99 Variations on a Proof

Ording, Philip

doi:10.1515/9780691185422

Cited by 5 publications

(2 citation statements)

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“…This activity aims at the relief of ignorance concerning particular mathematical questions; for instance, whether there are infinitely many prime numbers. Each proof is typically just one of many that resolves the problem at which it is aimed (Dawson (2015), Ording (2019)). Among this variety of proofs, mathematicians have opinions about which ones are better than others.…”

Section: Mathematical Hygienementioning

confidence: 99%

Mathematical hygiene

Arana,

Burnett

2023

Synthese

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Mathematical Hygienementioning

confidence: 99%

Mathematical hygiene

Arana,

Burnett

2023

Synthese

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“…This work started as a reaction to [6] who collected together different proofs of the same theorem as a vehicle through which to discuss mathematical style. Mathematical style is also discussed by [7] who collected together proofs that is irrational, and the famous work of [8] provides many proofs of the Pythagorean proposition.…”

Section: Introductionmentioning

confidence: 99%

Developing new picture proofs that the sums of the first n odd integers are squares

Sangwin¹,

Tanswell²

2023

Math. Gaz.

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What is it that makes us judge two proofs of the same theorem to be the same or different? This is not an idle question: one central aspect of judging mathematics is the novelty of the mathematics presented. This is important everywhere, from the peer-review system, to assigning international prestige, to funding agencies’ grant decisions. It even matters to some extent in examinations, to avoid accusations of collusion. Surprisingly, philosophers of mathematics have not paid the question of novelty much attention. In this Article, we will consider the appealing conjecture that the main ideas that make up the proof, the essence of a proof, can indeed be identified and that very different styles of proofs can share common main ideas. Further, that a particular theorem can be proved using quite different, independent main ideas. As a means of exploring whether this is plausible, we will present a number of novel proofs of the following theorem.

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Mathematicians’ Assessments of the Explanatory Value of Proofs

et al. 2021

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The literature on mathema.cal explana.on contains numerous examples of explanatory, and not so explanatory proofs. In this paper we report results of an empirical study aimed at inves.ga.ng mathema.cians' no.on of explanatoriness, and its rela.onship to accounts of mathema.cal explana.on. Using a Compara.ve Judgement approach, we asked 38 mathema.cians to assess the explanatory value of several proofs of the same proposi.on. We found an extremely high level of agreement among mathema.cians, and some inconsistencies between their assessments and claims in the literature regarding the explanatoriness of certain types of proofs.

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99 Variations on a Proof

Cited by 5 publications

References 0 publications

Mathematical hygiene

Mathematical hygiene

Developing new picture proofs that the sums of the first n odd integers are squares

Mathematicians’ Assessments of the Explanatory Value of Proofs

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