动机证明：它们是什么，为什么重要以及如何编写它们
Motivated proofs: What they are, why they matter and how to write them
摘要：
数学家判断证明是否具有各种不同的品质，包括解释力，深度，纯度，美感和适合性。数学实践的哲学家们已经开始研究这种性质的本质。然而，数学家们经常注意另一个令人满意的证明质量：动机。直观的、有动机的证明不包含“令人费解”的步骤，但它们几乎没有得到进一步的分析。在本文中，我开始对动机证明进行哲学研究。我认为，一个证明是有动机的，当且仅当数学家能够确定（i）每一步要执行的任务;（ii）每一步可以合理地从哪里来。我认为，动机证明促进理解，传达新的数学资源，并刺激新的发现。因此，他们有显着的认知效益，并直接有助于有效的传播和数学知识的进步。考虑到它们的好处，我还讨论了更实际的问题，即我们如何产生有动机的证明。最后，我考虑动机证明和证明是解释性的，美丽的和合适的之间的关系。
英文摘要：
Mathematicians judge proofs to possess, or lack, a variety of different qualities, including, for example, explanatory power, depth, purity, beauty and fit. Philosophers of mathematical practice have begun to investigate the nature of such qualities. However, mathematicians frequently draw attention to another desirable proof quality: being motivated. Intuitively, motivated proofs contain no "puzzling" steps, but they have received little further analysis. In this paper, I begin a philosophical investigation into motivated proofs. I suggest that a proof is motivated if and only if mathematicians can identify (i) the tasks each step is intended to perform; and (ii) where each step could have reasonably come from. I argue that motivated proofs promote understanding, convey new mathematical resources and stimulate new discoveries. They thus have significant epistemic benefits and directly contribute to the efficient dissemination and advancement of mathematical knowledge. Given their benefits, I also discuss the more practical matter of how we can produce motivated proofs. Finally I consider the relationship between motivated proofs and proofs which are explanatory, beautiful and fitting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
