Related papers: Artificial Intelligence and the Structure of Mathe…
Within one decade, Deep Learning overtook the dominating solution methods of countless problems of artificial intelligence. ``Deep'' refers to the deep architectures with operations in manifolds of which there are no immediate observations.…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
Artificial Intelligence (AI) agents have rapidly evolved from specialized, rule-based programs to versatile, learning-driven autonomous systems capable of perception, reasoning, and action in complex environments. The explosion of data,…
This paper introduces Orthogonal Art, a proposed artistic discipline that emerges in dialectical response to artificial intelligence rather than in service of it. Unlike AI-augmented creative practices, Orthogonal Art is structurally…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
We discuss the objectives of any endeavor in creating artificial intelligence, AI, and provide a possible alternative. Intelligence might be an unintended consequence of curiosity left to roam free, best exemplified by a frolicking infant.…
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…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
Artificial intelligence (AI) is commonly depicted as transformative. Yet, after more than a decade of hype, its measurable impact remains modest outside a few high-profile scientific and commercial successes. The 2024 Nobel Prizes in…
Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…
This article explores the transformative impact of artificial intelligence (AI) on scientific research. It highlights ten ways in which AI is revolutionizing the work of scientists, including powerful referencing tools, improved…
Like any field of empirical science, AI may be approached axiomatically. We formulate requirements for a general-purpose, human-level AI system in terms of postulates. We review the methodology of deep learning, examining the explicit and…
In AI-rich higher education, polished written mathematics has become easier to produce than trustworthy evidence of understanding. This article develops a human-scale methodology for service mathematics, with informatics as its main running…
Students in introductory physics courses often rely on ineffective strategies, focusing on final answers rather than understanding underlying principles. Integrating scientific argumentation into problem-solving fosters critical thinking…
Artificial intelligence (AI) is rapidly emerging as a new paradigm of scientific discovery, namely data-driven science, across nearly all scientific disciplines. In materials science and engineering, AI has already begun to exert a…
In recent decades the set of knowledge, tools and practices, collectively referred to as "artificial intelligence" (AI), have become a mainstay of scientific research. Artificial intelligence techniques have not only developed enormously…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
The ongoing artificial intelligence (AI) revolution has the potential to change almost every line of work. As AI capabilities continue to improve in accuracy, robustness, and reach, AI may outperform and even replace human experts across…
This paper offers a roadmap for the development of scalable aligned artificial intelligence (AI) from first principle descriptions of natural intelligence. In brief, a possible path toward scalable aligned AI rests upon enabling artificial…