Related papers: On definitions of "mathematician"
Much of the controversy about methods for automated decision making has focused on specific calculi for combining beliefs or propagating uncertainty. We broaden the debate by (1) exploring the constellation of secondary tasks surrounding…
This article analyzes the emerging ethical turn in mathematics education, arguing that it is a nuanced extension of the sociopolitical turn. While sociopolitical studies of mathematics have highlighted systemic issues and group concerns…
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…
Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously. As a case study, the story of Szemer\'edi's theorem is presented.
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by…
A recent flurry of research activity has attempted to quantitatively define "fairness" for decisions based on statistical and machine learning (ML) predictions. The rapid growth of this new field has led to wildly inconsistent terminology…
Data scientists are not mathematicians, but they make heavy use of mathematics in their daily work. While mathematicians can study a mathematical object which is inaccessible to our five senses, data scientists must deal with real-world…
Technology is currently ubiquitous and is also part of the educational system at all levels. It started with communication technology systems, and later continued with digital competence. Nowadays, although these previous concepts are still…
We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that…
The author describes some of his experiences as a mathematician cooperating with diabetes specialists.
Category theory provides a powerful tool to organize mathematics. A sample of this descriptive power is given by the categorical analysis of the practice of "classes as shorthands" in ZF set theory. In this case category theory provides a…
I give a short introduction to data ethics. I begin with some background information and societal context for data ethics. I then discuss data ethics in mathematical-science education and indicate some available course material. I briefly…
Means are used in several applications from electronic engeneering to information theory, however there is no general theorem on how to extend a given M(x, y) mean function to multiple variable forms. In this article we would like to…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…
Representativeness is a foundational yet slippery concept. Though familiar at first blush, it lacks a single precise meaning. Instead, meanings range from typical or characteristic, to a proportionate match between sample and population, to…