奇怪的新宇宙：证明助手与合成基础

IF 2 3区数学 Q1 MATHEMATICS

Bulletin of the American Mathematical Society Pub Date : 2024-02-15 DOI:10.1090/bull/1830

Michael Shulman

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引用次数: 0

摘要

被称为证明助手的现有计算机程序可以验证数学证明的正确性，但其专门的证明语言对许多数学家来说是一个准入门槛。大型语言模型有可能降低这一门槛，使数学家能够用更熟悉的语言与证明助手互动。除其他优势外，这可能会让数学家利用由 LLM 驱动的证明助手来训练他们的直觉，并确保他们的论证是正确的，从而探索全新的数学类型。现有的证明助手已经在同调类型理论等领域发挥了这种作用。

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Strange new universes: Proof assistants and synthetic foundations

Existing computer programs called proof assistants can verify the correctness of mathematical proofs but their specialized proof languages present a barrier to entry for many mathematicians. Large language models have the potential to lower this barrier, enabling mathematicians to interact with proof assistants in a more familiar vernacular. Among other advantages, this may allow mathematicians to explore radically new kinds of mathematics using an LLM-powered proof assistant to train their intuitions as well as ensure their arguments are correct. Existing proof assistants have already played this role for fields such as homotopy type theory.

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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.