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Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld\u2019s (Synthese 191:3367\u20133391, 2014) suggestion that explanations are those sorts of things that (in the right circumstances, and in the right manner) generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all derivable consequences of Wilkenfeld\u2019s \u2018functional explanation\u2019 proposal. We therefore argue that the explanatory criteria offered by earlier accounts can all be thought of as features that make it more likely that a mathematical proof will generate understanding. On the functional account, features such as characterising properties, unification, and salience correlate with explanatoriness, but they do not define explanatoriness.<\/jats:p>","DOI":"10.1007\/s11229-019-02234-5","type":"journal-article","created":{"date-parts":[[2019,5,22]],"date-time":"2019-05-22T19:02:50Z","timestamp":1558551770000},"page":"6369-6392","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Functional explanation in mathematics"],"prefix":"10.1007","volume":"198","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7617-4689","authenticated-orcid":false,"given":"Matthew","family":"Inglis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Pablo","family":"Mej\u00eda-Ramos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,5,22]]},"reference":[{"key":"2234_CR1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0079-7421(08)60422-3","volume":"2","author":"RC Atkinson","year":"1968","unstructured":"Atkinson, R. 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