Yehuda Rav's inspiring paper “Why do we prove theorems?” published in Philosophia
Mathematica (1999; 7: 5–41) has interesting implications for mathematics education. We …

In recent years, philosophical work directly concerned with the practice of mathematics has
intensified, giving rise to a movement known as the philosophy of mathematical practice. In …

Realizing Reason pursues three interrelated themes. First, it traces the essential moments in
the historical unfolding—from the ancient Greeks, through Descartes, Kant, and …

Of all the demands that mathematics imposes on its practitioners, one of the most
fundamental is that proofs ought to be correct. It has been common since the turn of the …

This article is a philosophical study of mathematical proof and provability. In contrast with the
prevailing tradition in philosophy of mathematics, we will not so much focus on “proof” in the …

Mathematical proof is the primary form of justification for mathematical knowledge, but in
order to count as a proper justification for a piece of mathematical knowledge, a …

'Now, in calm weather, to swim in the open ocean is as easy to the practised swimmer as to
ride in a spring-carriage ashore. But the awful lonesomeness is intolerable. The intense …

Mathematical explanations are poorly understood. Although mathematicians seem to
regularly suggest that some proofs are explanatory whereas others are not, none of the …

The aim of this paper is to provide epistemic reasons for investigating the notions of informal
rigour and informal provability. I argue that the standard view of mathematical proof and …

The literature on mathematical explanation contains numerous examples of explanatory,
and not so explanatory proofs. In this paper we report results of an empirical study aimed at …