A mathematical proof necessarily entails an explanation.
the verdict
REFUTED
the evidence says no
refutedsupported
the weight of evidence
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Evidence indicates that insight and explanation can be separated from formal rigour and proof, showing that a mathematical proof does not necessarily entail an explanation.
In this paper we investigate undergraduate mathematics students' conceptions of rigour and insight. We conducted comparative judgement experiments in which students were asked to judge different proofs of the same theorem with five separate criteria: rigour, insight, understanding, simplicity and assessment marks. We predicted, and our experiment found, that rigour is a reliable construct. We predicted that insight is also a reliable construct but asking students to judge on the basis of ``which proof gives you more insight into why a theorem is true'' did not result in a reliable judging scal