Related papers: Helmut Salzmann and his Legacy
The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…
This paper, commissioned as a survey of the Riemann Hypothesis, provides a comprehensive overview of 165 years of mathematical approaches to this fundamental problem, while introducing a new perspective that emerged during its preparation.…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Patrick Moss (1947--2024) had two distinct lives as a mathematician. The first was as a ring theorist in the late 1970s, in which he worked with Ginn and Lenagan as a student. After a long career as an inspirational mathematics teacher,…
Several thoughts are presented on the long ongoing difficulties both students and academics face related to Calculus 101. Some of these thoughts may have a more general interest.
Analyzing in detail the analytic continuation of the Riemann zeta function we are able to generate several new identities which may be useful for application in physics and mathematics.
A short essay on the life and mathematical heritage of Coble. A substantially edited version will be part of the series of biographical memoirs of past members of the National Academy of Sciences. Version 2: minor changes. Version 3. Typo…
Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics as optimization problems over these varieties. The measure…
We prove some new results and unify the proofs of old ones involving complete monotonicity of expressions involving gamma and $q$-gamma functions, $0 < q < 1$. Each of these results implies the infinite divisibility of a related probability…
By some hypergeometric summation theorems, the authors establish a series of new infinite summation formulas involving generalized harmonic numbers related to Riemann-Zeta function, with three different patterns.
Santosh Kumar was an active researcher on the topic of exact results in random matrix theory and their various applications, particularly to quantum chaos and information theory. Barely entering his mid-career, he died unexpectedly on the…
We give a general overview of the influence of William Thurston on the French mathematical school and we show how some of the major problems he solved are rooted in the French mathematical tradition. At the same time, we survey some of…
This is an intrusion in the life and the mathematics of Norbert A'Campo, intended to be a tribute to him and an acknowledgement of his impact on those who know him and his work. The final version of this paper appears in the book ``Essays…
Riemann's hypothesis, formulated in 1859, concerns the location of the zeros of Riemann's Zeta function. The history of the Riemann hypothesis is well known. In 1859, the German mathematician B. Riemann presented a paper to the Berlin…
Professor Sir Karl Popper (1902-1994) was one of the most influential philosophers of science of the twentieth century. However, in his most famous work he displays misunderstandings of science and mathematics at a basic level.
Freeman J. Dyson, a brilliant theoretical physicist and a gifted mathematician, passed away on 28 February 2020 at the age of 96. A vignette of his outstanding contributions to physical sciences, ranging from the subject of quantum…
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…
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…
A tribute to the life and work of Pal Revesz. The Hungarian mathematical community lost one of his leading members, when Pal Revesz passed away on 14 of November 2022.
This is an overview article. In his Habilitationsvortrag, Riemann described infinite dimensional manifolds parameterizing functions and shapes of solids. This is taken as an excuse to describe convenient calculus in infinite dimensions…