Conference on Explanation & Proof
at Essen, November 1–4, 2006

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Gila Hanna (Toronto), Hans Niels Jahnke (Essen) and Helmut Pulte (Bochum) organised a multi-disciplinary conference on Explanation and Proof in Mathematics involving mathematicians, philosophers and mathematics educators at the Essen campus of the University of Duisburg-Essen.

Hans-Niels Jahnke (Essen) introduces the conference.

Gila Hanna (Toronto) chairs a discussion

Marcus Giaquinto (University College London) talks about the relationship between algebraic and geometric thinking

Mary Leng (Liverpool) discusses the difference between Frege’s assertory vie and the algebraic approach of Hilbert

Evelyne Barbin (Nantes) speaks on geometric proportion relating ‘icons’ to ‘symbols’

Ken Manders (Pittsburgh) discusses the use of diagrams in ancient geonmetric analysis

Willi Dörfler (Klagenfurt) talks on verbal argumetation as talk about diagrams

Alfred Nordmann (Technische Universität Darmstardt) on Proof as experiment in Wittgenstein

Moritz Epple (Universität Frankfurt) Vague Intuition vs rigorous proof (in knot theory)

David Tall pays attention ...

Teun Koetsier (Vrije Universiteit Amsterdam): Motion and Geometry in Antiquity

... discussion from Moritz Epple ...

Michael Stölzner and The Principle of`Least Action

Maria Alessandria Mariotti (Siena) and The Function of Artefacts of Information Technologies

Michael de Villiers (Durban Westville), What’s the role of proof and experimentation

Helmut Pute (Bochum) leads a round table discussion on Proofs, diagramatic thinking & empirical contexts

Aiso Heinze (München) asked mathematicians about the acceptance of mathematical proofs

Jean Paul van Bendegem (Vrije Universiteit, Brussels) What turns a proof into an argument

Thomas Mormann (University of the Basque Country): Proof & Idealization in Mathematics

Nicholas Balacheff (Grenoble): Bridging knowing & proving: the complexity of the epistemelogical genesis of mathematical proof

Brendan Larvor (University of Hertfordshire):
What can Lakotos teach about teaching?

Reflecting and discussing ...

Karine Chemla (CNRS Paris) discusses understanding proving and describing algorithms from China c. 186 BCE

Mariolina Bartolini-Bussi (Modena)
Contexts for Approaching Validation:
The Function of Artefacts of Ancient Techologies

Kahuziko Nunokawa
(Joetsu University of Education, Japan): Explanations in mathematical problem solving

Hans Niels Jahnke (Universität Duisburg-Essen)
Proofs and Hypotheses

Juan Pablo Mejia-Ramos & David Tall (Warwick): Long-term Cognitive Development of Different Types of Reasoning and Proof
[the paper can be downloaded from here]

Erich Wittmann (Dortmund) closes the conference speaking on Operative Proofs

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