Related papers: The Shape of Math To Come
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…
The formalisation of mathematics is starting to become routine, but the value of this technology to the work of mathematicians remains to be shown. There are few examples of using proof assistants to verify brand-new work. This paper…
Work in progress concerning alternative formalizations of arithmetic.
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared…
In this paper we aim at providing a general reflection around the present and future of social media metrics (or altmetrics) and how they could evolve into a new discipline focused on the study of the relationships and interactions between…
We briefly discuss the current state, and future computational implications, of quantum type theory.
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such…
Generative AI models, including large language models and multimodal models that include text and other media, are on the cusp of transforming many aspects of modern life, including entertainment, education, civic life, the arts, and a…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
Living systems are subject to the arrow of time; from birth, they undergo complex transformations (self-organization) in a constant battle for survival, but inevitably ageing and disease trap them to death. Can ageing be understood and…
With the rapid rise of generative AI in higher education and the unreliability of current AI detection tools, developing policies that encourage student learning and critical thinking has become increasingly important. This study examines…
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…
AI-based decision-making tools are rapidly spreading across a range of real-world, complex domains like healthcare, criminal justice, and child welfare. A growing body of research has called for increased scrutiny around the validity of AI…
Context: With artificial intelligence (AI) being well established within the daily lives of research communities, we turn our gaze toward formal methods (FM). FM aim to provide sound and verifiable reasoning about problems in computer…
With the advent of large multimodal language models, science is now at a threshold of an AI-based technological transformation. An emerging ecosystem of models and tools aims to support researchers throughout the scientific lifecycle,…
The introduction of new tools in people's workflow has always been promotive of new creative paths. This paper discusses the impact of using computational tools in the performance of creative tasks, especially focusing on graphic design.…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…