Mathematics
Dedicated to Solomon Marcus, the current paper continues a recent series about our meetings. Trying to recreate the spirit of those meetings, we first propose a discussion which started as a high-school problem. The main part of the current…
The Ishango Bone is a prehistoric artifact dated to approximately 20,000 years ago, discovered near the Semliki River in what is now the Democratic Republic of Congo, and has been the subject of scholarly debate for decades. The artifact…
Sophie Germain (1776-1831) was the first woman we know who did important original research in mathematics, specifically in elasticity theory and number theory. Celebrating her semiquincentennial year, we outline Germain's recently unearthed…
We explore the issue of providing a foundational framework for Leibnizian infinitesimals in the light of modern standard and nonstandard approaches. We outline a trichotomy of ordinals, cardinals and ringinals as a historiographic tool. A…
Recent research in mathematics education points to an "epistemic clash" when programming and computational thinking (CT) are leveraged alongside more established forms of mathematical thinking (MT). The emergence of generative AI emphasises…
We revisit several entries from Ramanujan's notebooks which follow from more elementary arguments than a first glance may suggest. Our goal is to demystify these results through more accessible proofs, while also shining some light on the…
Eugenio Beltrami published his seminal 'Essay on the Interpretation of Non-Euclidean Geometry' in 1868, where he showed that geodesics on a surface of constant negative curvature can be mapped as straight lines on a Euclidean disc. More…
Artificial intelligence is transforming mathematics at a speed and scale that demand active engagement from the mathematical community. We examine five areas where this transformation is particularly pressing: values, practice, teaching,…
Flipped classroom pedagogy is widely used in undergraduate mathematics to promote active learning, yet it remains unclear whether students experience it in systematically different ways. In this study, we analyze student perceptions from an…
These notes provide a pedagogical introduction to the role of transversality theory in the analysis of statistical degeneracies within the framework of distributional statistical models. The classical question of when a statistical model is…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
This is an overview of Nasir al-Din al-Tusi's Treatise of the quadrilateral, an invaluable 13th century document on spherical geometry which was translated into French in 1891. The title we are using here is the one given by the translator…
Conway's Doomsday Algorithm (1973) determines the day of the week for any date in the Gregorian calendar via three additive components: a century anchor, a year offset, and a month-day offset. The century anchor is a fixed four-entry table.…
This article describes the use of Claude CLI and its Opus 4.6 model, as a tool for writing an entirely AI-generated mathematics research paper. The resulting paper is comparable in scope and quality to papers previously produced by advanced…
The article is dedicated to the memory and enduring legacy of Professor Robert V. Kohn, Courant Institute, NYU. In this memorial article, we record thoughts and reminiscences of his exemplary life.
AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully…
In many proofs of Fermat's Two Squares Theorem, the smallest least residue solution $x_0$ of the quadratic congruence $x^2 \equiv -1 \bmod p$ plays an essential role; here $p$ is prime and $p \equiv 1 \bmod 4$. Such an $x_0$ is called a…
The topic is the history of the concepts of equivalence relation, Cauchy sequence, and metric space. The thesis is that disused definitions of these notions could profitably be revived.
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
The studies of Bonaventura Cavalieri's indivisibles by Giusti, Andersen, Mancosu and others provide a comprehensive picture of Cavalieri's mathematics, as well as of the mathematical objections to it as formulated by Paul Guldin and other…