Citations of:
Envisioning Transformations – The Practice of Topology
In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 20122014. Zurich, Switzerland: Birkhäuser. pp. 2550 (2016)
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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 twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of (...) 

In this paper, I argue that there are cases of explanatory induction in mathematics. To do so, I first introduce the notion of explanatory definition in the context of mathematical explanation. A large part of the paper is dedicated to introducing and analyzing this notion of explanatory definition and the role it plays in mathematics. After doing so, I discuss a particular inductive definition in advanced mathematics—\complexes—and argue that it is explanatory. With this, we see that there are cases of (...) 