Related papers: The decolonisation of mathematics
Our introductory classes in statistics and data science use too much mathematics. The key causal effect which our students want our classes to have is to improve their future performance and opportunities. The more professional their…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
If there is a "platonic world" M of mathematical facts, what does M contain precisely? I observe that if M is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
This paper is an introduction to our ongoing more comprehensive work on a critically important period in the history of Russian mathematics education; it provides a glimpse into the socio-political environment in which the famous Soviet…
Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
University students taking introductory physics are generally successful executing mathematical procedures in context, but often struggle with the use of mathematical concepts for sense making. Physics instructors note that their students…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called "Plato's problem," in line with the program of a philosophy of mathematical practice. It then provides a sketch of a…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
The multi-layered nature of societal developments poses a challenge in the teaching and learning of history of mathematics. As an attempt to tackle this challenge we experimented with the use of Knowledge-Maps. The focus of our interest…
Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large variety of visualization techniques. In this chapter, we sample the visualization literature to…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…
In the article, we would like to take part in a discussion over the problem of ethnomathematics, which has been under way for several years. We would like to express our opinion, our ideas concerning this problem and suggest our point of…
This paper is a critical reflection on the epistemic culture of contemporary computational linguistics, framed in the context of its growing obsession with tables with numbers. We argue against tables with numbers on the basis of their…
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…