Related papers: On merit and equity in math
Computer science is also an experimental science. This is particularly the case for parallel computing, which is in a total state of flux, and where experiments are necessary to substantiate, complement, and challenge theoretical modeling…
The "reproducibility crisis" has been a highly visible source of scientific controversy and dispute. Here, I propose and review several avenues for identifying and prioritizing research studies for the purpose of targeted validation. Of the…
Despite the effort put into the detection of academic plagiarism, it continues to be a ubiquitous problem spanning all disciplines. Various tools have been developed to assist human inspectors by automatically identifying suspicious…
This article is a part of the report for the research project ``Reform of the Course System and Teaching Content of Higher Mathematics (For Non-Mathematical Specialties)'' in 1995, supported by the National Ministry of Education. There are…
Researchers must ensure that the claims about the knowledge produced by their work are valid. However, validity is neither well-understood nor consistently established in design science, which involves the development and evaluation of…
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…
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…
Goedel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Goedel to…
The resources compiled in this document provide an approach to embed and teach Ethics in Mathematics at the undergraduate level. We provide mathematical exercises and homework problems that teach students ethical awareness and transferable…
Like many other voting systems, Majority Judgement suffers from the weaknesses of the underlying mathematical model: Elections as problem of choice or ranking. We show how the model can be enhanced to take into account the complete process…
An academic scientist's professional success depends on publishing. Publishing norms emphasize novel, positive results. As such, disciplinary incentives encourage design, analysis, and reporting decisions that elicit positive results and…
As Large Language Models (LLMs) become increasingly embedded in empirical research workflows, their use as analytical tools for quantitative or qualitative data raises pressing concerns for scientific integrity. This opinion paper draws a…
In the field of algorithmic fairness, many fairness criteria have been proposed. Oftentimes, their proposal is only accompanied by a loose link to ideas from moral philosophy -- which makes it difficult to understand when the proposed…
In an ideal world, every scientist's contribution would be fully recognized, driving collective scientific progress. In reality, however, only a few scientists are recognized and remembered. Sociologist Robert Merton first described this…
We are concerned with the problem of introducing credibility type information into reasoning systems. The concept of credibility allows us to discount information provided by agents. An important characteristic of this kind of procedure is…
Some attack scientific rationality, others defend it, but both miss the point. What both parties take to be scientific rationality is actually a species of irrationality masquerading as scientific rationality. The current orthodox…
It is widely agreed that exams must be fair; yet what this exactly means is not made clear. One may mean fairness of treatment, but this merely propagates the fairness or unfairness of pre-existing rules. Fairness of opportunity on the…
Existing benchmarks for evaluating mathematical reasoning in large language models (LLMs) rely primarily on competition problems, formal proofs, or artificially challenging questions -- failing to capture the nature of mathematics…
Quantifying success in science plays a key role in guiding funding allocations, recruitment decisions, and rewards. Recently, a significant amount of progresses have been made towards quantifying success in science. This lack of detailed…
This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…