Related papers: Euler's lute and Edwards' oud
We start by summarising very briefly the various prior attempts (during the last one and half a decade), some of which were made as independent research centres and others as visiting centres with extensive visiting programs for luminaries…
As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…
In the Proceedings of the AMS Boulder conference in 1965 Langlands states a combinatorial lemma involving families of characteristic functions attached to ordered partitions of an obtuse basis in a finite dimensional euclidean vector space.…
We consider the question of how mathematicians view themselves and how non-mathematicians view us. What is our role in society? Is it effective? Is it rewarding? How could it be improved? This paper will be part of a forthcoming volume on…
Observe and understand users of the Scientific and Technical Information, is preparing to offer them appropriate services. This exploratory study provides answers about the uses in the humanities, social sciences as well as technical…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by…
Human guidance is often desired in reinforcement learning to improve the performance of the learning agent. However, human insights are often mere opinions and educated guesses rather than well-formulated arguments. While opinions are…
The purpose of this paper is to present a syatemic study of some familes of higher-order Euler numbers and polynomials. In particular, by using the basis property of higher-order Euler polynomials for the space of polynomials of degree less…
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
The Lecture-Tutorials for Introductory Astronomy have been designed to help introductory astronomy instructors actively engage their students in developing their conceptual understandings and reasoning abilities across a wide range of…
Research on writing tools started with the increased availability of computers in the 1970s. After a first phase addressing the needs of programmers and data scientists, research in the late 1980s started to focus on writing-specific needs.…
Large Language Models (LLMs) have shown the potential to be valuable teaching tools, with the potential of giving every student a personalized tutor. However, one challenge with using LLMs to learn new concepts is that when learning a topic…
Scientific writing builds upon already published papers. Manual identification of publications to read, cite or consider as related papers relies on a researcher's ability to identify fitting keywords or initial papers from which a…
This paper calls on the research community not only to investigate how human biases are inherited by large language models (LLMs) but also to explore how these biases in LLMs can be leveraged to make society's "unwritten code" - such as…
Since its introduction by P.L. Lions in his lectures and seminars at the College de France, see [9], and also the very helpful notes of Cardialaguet [4] on Lions' lectures, the Master Equation has attracted a lot of interest, and various…
In supervised machine learning, privileged information (PI) is information that is unavailable at inference, but is accessible during training time. Research on learning using privileged information (LUPI) aims to transfer the knowledge…
We qualitatively compared literature reviews produced with varying degrees of AI assistance. The same LLM, given the same corpus of 280 papers but different selections, produced dramatically different reviews, from mainstream and…
The recognition of academic excellence is fundamental to the scientific and academic endeavor. However, the term "academic excellence" is often interpreted in different ways, typically, using popular scientometrics such as the H-index,…
This is a translation of Leonhard Euler's ``De quadratis magicis'' . It is E795 in the Enestrom index. This paper studies how to construct magic squares with certain numbers of cells, in particular 9, 16, 25 and 36. It considers some…