Related papers: Interview with Hyman Bass
A century ago physicists and mathematicians worked in tandem and established quantum mechanism. Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism. Currently,…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
Steven Weinberg was a giant of late 20th Century physics on whose shoulders we stand while groping for the science of the 21st Century. This article provides a too-brief summary of a selection of his many achievements -- eight decades of…
Remarks at the Irving Kaplansky Memorial about a collaboration during the early period of the renewal of contacts between mathematicians and theoretical physicists.
I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
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…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
We answer to criticisms of O. Keller about our interpretation work on the Ishango rod, the oldest mathematical tool of humankind. Our hypothesis, that is widely accepted, is that this prehistoric rod is the first mankind manifestation of a…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
This paper presents a comprehensive survey of various established mathematical models pertaining to Somitogenesis, a biological process. The study begins by revisiting and replicating the findings from prominent research papers in this…
We review some of Olivier Messiaen's use of mathematics in his composition and his theoretical writings. The final version of this paper appeared in the book Twentieth-Century Music and Mathematics, R. Illiano (ed.), Brepols, Turnhout,…
The situation surrounding the Olympiads is paradoxical. On the one hand, considerable resources are spent on the Olympiads. On the other hand, there are widespread arguments about the harm of the Olympiads, often very strange ones. For…
The central nervous system and particularly the brain was designed to control the life cycle of a living being. With increasing size and sophistication, in mammals, the brain became capable of exercising significant control over life. In…
Gerhard Hochschild's contribution to the development of mathematics in the XX century is succinctly surveyed. We start with a personal and mathematical biography, and then consider with certain detail his contributions to algebraic groups…
This article focuses on evolvement of the history of mathematics as a science and development of its methodology from the 4th century B.C. to the age of Enlightenment.
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
We present some episodes from the history of interactions between geometry and physics over the past century.
The article describes the biography and manifold contributions to research in mathematics of Mikhail Aleksandrovich Shubin.
Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and…