Related papers: Euler's lute and Edwards' oud
This is the classical monograph on the combinatorial study of Eulerian polynomials, published in 1970. It has been retyped in TeX and made available on the web with the kind permission of Springer-Verlag. This on-line version has an ouput…
Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in…
Epistemic reasoning requires agents to infer the state of the world from partial observations and information about other agents' knowledge. Prior work evaluating LLMs on canonical epistemic puzzles interpreted their behavior through a…
A new and rapidly growing econometric literature is making advances in the problem of using machine learning methods for causal inference questions. Yet, the empirical economics literature has not started to fully exploit the strengths of…
The ability to learn from others (social learning) is often deemed a cause of human species success. But if social learning is indeed more efficient (whether less costly or more accurate) than individual learning, it raises the question of…
To determine Euler numbers modulo powers of two seems to be a difficult task. In this paper we achieve this and apply the explicit congruence to give a new proof of a classical result due to M. A. Stern.
In recent years, Artificial Intelligence has become more and more relevant in our society. Creating AI systems is almost always the prerogative of IT and AI experts. However, users may need to create intelligent solutions tailored to their…
In scientific research, the method is an indispensable means to solve scientific problems and a critical research object. With the advancement of sciences, many scientific methods are being proposed, modified, and used in academic…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
The following translation of Leonhard Euler's "Examination of an Artifice for Propelling a Ship by the Principle of Internal Motion," originally published in 1750, offers a glimpse into a fascinating historical debate in the field of…
Macroeconomics essentially discusses macroeconomic phenomena from the perspectives of various schools of economic thought, each of which takes different views on how macroeconomic agents make decisions and how the corresponding markets…
Mastering a musical instrument requires time-consuming practice even if students are guided by an expert. In the overwhelming majority of the time, the students practice by themselves and traditional teaching materials, such as videos or…
In this paper, we analyse how learning is measured and optimized in Educational Recommender Systems (ERS). In particular, we examine the target metrics and evaluation methods used in the existing ERS research, with a particular focus on the…
The paper gives a review of very recent results related to the Poncelet Theorem, on the occasion of its bicentennial. We are telling the story of one of the most beautiful theorems of Geometry, recalling for the general mathematical…
This paper reconstructs the derivations underlying the kinematical part of Einstein's 1905 special relativity paper, emphasizing their operational clarity and minimalist use of mathematics. Einstein employed modest tools-algebraic…
This work analyzes the difficulties in learning and teaching Einstein's theory of special relativity. An extensive bibliographic review has been performed, considering articles published in the most relevant journals on science education,…
Euclidean functions with values in an arbitrary well-ordered set were first considered in a 1949 work of Motzkin and studied in more detail in work of Fletcher, Samuel and Nagata in the 1970's and 1980's. Here these results are revisited,…
The h-index can be used as a predictor of itself. However, the evolution of the h-index with time is shown in the present investigation to be dominated for several years by citations to previous publications rather than by new scientific…
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
In recent paper "Quantifying Inequities and Documenting Elitism in PhD-granting Mathematical Sciences Departments in the United States" (arXiv:2308.13750) by a group of accomplished and/or aspiring mathematicians, the authors use data to…