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We dedicate this to the life and work of Robin Hudson -- a mathematical physicist who developed the peerless quantum stochastic calculus, but who also inspired generations of researchers with both his intellect and wit.
We survey briefly the life and work of P. L. Chebyshev, and his ongoing influence. We discuss his contributions to probability, number theory and mechanics, his pupils and mathematical descendants, and his role as the founding father of…
This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.
Several authors, including the American Statistician (ASA), have noted the challenges facing statisticians when attacking large, complex, unstructured problems, as opposed to well-defined textbook problems. Clearly, the standard paradigm of…
These are notes related to a 12-hour course of lectures given at the Centre de Recerca Mathem\`atica near Barcelona in February, 2010. The aim of the course was to explain results on curves and their Jacobians over function fields, with…
The paper "Evaluation of Colorado Learning Attitudes about Science Survey" [1] proposes a new, much shorter, version of the CLASS based on standard factor analysis. In this comment we explain why we believe the analysis that is used is…
This is a survey talk on one of the best known quantum knot invariants, the colored Jones polynomial of a knot, and its relation to the algebraic/geometric topology and hyperbolic geometry of the knot complement. We review several aspects…
After the language of module and theirs morphisms, this short course presents matricial calculus and determinants in a commutative ring as appliction of ``remarquable identities'' in the ring of polynomials with integer coefficients with…
This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between…
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the…
It's hard to imagine human life in the digital and AI age without polynomials because they are everywhere but mostly invisible to ordinary people: in data trends, on computer screens, in the shapes around us, and in the very fabric of…
The topic of this paper is, on the one hand to introduce algebraic analysis results of \'Etienne B\'ezout (1730- 1783) not as we know them today but as he found them in his time, and on the other hand to emphasize his innovating viewpoints.…
Recent developments in computer programming and in mathematics suggest that there is a strong case for a new way of introducing programming to enhance the learning of school mathematics. The article describes a collaboration of mathematics…
Herman Melville's novel Moby-Dick contains a surprising number of mathematical allusions. In this article we explore some of these, as well as discussing the questions that naturally follow: why did Melville choose to use so much…
I want to write about what I know and remember about the activities of Leonid Vital'evich Kantorovich, an outstanding scientist of the 20th century; about his dramatic struggle for recognition of his mathematical economic theories; about…
Professor Sir Karl Popper (1902-1994) was one of the most influential philosophers of science of the twentieth century, best known for his doctrine of falsifiability. His axiomatic formulation of probability, however, is unknown to current…
The last half-dozen years have seen The American Statistician publish well-argued and provocative calls to change our thinking about statistics and how we teach it, among them Brown and Kass (2009), Nolan and Temple-Lang (2010), and Legler…
The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Using an example from my own mathematical life, I argue that…
Despite ongoing calls for inclusive and culturally responsive pedagogy in computing education, the teaching of algorithms remains largely decontextualized. Foundational computer science courses often present algorithmic thinking as purely…
We describe a mainstream "universalist" approach to the understanding of mathematics. We then conduct a systematic (but not exhaustive) review of the academic literature on the decolonisation of mathematics and identify how this challenges…