Workshop: Proofs and Representations (6 - 8 July 2018)
Idea and Motivation
The notion of representation plays a central role in mathematics: without particular representations the abstract objects of mathematics would be unthinkable. Reflections on the means of expression of abstract thoughts have a long tradition in philosophy, for example in the work of Leibniz and Frege. Notation systems, spatial and symbolic representations, and representation theorems are among key notions across all mathematical subfields. In this vein, the aim of this workshop is to explore various ways in which proofs and representations advance mathematical knowledge and mathematical understanding. This workshop will address questions such as: Are representations mere instruments for conveying and illustrating mathematics, or do they play a more substantial role in the generation of mathematical knowledge and understanding, and if so, how? What is the relation between conceptual shifts in the history of mathematics and logic, and changes of representations? How do representations inform us about theoretical virtues of proofs and arguments, such as explanatoriness and purity? These are just some of the questions that we intend to get a better grasp of during this workshop, by looking at a wide range of representations––models, diagrams, notations, and more––as they have been used in historical cases, as well as through empirically based reflection and systematic analysis.
Invited Speakers
- Jeremy Avigad (Carnegie Mellon University)
- Karine Chemla (Université Paris 7 – CNRS)
- Silvia De Toffoli (Stanford University)
- Walter Dean (University of Warwick)
- Valeria Giardino (Université de Lorraine – CNRS)
- Yacin Hamami (Vrije Universiteit Brussel)
- Emmylou Haffner (Bergische Universität Wuppertal)
- Brendan Larvor (University of Hertfordshire)
- Sarah Ottinger (LMU Munich)
Organisers
- Marianna Antonutti Marfori (MCMP/LMU Munich)
- Dirk Schlimm (McGill University/MCMP)
Program
Day 1 (6 July 2018)
| Time | Event |
|---|---|
| 15:00 - 16:30 | Silvia De Toffoli: Heterogenous Notations for Mathematical Proofs |
| 16:30 - 17:00 | Coffee Break |
| 17:00 - 18:30 | Yacin Hamami: The Rationality of Mathematical Proofs |
| 20:00 | Informal Dinner |
Day 2 (7 July 2018)
| Time | Event |
|---|---|
| 09:00 - 10:30 | Sarah Ottinger: Content and Formal Representations of Proofs – How Do Both Quality Aspects Affect Each Other? |
| 10:30 - 10:50 | Coffee Break |
| 10:50 - 12:20 | Brendan Larvor: Conditions on the Possibility of Mathematical Proving Practices |
| 12:20 - 14:00 | Lunch Break |
| 14:00 - 15:30 | Jeremy Avigad: The History of Dirichlet's Theorem on Primes in an Arithmetic Progression |
| 15:30 - 17:00 | Emmylou Haffner: Arithmetic, computations and devices in the development of Dedekind's concept of Dualgruppe |
| 17:00 - 17:30 | Coffee Break |
| 17:30 - 19:00 | Walter Dean: Two Routes Between Number Theory and Set Theory |
| 20:00 | Workshop Dinner |
Day 3 (8 July 2018)
| Time | Event |
|---|---|
| 10:00 - 11:30 | Karine Chemla: Equations, Representations and Proofs in 13th Century China |
| 11:30 - 12:00 | Coffee Break |
| 12:00 - 13:30 | Valeria Giardino: Representations and Their Cognitive Significance in Mathematics |
Venue
Day 1 & 2
Ludwigstraße 28
80539 München
Day 3
Main University Building
Geschwister-Scholl-Platz 1
80539 München
Acknowledgement
This workshop is generously funded by the Alexander von Humboldt Foundation and the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 709265.