Related papers: Artificial Intelligence and the Structure of Mathe…
The scientific method is the cornerstone of human progress across all branches of the natural and applied sciences, from understanding the human body to explaining how the universe works. The scientific method is based on identifying…
Artificial intelligence (AI) advancements over the past few years have had an unprecedented and revolutionary impact across everyday application areas. Its significance also extends to technical challenges within science and engineering,…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
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…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment 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…
Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…
Investment in artificial intelligence (AI) has grown rapidly, yet its returns to scientific research remain poorly understood. We study how AI reshapes the production of science using a comprehensive dataset of research proposals submitted…
In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we…
We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most major branches of modern mathematics -- from…
In this comprehensive review, we describe a new mathematical problem in artificial intelligence (AI) from a mathematical modeling perspective, following the philosophy stated by Rudolf E. Kalman that "Once you get the physics right, the…
Recent progress in artificial intelligence (AI) has renewed interest in building systems that learn and think like people. Many advances have come from using deep neural networks trained end-to-end in tasks such as object recognition, video…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
This paper presents mathematics as a general science of computation in a way different from the tradition. It is based on the radical philosophical standpoint according to which the content, meaning and justification of experience lies in…
Inspired by recent and revolutionary developments in AI, particularly in language understanding and generation, we set about designing AI systems that are able to address complex scientific tasks that challenge human capabilities to make…
This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression via the matching and unification of patterns' (ICMUP). ICMUP is itself a novel approach to…
In an era of exponential technological advancement, artificial intelligence (AI) has emerged as a transformative force in architecture, reshaping traditional design and construction practices. This article explores the multifaceted roles of…
Research in Artificial Intelligence (AI) has focused mostly on two extremes: either on small improvements in narrow AI domains, or on universal theoretical frameworks which are usually uncomputable, incompatible with theories of biological…
This introductory chapter explores the transformative role of artificial intelligence (AI) in reshaping the landscape of science education. Positioned at the intersection of tradition and innovation, AI is altering educational goals,…
Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most…