Related papers: Advancements in Research Mathematics through AI: A…
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…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
We present four open conjectures in graph theory generated by the automated conjecturing system \texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariants, and empirically validated across hundreds of graphs.…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
We discuss the idea that computers might soon help mathematicians to prove theorems in areas where they have not previously been useful. Furthermore we argue that these same computer tools will also help us in the communication and teaching…
Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
The rapid evolution of artificial intelligence has led to expectations of transformative impact on science, yet current systems remain fundamentally limited in enabling genuine scientific discovery. This perspective contends that progress…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
Since its beginnings in the 1940s, automated reasoning by computers has become a tool of ever growing importance in scientific research. So far, the rules underlying automated reasoning have mainly been formulated by humans, in the form of…
Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to…
Forensic examination of evidence like firearms and toolmarks, traditionally involves a visual and therefore subjective assessment of similarity of two questioned items. Statistical models are used to overcome this subjectivity and allow…
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this…
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…
Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social…
Artificial intelligence (AI) is transforming the practice of science. Machine learning and large language models (LLMs) can generate hypotheses at a scale and speed far exceeding traditional methods, offering the potential to accelerate…
Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…