Related papers: Notes on a Path to AI Assistance in Mathematical R…
The recent efforts in automation of machine learning or data science has achieved success in various tasks such as hyper-parameter optimization or model selection. However, key areas such as utilizing domain knowledge and data semantics are…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
The human capability to reason about one domain by using knowledge of other domains has been researched for more than 50 years, but models that are formally sound and predict cognitive process are sparse. We propose a formally sound method…
Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions,…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
What do we want from machine intelligence? We envision machines that are not just tools for thought, but partners in thought: reasonable, insightful, knowledgeable, reliable, and trustworthy systems that think with us. Current artificial…
This note is a survey of Analysis on Metric spaces, in connection with the upcoming AMS Mathematics Research Communities program in June 2020.
Using the National Academies report, {\em Data Science for Undergraduates: Opportunities and Options}, we connect data science curricula to the more familiar pedagogy used by many mathematical scientists. We use their list of ``data acumen"…
Beginning with McCarthy's Advice Taker (1959), AI has pursued the goal of providing a system with explicit, general knowledge and having the system reason over that knowledge. However, expressing the knowledge in a formal (logical or…
Developing and implementing AI-based solutions help state and federal government agencies, research institutions, and commercial companies enhance decision-making processes, automate chain operations, and reduce the consumption of natural…
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…
Artificial intelligence (AI) is becoming increasingly complex, making it difficult for users to understand how the AI has derived its prediction. Using explainable AI (XAI)-methods, researchers aim to explain AI decisions to users. So far,…
Explanations have gained an increasing level of interest in the AI and Machine Learning (ML) communities in order to improve model transparency and allow users to form a mental model of a trained ML model. However, explanations can go…
The purpose of this article is to review the achievements made in the last few years towards the understanding of the reasons behind the success and subtleties of neural network-based machine learning. In the tradition of good old applied…
This document describes strategies for using Artificial Intelligence (AI) to predict some journal article scores in future research assessment exercises. Five strategies have been assessed.
Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as…
This paper was written in 2015, and published in the Journal of Humanistic Mathematics. This paper announces the first issue (2015) of Enchiridion: Mathematics User's Guides, a project to produce peer-reviewed User's Guides as companions to…
Explainable AI (XAI) aims to improve user understanding and decisions when using AI models. However, despite innovations in XAI, recent user evaluations reveal that this goal remains elusive. Understanding human cognition can help explain…
The author's goal in this paper is to explore how artificial intelligence (AI) has been utilised to inform our understanding of and ability to estimate at scale a critical aspect of musical creativity - musical tempo. The central importance…