The Derivation-Indicator View of Mathematical Practice

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

“…It is not only mathematics educators who make this claim. The philosopher Azzouni (2004) attempted to explain why "mathematicians are so good at agreeing with one another on whether 18 Whether mathematicians actually read a proof for its high-level ideas is currently under debate in the mathematics education community (e.g., Inglis & Alcock, 2012Weber & Mejia-Ramos, 2013b). 19 Note that we are not talking about alleged proofs whose validity is considered problematic by some members of the mathematical community, such as probabilistic proofs, picture proofs, or computer assisted proofs (cf., Aberdein, 2009).…”

Mathematics and Argumentation

“…One of the most crucial is that of the success of informal mathematics-if formality is essential to rigour, and rigour central to mathematical success, how does informal mathematical practice work at all? Jody Azzouni's paper addresses this question by a further defence of his view that informal proofs are 'derivation indicators' (see Azzouni, 2004). Another difficult concept concerning informal proof is that of 'surveyability.'…”

And so on . . . : reasoning with infinite diagrams

“…", Proofs are for the mathematician what experimental procedures are for the experimental scientist: in studying them one learns of new ideas, new concepts, new strategies⎯devices which can be assimilated for one's own research and be further developed. (Rav 1999, p. 20) The article Rav (2007) continues and elaborates these themes as part of his critique of Azzouni (2004 For his argument, Pelc defines a natural number M that is so large that no theorem T whose shortest possible derivation in ZFC is of length greater than M will be mechanically checkable by a physically realizable process within anything like feasible time. And then he goes on to suggest that the proof by Wiles of Fermat's Last Theorem could be a candidate for such T "in the present state of knowledge."…”