Related papers: From Euler to Today: Universal Mathematical Fallib…
We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad…
The use of machine learning (ML) methods for prediction and forecasting has become widespread across the quantitative sciences. However, there are many known methodological pitfalls, including data leakage, in ML-based science. In this…
Literature review tables are essential for summarizing and comparing collections of scientific papers. In this paper, we study the automatic generation of such tables from a pool of papers to satisfy a user's information need. Building on…
Given the large number of publications in software engineering, frequent literature reviews are required to keep current on work in specific areas. One tedious work in literature reviews is to find relevant studies amongst thousands of…
Nowadays, Machine Learning (ML) is seen as the universal solution to improve the effectiveness of information retrieval (IR) methods. However, while mathematics is a precise and accurate science, it is usually expressed by less accurate and…
This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory. Recent benchmarks of large language models have mainly focused on general mathematics problems and the currently infeasible…
In the evolving landscape of clinical informatics, the integration and utilization of software tools developed through governmental funding represent a pivotal advancement in research and application. However, the dispersion of these tools…
The Euler genus of a graph is a fundamental and well-studied parameter in graph theory and topology. Computing it has been shown to be NP-hard by [Thomassen '89 & '93], and it is known to be fixed-parameter tractable. However, the…
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 paper, we show how selecting and combining encodings of natural and mathematical language affect classification and clustering of documents with mathematical content. We demonstrate this by using sets of documents, sections, and…
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…
We describe a strategy for identifying the universe of research publications relevant to the application and development of artificial intelligence. The approach leverages the arXiv corpus of scientific preprints, in which authors choose…
Recent advancements in large language models have sparked interest in utilizing them to aid the peer review process of scientific publication amid the peer review crisis. However, having AI models generate full reviews in the same way as…
The statistics community, which has traditionally lacked a transparent and open peer-review system, faces a challenge of inconsistent paper quality, with some published work containing substantial errors. This problem resonates with…
Many people are interested in ChatGPT since it has become a prominent AIGC model that provides high-quality responses in various contexts, such as software development and maintenance. Misuse of ChatGPT might cause significant issues,…
We present several results related to statistics for elliptic curves over a finite field $\mathbb{F}_p$ as corollaries of a general theorem about averages of Euler products that we demonstrate. In this general framework, we can reprove…
Professionals in academia, law, and finance audit their documents because inconsistencies can result in monetary, reputational, and scientific costs. Language models (LMs) have the potential to dramatically speed up this auditing process.…
Identification of new concepts in scientific literature can help power faceted search, scientific trend analysis, knowledge-base construction, and more, but current methods are lacking. Manual identification cannot keep up with the torrent…
This is the translation of Leonhard Euler's paper "De Seriebus divergentibus" written in Latin into English. Leonhard Euler defines and discusses divergent series. He is especially interested in the example $1!-2!+3!-\text{etc.}$ and uses…
We use data from papers posted to the Mathematics section of the arXiv to explore the representation of women in mathematics research. We show that women are under-represented as authors of mathematics papers on the arXiv, even in…