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Accueil > Archives > Journées et colloques des années précédentes > Journées et colloques 2014-2015 > Case Studies in Mathematical Practice

Case Studies in Mathematical Practice

June 29 to July 4, 2015
Université Paris Diderot

The primary goal of this workshop is to shed light on mathematical thought and understanding by developing a rich collection of case studies drawn from the historical and current practice of mathematicians. A secondary goal is to examine the methodology of case studies with an eye towards determining which questions in the philosophy of mathematics are amenable to solution by case study methods, and which questions are not. One recurring theme of the workshop concerns the ways in which the development of new conceptual and representational resources can contribute to an increase in the intelligibility of a mathematical domain.

Workshop Leader : Kenneth Manders, University of Pittsburgh

Confirmed Participants :

L’information sur les financements accessibles aux étudiants et jeunes post-doc pour participer au workshop, ainsi que les informations pratiques, merci de visiter le site dédié du colloque :
Le colloque est ouvert au public sur inscription auprès de : au plus tard le 19 juin.
Case Studies in Mathematical Practice est co-organisé avec SΦHERE.


Programme to download
Mathematics is a strikingly powerful but strange intellectual form of Understand- ing. The seminar presents an approach, comparative case studies, to locating philo- sophical ideas that help explain how powerful intellectual understanding is achieved ; ideas beyond —well-understood— formal proof and axiomatic systematization. We present examples in depth, notably the contrast between Euclidean-style synthetic plane geometry and Descartes’ analytic geometry.
Such studies have, so far, led to a focus on how representations function. That is, primarily expressive-usage (not : metaphysical) differences directly address differences in power of contrasting approaches to problems, where we pre-theoretically recognize conceptual re-structuring.

My presentation/discussions on Monday-Thursday and Sat AM form one connected, many case-study based, argument for a representation-based functional-role
perspective on mathematical thought. (Some of the headers may be mysterious to
the uninitiate.) The Friday session aims to initiate an exploration of non-exact rep-
resentations in mathematical thought, of course taking off from geometrical diagrams
and the notion (if there be one) of geometricality.
Saturday afternoon is devoted to overall responses to the seminar (presumably,
including push-back from Fregeian-analytic/logical and historian’s perspectives).

The other presentations (precise titles not yet available) :
Tues PM : Jeremy Heis on : Early moderns on the ancient constructability of
conics through 5 given points. Davide Crippa comments.
Wed PM : Marco Panza on his paper “From Velocities to Fluxions”, in A. Janiak
and E. Schliesser (d.), Interpreting Newton : Critical Essays, Cambridge Univ. Press,
Cambridge, etc., 2012, pp. 219-254. Shay Logan comments.
Thurs PM : Jessica Carter on Mathematical Representation and Understanding.
Irina Starikova comments.
Fri AM (2) : Andy Arana and Jemma Lorenat on Diagrammaticality in 19th C
Projective geometry.
Fri PM : Douglas Marshall on Wedderburn’s theorem and the Pappus condition
in projective geometry. Josh Hunt comments.
Sat PM : Karine Chemla’s critical response to the seminar.

MON. 29

10:00–11:20 Intro PhilMath
11:20–12:30 Case study method
14:30–15:30 Euclidean Diagram (basic)
15:40–17:00 Euclidean Diagram (adv)

TUES. 30

10:00–11:20 Descartes’ geometrical Method (example)

11:20–12:30 Descartes’ geometrical Method (general)
14:30–15:30 Modularity (stages)
15:40–17:00 J. Heis : Descartes/Newton

WED. 1rst

10:00–11:20 Representation & Responsiveness Control
11:20–12:30 Representation & Responsiveness Control
14:30–15:30 lin. repr. groups
15:40–17:00 Marco Panza : Newton


Knots Over-specification

Knots Over-specification
Invariance Strategies
J.Carter : repres/underst

FRI. 3

Geometricality, Intro

A.Arana, J.Lorenat : 19c Projective
D. Marshall : Wedderburn

SAT. 4

Mathematical Intellibility/Enhancements Completions

Mathematical Intellibility/Enhancements Completions Conclusion
K. Chemla response

Room 366A, Université Paris Diderot – CNRS
Laboratoire SPHERE – UMR 7219, Building Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 Paris