Introduction

Gila Hanna, Hans N. Jahnke, Helmut Pulte

1-13

The conjoint origin of proof and theoretical physics

Hans N. Jahnke

17-32

Lakatos, Lakoff and Núñez

towards a satisfactory definition of continuity

Teun Koetsier

33-46

Preaxiomatic mathematical reasoning

an algebraic approach

Mary Leng

47-57

Completions, constructions, and corollaries

Thomas Mormann

59-70

Authoritarian versus authoritative teaching

Polya and Lakatos

Brendan Larvor

71-83

Proofs as bearers of mathematical knowledge

Gila Hanna, Ed Barbeau

85-100

Mathematicians' individual criteria for accepting theorems and proofs

An empirical approach

Aiso Heinze

101-111

Bridging knowing and proving in mathematics

a didactical perspective

Nicolas Balacheff

115-135

The long-term cognitive development of reasoning and proof

David Tall

137-149

Historical artefacts, semiotic mediation and teaching proof

Maria G. Bartolini Bussi

151-167

Proofs, semiotics and artefacts of information technologies

Maria A. Mariotti

169-188

Proof as experiment in Wittgenstein

Alfred Nordmann

191-204

Experimentation and proof in mathematics

Michael de Villiers

205-221

Proof, mathematical problem-solving, and explanation in mathematics teaching

Kazuhiko Nunokawa

223-236

Evolving geometric proofs in the seventeenth century

from icons to symbols

Evelyne Barbin

237-251

Proof in the wording

two modalities from ancient Chinese algorithms

Karine Chemla

253-285