Related papers: Some instructive mathematical errors
Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error of Mathematica computing determinants of…
This article discusses a number of incorrect statements appearing in textbooks on data analysis, machine learning, or computational methods; the common theme in all these cases is the relevance and application of statistics to the study of…
In Grammatical Error Correction, systems are evaluated by the number of errors they correct. However, no one has assessed whether all error types are equally important. We provide and apply a method to quantify the importance of different…
We report on an exploratory analysis of the forms of plagiarism observable in mathematical publications, which we identified by investigating editorial notes from zbMATH. While most cases we encountered were simple copies of earlier work,…
Context: Conducting experiments is central to research machine learning research to benchmark, evaluate and compare learning algorithms. Consequently it is important we conduct reliable, trustworthy experiments. Objective: We investigate…
In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…
This article discusses several erroneous claims which appear in textbooks on numerical methods and computational physics. These are not typos or mistakes an individual author has made, but widespread misconceptions. In an attempt to stop…
In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and…
The apparently trifling unexpected hanging paradox has generated an enormous philosophical literature. We introduce the mathematician to this literature, paying special attention to aspects that involve nontrivial mathematics. This xxx…
Large language models (LLMs) demonstrate considerable potential in various natural language tasks but face significant challenges in mathematical reasoning, particularly in executing precise, multi-step logic. However, current evaluation…
Uncertainty in probabilistic classifiers predictions is a key concern when models are used to support human decision making, in broader probabilistic pipelines or when sensitive automatic decisions have to be taken. Studies have shown that…
In this paper we propose a very specific educational challenge that teachers can use to motivate ambitious and enthusiastic mathematics students who have mastered basic trigonometry and trig functions. The objective is to lead students to a…
The problem of detecting scientific fraud using machine learning was recently introduced, with initial, positive results from a model taking into account various general indicators. The results seem to suggest that writing style is…
Understanding prediction errors and determining how to fix them is critical to building effective predictive systems. In this paper, we delineate four types of prediction errors and demonstrate that these four types characterize all…
Research on reasoning in language models (LMs) predominantly focuses on improving the correctness of their outputs. But some important applications require modeling reasoning patterns that are incorrect. For example, automated systems that…
Fifteen years of research studies have concluded unanimously that spreadsheet errors are both common and non-trivial. Now we must seek ways to reduce spreadsheet errors. Several approaches have been suggested, some of which are promising…
Insightful interdisciplinary collaboration is essential to the principled governance of technology. When such efforts address the interaction between computation and society, they often focus on modeling, the process by which computer…
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…
Large reasoning models (e.g., R1, o3) have demonstrated remarkable mathematical problem-solving abilities. However, the high reported accuracy of these advanced models on popular datasets, reliance on purely numerical evaluation and…
With the remarkable increase in the number of scientific entities such as publications, researchers, and scientific topics, and the associated information overload in science, academic recommender systems have become increasingly important…