Related papers: Mathematics, word problems, common sense, and arti…
A widely accepted definition of intelligence in the context of Artificial Intelligence (AI) still eludes us. Due to our exceedingly rapid development of AI paradigms, architectures, and tools, the prospect of naturally arising AI…
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…
A suite of impressive scientific discoveries have been driven by recent advances in artificial intelligence. These almost all result from training flexible algorithms to solve difficult optimization problems specified in advance by teams of…
Artificial intelligence (AI) is supposed to help us make better choices. Some of these choices are small, like what route to take to work, or what music to listen to. Others are big, like what treatment to administer for a disease or how…
This chapter provides an overview of the different Artificial Intelligence (AI) systems that are being used in contemporary digital tools for Mathematics Education (ME). It is aimed at researchers in AI and Machine Learning (ML), for whom…
This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research, highlighting the transformative role AI has begun to play in this domain. Traditionally, AI advancements have heavily…
This position paper argues that, in order to understand AI, we cannot rely on our existing vocabulary of human words. Instead, we should strive to develop neologisms: new words that represent precise human concepts that we want to teach…
The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their refinements, can pick up on patterns in higher mathematics…
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…
Solving mathematical word problems (MWPs) automatically is challenging, primarily due to the semantic gap between human-readable words and machine-understandable logics. Despite the long history dated back to the1960s, MWPs have regained…
This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…
Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical…
Currently, potential threats of artificial intelligence (AI) to human have triggered a large controversy in society, behind which, the nature of the issue is whether the artificial intelligence (AI) system can be evaluated quantitatively.…
We integrate foundational theories of meaning with a mathematical formalism of artificial general intelligence (AGI) to offer a comprehensive mechanistic explanation of meaning, communication, and symbol emergence. This synthesis holds…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
The mathematical capabilities of AI systems are complex and multifaceted. Most existing research has predominantly focused on the correctness of AI-generated solutions to mathematical problems. In this work, we argue that beyond producing…
A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we…
The capabilities of modern artificial intelligence (AI) as a ``scientific collaborator'' are explored by engaging it with three nuanced problems in quantum optics: state populations in optical pumping, resonant transitions between decaying…
Recent advancements in large language models have demonstrated that extended inference through techniques can markedly improve performance, yet these gains come with increased computational costs and the propagation of inherent biases found…
Artificial intelligence (AI) has been advancing at a fast pace and it is now poised for deployment in a wide range of applications, such as autonomous systems, medical diagnosis and natural language processing. Early adoption of AI…