{"title":"Theorem proving in artificial neural networks: new frontiers in mathematical AI","authors":"","doi":"10.1007/s13194-024-00569-6","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>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.</p>","PeriodicalId":48832,"journal":{"name":"European Journal for Philosophy of Science","volume":"84 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal for Philosophy of Science","FirstCategoryId":"98","ListUrlMain":"https://doi.org/10.1007/s13194-024-00569-6","RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
The European Journal for Philosophy of Science publishes groundbreaking works that can deepen understanding of the concepts and methods of the sciences, as they explore increasingly many facets of the world we live in. It is of direct interest to philosophers of science coming from different perspectives, as well as scientists, citizens and policymakers. The journal is interested in articles from all traditions and all backgrounds, as long as they engage with the sciences in a constructive, and critical, way. The journal represents the various longstanding European philosophical traditions engaging with the sciences, but welcomes articles from every part of the world.
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