Related papers: Through a Glass Darkly
In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…
A goal of PER is to understand how students use math in physics contexts. To investigate how students use math, we need to identify transitions between conceptual sense-making about physical systems and using mathematics to describe and to…
This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.
Good problems grab us. They invite us to find patterns, make conjectures, and prove-or perhaps disprove-a conjecture. When I first taught, I saw my work as tantalizing students with structures just beyond their reach, so that I could elicit…
This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into…
While the ``hierarchy of science'' has been widely analysed, there is no corresponding study of the status of subfields within a given scientific field. We use bibliometric data to show that subfields of mathematics have a different…
The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We…
Science is a crowning glory of the human spirit and its applications remain our best hope for social progress. But there are limitations to current science and perhaps to any science. The general mind-body problem is known to be intractable…
As AI agents become increasingly capable of tool use and long-horizon tasks, they have begun to be deployed in settings where multiple agents can interact. However, whereas prior work has mostly focused on human-AI interactions, there is an…
When we want to predict the future, we compute it from what we know about the present. Specifically, we take a mathematical representation of observed reality, plug it into some dynamical equations, and then map the time-evolved result back…
There has been a lively debate in many fields, including statistics and related applied fields such as psychology and biomedical research, on possible reforms of the scholarly publishing system. Currently, referees contribute so much to…
Transparency is often deemed critical to enable effective real-world deployment of intelligent systems. Yet the motivations for and benefits of different types of transparency can vary significantly depending on context, and objective…
Physics education research has probed for the relevance of physics in students' everyday lives. Attitudinal and epistemological surveys have asked students if they think of or use physics in their daily lives. We have previously documented…
As the impact of AI on various scientific fields is increasing, it is crucial to embrace interdisciplinary knowledge to understand the impact of technology on society. The goal is to foster a research environment beyond disciplines that…
In the paper different roles of users in social media, taking into consideration their strength of influence and different degrees of cooperativeness, are introduced. Such identified roles are used for the analysis of characteristics of…
Within the wide class of disordered materials, spin glasses occupy a special place because of their conceptually simple definition of randomly interacting spins. Their modelling has triggered spectacular developments of out-of-equilibrium…
Automated decision systems are increasingly used for consequential decision making -- for a variety of reasons. These systems often rely on sophisticated yet opaque models, which do not (or hardly) allow for understanding how or why a given…
The author describes some of his experiences as a mathematician cooperating with diabetes specialists.
University courses in conceptual physics and astronomy typically serve as the terminal science experience for non-science majors. Significant work has gone into developing research-verified pedagogical methods for the algebra- and…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…