Related papers: From Euler to Today: Universal Mathematical Fallib…

In this work, we study how URL extraction results depend on input format. We compiled a pilot dataset by extracting URLs from 10 arXiv papers and used the same heuristic method to extract URLs from four formats derived from the PDF files or…

We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem…

We prove joint universality theorems on the half plane of absolute convergence for general classes of Dirichlet series with an Euler-product, where in addition to vertical shifts we also allow scaling. This generalizes our recent joint…

Reference errors, such as citation and quotation errors, are common in scientific papers. Such errors can result in the propagation of inaccurate information, but are difficult and time-consuming to detect, posing a significant challenge to…

As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…

We used computer proof-checking methods to verify the correctness of our proofs of the propositions in Euclid Book I. We used axioms as close as possible to those of Euclid, in a language closely related to that used in Tarski's formal…

Identifying academic plagiarism is a pressing task for educational and research institutions, publishers, and funding agencies. Current plagiarism detection systems reliably find instances of copied and moderately reworded text. However,…

We develop a fully non-invasive use of machine learning in order to enable open research on Euclid-sized data sets. Our algorithm leaves complete control over theory and data analysis, unlike many black-box like uses of machine learning.…

The major hindrance in the study of earlier scientific literature is the availability of Latin translations into modern languages. This is particular true for the works of Euler who authored about 850 manuscripts and wrote a thousand…

Data errors are widespread in real-world databases and severely impact downstream applications, such as machine learning pipelines or business analytics reports. Causes of such errors are manifold and can arise during both the design phase…

Scientific articles published prior to the "age of digitization" (~1997) require Optical Character Recognition (OCR) to transform scanned documents into machine-readable text, a process that often produces errors. We develop a pipeline for…

While large language models (LLMs) excel at many domain-specific tasks, their ability to deeply comprehend and reason about full-length academic papers remains underexplored. Existing benchmarks often fall short of capturing such depth,…

In this article we construct a compact Riemannian manifold of high dimension on which the time dependent Euler equations are Turing complete. More precisely, the halting of any Turing machine with a given input is equivalent to a certain…

Euler gives a long introduction, giving all the arguments for and against the use of divergent series in calculus and then gives his own definition of the sum of a diverging series. Then in the second half of this paper he evaluates the the…

The automated generation of research workflows is essential for improving the reproducibility of research and accelerating the paradigm of "AI for Science". However, existing methods typically extract merely fragmented procedural components…

In the digital era, the exponential growth of scientific publications has made it increasingly difficult for researchers to efficiently identify and access relevant work. This paper presents an automated framework for research article…

We review and comment on some works of Euler and his followers on spherical geometry. We start by presenting some memoirs of Euler on spherical trigonometry. We comment on Euler's use of the methods of the calculus of variations in…

The On-Line Encyclopedia Of Integer Sequences , that wonderful resource that most combinatorialists, and many other mathematicians and scientists, use at least once a day, is a treasure trove of mathematical information, and, one of its…

In this paper, we investigate mathematical content representations suitable for the automated classification of and the similarity search in STEM documents using standard machine learning algorithms: the Latent Dirichlet Allocation (LDA)…

This paper describes the intense software filtering that has allowed the arXiv eprint repository to sort and process large numbers of submissions with minimal human intervention, making it one of the most important and influential cases of…