历史与综述
The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in the limit of small probabilities. The…
This paper studies the work of the French mathematician Francois Viete, known as the "father of modern algebraic notation". Along with this fundamental change in algebra, Viete adopted a radically new notation based on Greek geometric…
In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…
In this expository article, we outline the theory of harmonic differential forms and its consequences. We provide self-contained proofs of the following important results in differential geometry: (1) Hodge theorem, which states that for a…
We reconsider the classical equality 0.999. .. = 1 with the tool of circular words, that is: finite words whose last letter is assumed to be followed by the first one. Such circular words are naturally embedded with algebraic structures…
This paper contains a case study of the work and self-definition of two important mathematicians during the rise of modern mathematics: Felx Hausdorff (1868--1942) and Hermann Weyl (1885--1955). The two had strongly diverging positions with…
Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as in cryptography courses. Unfortunately, many experts expect…
Mathematical physics has many facets, of which we shall briefly give a (very partial) description, centered around those of main interest for Elliott and us (Moshe Flato and I). In our case these aspects had as a corollary a variety of…
We give one more proof of the fact that symplectic matrices over real and complex fields have determinant one. While this has already been proved many times, there has been lasting interest in finding an elementary proof. Our result is…
In the Soviet Union a reform movement in mathematics education was triggered by Andrey Kolmogorov in the 1970s, and followed by a counter-reform. This movement was rooted in the very different socioeconomic conditions of that time and…
In this article, we study the inscription on the reverse of Susa Mathematical Text No.\,2, a clay tablet held in the collection of the Louvre Museum and thought to date from between 1894--1595 BC. We focus on the formula given in this text…
Using data collected from the AMS websites, and the internet in general, we compute the weight-enumerator of the set of 145 AMS fellows who passed away before Aug. 2022, according to the statistics [Age, Number of Publications, Number of…
There is well-known problem of geometric probability which can be quote as the Broken Spaghetti Problem. It addresses the following question: A stick of spaghetti breaks into three parts and all points of the stick have the same probability…
Being asked to write about Asan D. Taimanov, I had a little problem. I knew Taimanov. I liked and respected him, and so I wanted to write something. But I didn't know him well. I didn't live in the Novosibirsk Akademgorodok where he lived…
This paper revisits Buridan's Bridge paradox (Sophismata, chapter 8, Sophism 17), itself close kin to the Liar paradox, a version of which also appears in Bradwardine's Insolubilia. Prompted by the occurrence of the paradox in Cervantes's…
This paper is concerned with the epistemic question of confirming a hypothesis -- the guilt of a defendant -- by way of testimony heard by a juror over the course of an American-style criminal trial. In it, I attempt to settle a dispute…
The paper gives a unified and simple proof of both theorems and Cousin's theorem.
In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.
Below, we summarize the appearances and possible uses of the two-sided approach and the two-sided counting in the most diverse areas of (secondary) school mathematics.
In this document, we provide both the original German version of Ljunggren's article, "Ein Satz \"{u}ber die Diophantische Gleichung $Ax^{2}-By^{4}=C$ ($C=1,2,4$)", Tolfte Skand. Matematikerkongressen, Lund, 1953, pp.~188--194 (1954), as…