Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, machine learning results in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities.

计算机辅助定理证明是数学方法论中日益重要的一部分，也是人工智能（AI）研究中长期存在的课题。然而，当前一代的定理证明软件在提供新证明方面的功能有限。重要的是，他们无法区分有趣的定理和证明与琐碎的定理和证明。为了使计算机在定理证明方面进一步发展，需要对软件的功能进行根本性的改变。最近，机器学习在解决数学任务方面的成果已经显示出早期的希望，即深度人工神经网络可以学习符号数学处理。在本文中，我分析了此类神经网络在证明数学定理方面的理论前景。我特别关注这样的问题：如何将此类人工智能系统纳入实践中进行定理证明以及可能产生什么后果。在最乐观的情况下，这包括自主自动化定理证明器（AATP）的可能性。在这里，我讨论这样的人工智能系统是否可以或应该被接受为数学界的活跃代理人。