Journal Article10.1093/PHILMAT/NKW015
Mathematical Fit: A Case Study
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TL;DR: The highest praise is that a proof is right, that is that the pr... as mentioned in this paper, that is, the pr is right and the proof is elegant, cumbersome, beautiful, or awkward.
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Abstract: Mathematicians routinely pass judgments on mathematical proofs. A proof might be elegant, cumbersome, beautiful, or awkward. Perhaps the highest praise is that a proof is right, that is that the pr ...
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Citations
Proofs from THE BOOK , by Martin Aigner and Günter M. Ziegler. Pp. 199. £19. 1999. ISBN 3 540 63698 6 (Springer-Verlag).
TL;DR: Aigner and Ziegler as discussed by the authors presented beautiful proofs of some of the most exciting and historically important mathematical theorems, focusing on human endeavour to make the proofs more and more simple and striking.
230
Proving quadratic reciprocity: explanation, disagreement, transparency and depth
TL;DR: After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, some morals about the nature of mathematical explanation are drawn.
Sums of the first n odd integers
TL;DR: In this article , a discussion of mathematical style via a comparison of 99 different proofs of the Pythagorean Theorem is presented. But the focus is on the irrationality of the Theorem and not the style of the proofs.
2
Motivated proofs: What they are, why they matter and how to write them
TL;DR: In this article, the authors suggest that a proof is motivated if and only if mathematicians can identify the tasks each step is intended to perform and where each step could have reasonably come from.
1
Motivated proofs: What they are, why they matter and how to write them
TL;DR: It is argued that motivated proofs promote understanding, convey new mathematical resources and stimulate new discoveries, thus have significant epistemic benefits and directly contribute to the efficient dissemination and advancement of mathematical knowledge.
References
Processing Fluency and Aesthetic Pleasure: Is Beauty in the Perceiver's Processing Experience?
TL;DR: This work proposes that aesthetic pleasure is a funnction of the perceiver's processing dynamics: the more fluently perceivers can process an object, the more positive their aesthetic response, and reviews variables known to influence aesthetic judgments, and traces their effects to changes in processing fluency.
Love as a Moral Emotion
TL;DR: In this article, the authors propose a synonyme de partialite, l'autre d'impartialite, dans la cadre des theories consequentialistes telles que la morale kantienne converges with l'amour a travers la notion d'emotion morale.
Proofs from THE BOOK , by Martin Aigner and Günter M. Ziegler. Pp. 199. £19. 1999. ISBN 3 540 63698 6 (Springer-Verlag).
TL;DR: Aigner and Ziegler as discussed by the authors presented beautiful proofs of some of the most exciting and historically important mathematical theorems, focusing on human endeavour to make the proofs more and more simple and striking.
230
Against Mathematical Explanation
TL;DR: The authors argue that given the way philosophers have been using "explanation", the term is not applicable to mathematics as it is in science, and they argue that the notion of mathematical explanation within mathematics cannot be applicable to science.
155