Related papers: From Euler to Today: Universal Mathematical Fallib…
The assumption of real-number arithmetic, which is at the basis of conventional geometric algorithms, has been seriously challenged in recent years, since digital computers do not exhibit such capability. A geometric predicate usually…
We design an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two…
Large language models can generate fluent peer reviews, yet their assessments often lack sufficient critical rigor when substantive issues are subtle and distributed across a paper. In this paper, we introduce PaperAudit-Bench, which…
Leonhard Euler likely developed his summation formula in 1732, and soon used it to estimate the sum of the reciprocal squares to 14 digits --- a value mathematicians had been competing to determine since Leibniz's astonishing discovery that…
Large Language Models (LLMs) are transforming scholarly tasks like search and summarization, but their reliability remains uncertain. Current evaluation metrics for testing LLM reliability are primarily automated approaches that prioritize…
Computational reproducibility is fundamental to trustworthy science, yet remains difficult to achieve in practice across various research workflows, including Jupyter notebooks published alongside scholarly articles. Environment drift,…
This study evaluates $n = 300$ short-form physics essay submissions, equally divided between student work submitted before the introduction of ChatGPT and those generated by OpenAI's GPT-4. In blinded evaluations conducted by five…
Double-blind peer review is considered a pillar of academic research because it is perceived to ensure a fair, unbiased, and fact-centered scientific discussion. Yet, experienced researchers can often correctly guess from which research…
This paper explores articles hosted on the arXiv preprint server with the aim to uncover valuable insights hidden in this vast collection of research. Employing text mining techniques and through the application of natural language…
Translated from the Latin original, "De numeris amicabilibus" (1747). E100 in the Enestroem index. Euler starts by saying that with the success of mathematical analysis, number theory has been neglected. He argues that number theory is…
Half a billion citation edges extracted from 100.7 million Ukrainian court decisions reveal that judicial citation structure encodes legal domain boundaries without supervision and predicts future legislative importance with near-perfect…
Large Language Models (LLMs) have demonstrated remarkable capabilities across various domains. Math Word Problems (MWPs) serve as a crucial benchmark for evaluating LLMs' reasoning abilities. While most research primarily focuses on…
Computing the Euler genus of a graph is a fundamental problem in graph theory and topology. It has been shown to be NP-hard by [Thomassen '89] and a linear-time fixed-parameter algorithm has been obtained by [Mohar '99]. Despite extensive…
Academic researchers often need to face with a large collection of research papers in the literature. This problem may be even worse for postgraduate students who are new to a field and may not know where to start. To address this problem,…
Patents and scientific papers provide an essential source for measuring science and technology output, to be used as a basis for the most varied scientometric analyzes. Authors' and inventors' names are the key identifiers to carry out…
The recognition of individual contributions is central to the scientific reward system, yet coauthored papers often obscure who did what. Traditional proxies like author order assume a simplistic decline in contribution, while emerging…
This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter…
We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leibniz, Euler, Cauchy and other giants of infinitesimal…
We extend several celebrated methods in classical analysis for summing series of complex numbers to series of complex matrices. These include the summation methods of Abel, Borel, Ces\'aro, Euler, Lambert, N\"orlund, and Mittag-Leffler,…
Objective: To determine the completeness of argumentative steps necessary to conclude effectiveness of an algorithm in a sample of current ML/AI supervised learning literature. Data Sources: Papers published in the Neural Information…