标题： 第二次机器转向：从检查证明到创造概念 显示英文标题

标题： The Second Machine Turn: From Checking Proofs to Creating Concepts

摘要： 我们识别出数学发现过程中的第二个机器轮次：在自动化证明检查之后，人工智能现在有望自动化数学概念本身的*创造*。 我们讨论了当前的技术状态、障碍和潜在解决方案，以及对概念本身进行数学化的初步尝试。 论文最后评估了这些能力如何重塑数学和人机协作，以及我们可能会陷入的几种不同未来。 显示英文摘要

摘要： We identify a second machine turn in the process of mathematical discovery: after automating proof-checking, AI is now poised to automate the *creation* of mathematical concepts themselves. We discuss the current state of the art, obstacles and potential solutions as well as a preliminary attempt at mathematizing the creation of concepts itself. The paper ends with an assessment of how these capabilities could reshape mathematics and human-machine collaboration, and a few different futures we might find ourselves in.