Related papers: Artificial Intelligence and the Structure of Mathe…
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…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
Understanding is a crucial yet elusive concept in artificial intelligence (AI). This work proposes a framework for analyzing understanding based on the notion of composability. Given any subject (e.g., a person or an AI), we suggest…
The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may…
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…
There are two big unsolved mathematical questions in artificial intelligence (AI): (1) Why is deep learning so successful in classification problems and (2) why are neural nets based on deep learning at the same time universally unstable,…
Artificial intelligence (AI) is revolutionizing research by enabling the efficient analysis of large datasets and the discovery of hidden patterns. In astrophysics, AI has become essential, transforming the classification of celestial…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
Explainability in AI is gaining attention in the computer science community in response to the increasing success of deep learning and the important need of justifying how such systems make predictions in life-critical applications. The…
Recently, there is an increasing interest in understanding the performance of AI systems in solving math problems. A multitude of tests have been performed, with mixed conclusions. In this paper we discuss an experiment we have made in the…
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…
Artificial intelligence is gaining strength and materials science can both contribute to and profit from it. In a simultaneous progress race, new materials, systems and processes can be devised and optimized thanks to machine learning…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
Artificial Intelligence (AI) in Education has been said to have the potential for building more personalised curricula, as well as democratising education worldwide and creating a Renaissance of new ways of teaching and learning. Millions…
This paper reviews the historical development of AI and representative philosophical thinking from the perspective of the research paradigm. Additionally, it considers the methodology and applications of AI from a philosophical perspective…
Cognitive Science has profoundly shaped disciplines such as Artificial Intelligence (AI), Philosophy, Psychology, Neuroscience, Linguistics, and Culture. Many breakthroughs in AI trace their roots to cognitive theories, while AI itself has…
The Axiom-Based Atlas is a novel framework that structurally represents mathematical theorems as proof vectors over foundational axiom systems. By mapping the logical dependencies of theorems onto vectors indexed by axioms - such as those…
Mathematical reasoning and optimization are fundamental to artificial intelligence and computational problem-solving. Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem…
Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…