Related papers: Through a Glass Darkly
This is a presentation of the purpose of astronomy in the context of modern society. After exposing two misconceptions about astronomy, I detail its role in five domains, certified knowledge, incorporated abilities, innovations, collective…
The job of a physicist is to describe Nature. General features, hypotheses and theories help to describe physics phenomena at a more abstract, fundamental level, and are sometimes tacitly assigned some sort of real existence; doing so…
Any system based on axioms is incomplete because the axioms cannot be proven from the system, just believed. But one system can be less-incomplete than other. Neutrosophy is less-incomplete than many other systems because it contains them.…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
As the role of algorithmic systems and processes increases in society, so does the risk of bias, which can result in discrimination against individuals and social groups. Research on algorithmic bias has exploded in recent years,…
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical)…
We present an exploratory study of the perception of professional astronomers about the societal impact of astronomy. Ten semi-structured interviews with astronomers from a range of career and cultural backgrounds have been conducted to…
It is rare to succeed in getting mathematics into ordinary conversation without meeting all kinds of reservations. In order to raise public awareness of mathematics effectively, it is necessary to modify such attitudes. In this paper, we…
When we devise a method to address a particular research question, we think about many things, including the unit of study. But do we think about the perspective from which we observe whatever it is that's within our field of view? In the…
In this article, we suggest the use of Mathematical Relationships as a possible way to decrease the students' disinterest in Mathematics. First we made a consideration of the environment of the classroom from the perspective of teachers and…
Objects are a centerpiece of the mathematical realm and our interaction with and reasoning about it, just as they are of the physical one (if not more). And humans' mathematical reasoning must ultimately be grounded in our general…
Knowledge can't be disentangled from people. As AI knowledge systems mine vast volumes of work-related data, the knowledge that's being extracted and surfaced is intrinsically linked to the people who create and use it. When predictive…
In physics, there is the prevailing intuition that we are part of a unique external world, and that the goal of physics is to understand and describe this world. This assumption of the fundamentality of objective reality is often seen as a…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
This chapter takes a historical view of the development of mathematics education, from its initial status as a business mostly managed by mathematicians to the birth of mathematics education as a scientific field of research. Starting from…
We discuss the idea that computers might soon help mathematicians to prove theorems in areas where they have not previously been useful. Furthermore we argue that these same computer tools will also help us in the communication and teaching…
Astronomy and related fields are at the forefront of science and technology; answering fundamental questions and driving innovation. Although blue-skies research like astronomy rarely contributes directly with tangible outcomes on a short…
We contemplate the notion of ambiguity in mathematical discourse. We consider a general method of resolving ambiguity and semantic options for sustaining a resolution. The general discussion is applied to the case of `fraction' which is…