Sciences, Philosophie, Histoire – UMR 7219, laboratoire SPHERE

Title : Interactions entre mathématiques et histoire des mathématiques : approche historique et perspectives contemporaines appuyée sur le rapport d’Alexander Brill et Max Noether, Die Entwicklung der Theorie der algebraischen Functionen in älterer und neuerer Zeit (1894).

Directors : Karine Chemla & Patrick Popescu-Pampu

Thesis project :
The aim of this thesis is to study the text of Alexander Brill and Max Noether, Die Entwicklung der Theorie der algebraischen Functionen in älterer und neuerer Zeit published in 1894. This text is at the centre of questions from a group of historians, philosophers of mathematics and mathematicians with whom I will be working.
My work will consist of translating part of this work into English. I have chosen Section VI, which deals with the theory of singular points. In parallel to this translation, I will conduct an in-depth study of the mathematics used in this section by modernising the notations, statements and demonstrations. If it turns out that results are not yet proven, I will work on their demonstration.
Then, at the heart of this work, I will conduct a study of the history of mathematics written by mathematicians, which is the case with this text. Indeed, Die Entwicklung der Theorie der algebraischen Functionen in älterer und neuerer Zeit proposes a historical approach to algebraic functions. It was composed in a context where the German mathematical society launched the production of synthetic reports on the different branches of mathematics. Brill and Noether give a treatment that has real historical depth to algebraic functions and their use in the study of algebraic curves and abelian integrals, a generalisation of elliptic integrals.
Thus, the questions that will drive the thesis are of the following type: What is the role of the history of mathematics for these German scientists who practice it in depth? First of all, how do they practice history? How does the synthesis of knowledge explain historical reflection, and how does historical reflection underlie the practice of synthesis? Finally, and most importantly, how does the work of these mathematicians in this area relate to their more purely mathematical research?

• Algebraic function theory of the XIX^th century.
  

• German mathematical society of the late XIX^th century.
  

• Singularity theory
  
  

• 2021-2022 : Master 2 of fundamental mathematics in University Paris Cité.
  

• 2020-2021 : Master 1 of fundamental and applied mathematics (cursus Jacques Hadarmard) in University Paris-Saclay.
  

• 2019-2020 : Licence 3 of fundamental and applied mathematics in University Paris-Saclay.
  

• 2017-2019 : CPGE MPSI/MP in Collège Stanislas Paris.