Séminaire – Histoire et Philosophie des Mathématiques

History of science as a scientists’ pursuit

The session will aim at understanding what is at stake for scientists when they practice history of science as part of their practice of mathematics. What is at stake for them ? Which practice of the history of science do they have ? What kind of history do they write and how are these reflections they develop related to their own scientific work ?

Organisation : Karine Chemla

Program

• 9.45 am-11.00 am

Yuan Rui (SPHERE, CNRS & Université Paris Cité)
The Work on the History of Mathematics Carried Out by Qing China Mathematicians :
The Case of Li Rui’s 李銳 (1769– 1817) Editorial and Historical Work on the Sea Mirror of Circle Measurements (測圓海鏡 Ce yuan hai jing, 1248)
Abstract :
Modern historians of mathematics generally agree that the Song-Yuan times period (around the 12th and the 13th centuries) was an important period for mathematics in ancient China. After that, for reasons that remain to be uncovered, some mathematical methods and theories appeared to have become incomprehensible for scholars of the subsequent centuries. Among these methods, the “celestial source procedure” (天元術, tian yuan shu) became particularly difficult to understand, and then, starting from the 18th century, it aroused strong interest, becoming a focus for scholars. Since the mid-18th century, Mei Juecheng 梅瑴成 (1681–1763) reflected on the mathematics in ancient China through his Precious Relic along the Red River (赤水遗珍, chi shui yi zhen, 1761). His work enormously influenced contemporary scholars, especially the idea that “the ‘celestial source procedure’ is essentially the same as ‘algebra/borrowing the root’ ” (天元一即借根方解, tian yuan yi ji jie gen fang jie). This idea was generally accepted among scholars attempting to understand the mathematical methods and theories in ancient China. Li Rui 李銳 (1769 – 1817) was a polymath scholar active during the mid-Qing time
period. He worked on both mathematics and the history of mathematics. This talk will mainly discuss his editorial works on the 13th-century mathematical monograph, the Sea Mirror of Circle Measurements (測圓海鏡 Ce yuan hai jing, 1248), a book which reflects how to use the “celestial source procedure”. I will focus on Li Rui’s editorial work, also, comparing Li Rui’s edition with the editions of the Sea Mirror before him. Through the comparison, this talk will emphasize how Li Rui carried out work in philology and the history of mathematics, and will aim to understand why Li Rui’s works are important and
influential.

• 11.00 am-12.15 pm

Ivahn Smadja (CAPHI, Nantes, & SPHERE)
Coming to grips with Abel’s Theorem : A late nineteenth-century historiographical approach
Abstract :
In their 1894 report to the German Mathematical Society on The
development of the theory of algebraic functions in ancient and modern times,
Alexander Brill and Max Noether devoted a whole section to Abel’s theorem. This contribution will analyze how they dealt with it and tackled some of its
mathematical intricacies, by putting it into a historical sequence owing to an aptly constructed historiographical framework. It will be shown in particular how they strove to bridge the gap between Euler’s algebraic and computational thinking and Abel’s highly general approach.

• 12.15 pm-1.30 pm
• 1.30 pm-2.25 pm

Laurent Loison (SPHERE, CNRS & Université Paris Cité)
Three biologists grappling with history of science : Ernst Mayr, François Jacob, and Stephen-Jay Gould
Abstract :
Interest in the history of science is generally uncommon among
biologists of the second half of the 20th century. There are, however, some
notable exceptions, such as Ernst Mayr (systematist and evolutionary theorist),
François Jacob (molecular biologist) and Stephen-Jay Gould (paleo-biologist). In
this talk, I will try to characterize their practice of the history of science, focusing on its possible interaction with their scientific activity. We will see that this interaction was minimal for Mayr, important but occasional for Jacob and nothing less than consubstantial for Gould.

• 2.25 pm-3.15 pm

General Discussion
Break

• 3.30 pm-5.30 pm

Preparation of the program of next year

Salle : 628 (6è étage, bâtiment Olympes de Gouges)