Document Type : Original Article
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Abstract
Most mathematicians are reluctant to accept the visual proof as a genuine type of mathematical proof. In this paper, I paraphrase 10, common or new, objections to this type of proof and evaluate them separately and critically. On each of the objections, indeed, at least one of these central features is absent from the visual proofs: formality, symbolicness, rigority, reliability, surveyability, universality, legitimacy, self-sufficiency, uniformity, and fertility.
The paper argues that none of these objections are accurate. So the rejection of this kind of proofs is mostly due to psychological and sociological factors, especially domination of formalistic attitude among the mathematics community, rather than logical, or methodological reasons. There are not any strong reasons to reject these kinds of proofs, as a pattern of reasoning in mathematics; on the contrary, there are good reasons to accept and recognize them. An awareness of the role of this type of proof in the mathematics as a whole, no less and no more, is of critical importance.
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