Related papers: Artifical intelligence and inherent mathematical d…
The paper discusses the capacities and limitations of current artificial intelligence (AI) technology to solve word problems that combine elementary knowledge with commonsense reasoning. No existing AI systems can solve these reliably. We…
A suite of impressive scientific discoveries have been driven by recent advances in artificial intelligence. These almost all result from training flexible algorithms to solve difficult optimization problems specified in advance by teams of…
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the province of humans. As these tools become…
We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has two objectives. The first is to reconcile the way of…
Can artificial intelligence truly contribute to creative mathematical research, or does it merely automate routine calculations while introducing risks of error? We provide empirical evidence through a detailed case study: the discovery of…
This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and…
Artificial Intelligence (AI) provides many opportunities to improve private and public life. Discovering patterns and structures in large troves of data in an automated manner is a core component of data science, and currently drives…
Since Artificial Intelligence (AI) software uses techniques like deep lookahead search and stochastic optimization of huge neural networks to fit mammoth datasets, it often results in complex behavior that is difficult for people to…
Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions,…
Artificial Intelligence (AI) increasingly shows its potential to outperform predicate logic algorithms and human control alike. In automatically deriving a system model, AI algorithms learn relations in data that are not detectable for…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
Much artificial intelligence research focuses on the problem of deducing the validity of unobservable propositions or hypotheses from observable evidence.! Many of the knowledge representation techniques designed for this problem encode the…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…