Related papers: Memories with Solomon Marcus
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…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
I was lucky to meet (and even cooperate at some extent) with Israel M. Gelfand, and tried to write down (mainly in 2003-2013) my recollections about his work style and lessons I learned from him about teaching and writing mathematics…
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…
Remarks at the Irving Kaplansky Memorial about a collaboration during the early period of the renewal of contacts between mathematicians and theoretical physicists.
We provide some historical context to the study of solid angles carried out by Euler in his memoir \emph{De mensura angulorum solidorum} (On the measure of solid angles). We extend our study to the general notion of angle (not only solid).…
The authors provide a survey of certain aspects of their joint work with the late M. K. Vamanamurthy. Most of the results are simple to state and deal with special functions, a topic of research where S. Ramanujan's contributions are…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
I give an account of what it was like to be a PhD student of Abdus Salam and also to take part during the early stages of the development of supersymmetry.
The current work will appear in a Celebratio Mathematica volume in honor of Walter Neumann. We summarize results and methods from our long-time collaboration with Neumann, especially the motivation for the introduction of splice diagrams to…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on independent subsets of powers of paths and cycles, trying to…
Based on Plato's Timaeus, we present some reflections on music, cosmology and mathematics and their mutual influence.The article is dedicated to the composer Walter Zimmermann. The final version of this article will appear in the volume…
We use large language models (LLM) to approach a question about Lagrangian smoothability proposed by Abouzaid et al. in "First Proof" arXiv:2602.05192.
This is a survey of Magnus representations with particular emphasis on their applications to mapping class groups and monoids (groups) of homology cobordisms of surfaces. In the first half, we begin by recalling the basics of the Fox…
Children can take many paths to become scientists. But they undoubtedly include the following steps Play, play and play; Observe; Ask (themselves). In this paper I will talk about some of my experiences teaching girls and boys, teenagers…
Previous work of the author has developed coordinates on bundles over the classical Teichmueller spaces of punctured surfaces and on the space of cosets of the Moebius group in the group of orientation-preserving homeomorphisms of the…
These are lecture notes on scale calculus and M-polyfolds written for a graduate course at UNICAMP March-June 2018 and an advanced mini-course given during the biannual meeting of Brazilian mathematicians, CBM-32, at IMPA in August 2019.
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.