No Arabic abstract
In November 2014 Alexander Grothendieck passed away at the age of 86. There is no doubt that he was one of the greatest and most innovative mathematicians of the 20th century. After a bitter childhood, his meteoric ascent started in the Cartan Seminar in Paris, it led to a breakthrough while he worked in Sao Paulo, and to the Fields Medal. He introduced numerous new concepts and techniques, which were involved in the groundbreaking solutions to long-standing problems. However, dramatic changes were still ahead of him. In recent years hardly anybody knew where he was living, and even if he was still alive; he had withdrawn to a modest life in isolation. Also beyond his achievements in mathematics, Grothendieck was an extraordinary person. This is a tribute of his fascinating life.
This article is a tribute to one of the most prominent Polish mathematicians Jozef Marcinkiewicz who perished 80 years ago in the Katyn massacre. His personality and main mathematical achievements are described.
We survey recent results on the mathematical stability of Bitcoin protocol. Profitability and probability of a double spend are estimated in closed form with classical special functions. The stability of Bitcoin mining rules is analyzed and several theorems are proved using martingale and combinatorics techniques. In particular, the empirical observation of the stability of the Bitcoin protocol is proved. This survey article on the mathematics of Bitcoin is published by the Newsletter of the European Mathematical Society, vol.115, 2020, p.31-37. Continuation of arXiv:1601.05254 (EMS Newsletter, 100, 2016 p.32).
Given the profound and uncritiqued changes that have been implemented in Aotearoa New Zealand education since the 1990s, this paper provides a critical commentary on the characterising features of the New Zealand mathematics curriculum in the context of the first stage of a study. The emphasis is on the importance of research design that begins with an explicit, evidence-based hypothesis. To that end, we describe evidence that informs and identifies the studys hypothesised problem and causes. The study itself will show whether or not the hypothesis is justified; that is, is the absence of standardised prescribed content in New Zealand mathematics curriculum the reason for the countrys declining mathematics rankings? The study aims to increase understanding in the field of mathematics education by exploring the effects on New Zealand year 7 public school teachers mathematics curriculum selection and design practices, teaching practices, and subsequently student achievement.
We give a purely mathematical interpretation and construction of sculptures rendered by one of the authors, known herein as Fels sculptures. We also show that the mathematical framework underlying Fergusons sculpture, {it The Ariadne Torus}, may be considered a special case of the more general constructions presented here. More general discussions are also presented about the creation of such sculptures whether they be virtual or in higher dimensional space.
This is the opening article of the abstract book of conference Set-Theoretic Topology and Topological Algebra in honor of professor Alexander Arhangelskii on the occasion of his 80th birthday held in 2018 at Moscow State University.