Related papers: Artificial Intelligence and the Structure of Mathe…
The pursuit of creating artificial intelligence (AI) mirrors our longstanding fascination with understanding our own intelligence. From the myths of Talos to Aristotelian logic and Heron's inventions, we have sought to replicate the marvels…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
As Artificial Intelligence (AI) becomes increasingly integrated into our lives, the need for new norms is urgent. However, AI evolves at a much faster pace than the characteristic time of norm formation, posing an unprecedented challenge to…
Artificial intelligence (AI) represents a technological upheaval with the potential to change human society. Because of its transformative potential, AI is increasingly becoming subject to regulatory initiatives at the global level. Yet, so…
Can artificial intelligence discover, from raw experience and without human supervision, concepts that humans have discovered? One challenge is that human concepts themselves are fluid: conceptual boundaries can shift, split, and merge as…
Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have…
Artificial intelligence (AI) in the form of deep learning bears promise for drug discovery and chemical biology, $\textit{e.g.}$, to predict protein structure and molecular bioactivity, plan organic synthesis, and design molecules…
Can mathematics help us find our way through all the wonders and mysteries of the universe? When physicists describe the laws governing the physical world, mathematics is always involved. Is this due to the fact that the universe is, at…
High throughput experimentation tools, machine learning (ML) methods, and open material databases are radically changing the way new materials are discovered. From the experimentally driven approach in the past, we are moving quickly…
Artificial intelligence (AI) is reshaping scientific discovery, evolving from specialized computational tools into autonomous research partners. We position Agentic Science as a pivotal stage within the broader AI for Science paradigm,…
Humans often rely on underlying structural patterns-schemas-to create, whether by writing stories, designing software, or composing music. Schemas help organize ideas and guide exploration, but they are often difficult to discover and…
Artificial Intelligence has proven to be a transformative tool for advancing scientific research across a wide range of disciplines. However, a significant gap still exists between AI and scientific communities, limiting the full potential…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
This is an essay about the value of mathematical and symbolic reasoning in the age of AI.
Mastering one or more programming languages has historically been the gateway to implementing ideas on a computer. Today, that gateway is widening with advances in large language models (LLMs) and artificial intelligence (AI)-powered coding…
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…
Integrating artificial intelligence (AI) techniques such as machine learning and deep learning into freeform optics design has significantly enhanced design efficiency, expanded the design space, and led to innovative solutions. This…
Of primary importance in formulating a response to the increasing prevalence and power of artificial intelligence (AI) applications in society are questions of ontology. Questions such as: What "are" these systems? How are they to be…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…