the introduction of ideal entities in mathematics

by Ioannis Vandoulakis

I. Strangas, A. Hanos (Eds) Proceedings of the Greek Association of Research in History and Philosophy of Law. Circle: Concepts of Freedom and Law. Vol. 3, 189-227, Athens-Thessalonica: Sakkulas Publishers, Paris-Torino-Budapest: L’Harmattan, 2006 [in Greek with extended summary in French]

A Genetic Interpretation of Neo-Pythagorean Arithmetic

by Ioannis Vandoulakis

Oriens - Occidens Cahiers du Centre d’histoire des Sciences et des philosophies arabes et Médiévales, 7 (2010), 113-154