Related papers: First Proof
$L$-functions typically encode interesting information about mathematical objects. This paper reports 29 identities between such functions that hitherto never appeared in the literature. Of these we have a complete proof for 9; all others…
We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently…
While LLMs have shown impressive capabilities in solving math or coding problems, the ability to make scientific discoveries remains a distinct challenge. This paper proposes a "Turing test for an AI scientist" to assess whether an AI agent…
Experiential AI is proposed as a new research agenda in which artists and scientists come together to dispel the mystery of algorithms and make their mechanisms vividly apparent. It addresses the challenge of finding novel ways of opening…
A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we…
AI models like GPT-5 are an increasingly valuable tool for scientists, but many remain unaware of the capabilities of frontier AI. We present a collection of short case studies in which GPT-5 produced new, concrete steps in ongoing research…
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…
Artificial intelligence (AI) has been advancing at a fast pace and it is now poised for deployment in a wide range of applications, such as autonomous systems, medical diagnosis and natural language processing. Early adoption of AI…
Intelligent tutoring systems have long enabled automated immediate feedback on student work when it is presented in a tightly structured format and when problems are very constrained, but reliably assessing free-form mathematical reasoning…
Misleading or false information has been creating chaos in some places around the world. To mitigate this issue, many researchers have proposed automated fact-checking methods to fight the spread of fake news. However, most methods cannot…
Since the publication of the first International AI Safety Report, AI capabilities have continued to improve across key domains. New training techniques that teach AI systems to reason step-by-step and inference-time enhancements have…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
The use of artificial intelligence (AI) offers various possibilities to expand and support educational research. Specifically, the implementation of AI can be used to develop new frameworks to establish new research tools that accelerate…
Computers have already changed the way that humans do mathematics: they enable us to compute efficiently. But will they soon be helping us to reason? And will they one day start reasoning themselves? We give an overview of recent…
Artificial intelligence (AI) has been increasingly applied in scientific activities for decades; however, it is still far from an insightful and trustworthy collaborator in the scientific process. Most existing AI methods are either too…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
Artificial intelligence is already being applied in and impacting many important sectors in society, including healthcare, finance, and policing. These applications will increase as AI capabilities continue to progress, which has the…
The purpose of this paper is to analyse the opacity of algorithms, contextualized in the open debate on responsibility for artificial intelligence causation; with an experimental approach by which, applying the proposed conversational…