证明是有代价的：明日的超严格数学文化

IF 2 3区数学 Q1 MATHEMATICS

Bulletin of the American Mathematical Society Pub Date : 2024-05-15 DOI:10.1090/bull/1823

Silvia De Toffoli

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引用次数: 0

摘要

计算工具可能会诱使我们放弃完全的确定性。通过放弃严格的证明，我们可以用很小的代价得到（非常）可能的结果。但是，证明（我们所熟知和喜爱的证明）真的能让我们获得确定性吗？也许不是。证明的正确性并不体现在它们的袖子上，我们在检查它们时也并非无懈可击。这表明，我们需要帮助来检查我们的结果。当我们的数学家同事太累或太忙而无法仔细检查我们的推定证明时，计算机证明助手就能帮上忙。但是，把数学论证交给计算机是很难的。尽管如此，考虑到形式化可能带来的额外好处--其中最主要的是增强对数学的理解，我们还是愿意做这项工作。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proofs for a price: Tomorrow’s ultra-rigorous mathematical culture

Computational tools might tempt us to renounce complete certainty. By forgoing of rigorous proof, we could get (very) probable results for a fraction of the cost. But is it really true that proofs (as we know and love them) can lead us to certainty? Maybe not. Proofs do not wear their correctness on their sleeve, and we are not infallible in checking them. This suggests that we need help to check our results. When our fellow mathematicians will be too tired or too busy to scrutinize our putative proofs, computer proof assistants could help. But feeding a mathematical argument to a computer is hard. Still, we might be willing to undertake the endeavor in view of the extra perks that formalization may bring—chiefly among them, an enhanced mathematical understanding.

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来源期刊

Bulletin of the American Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.