历史与综述

Dirichlet's proof of infinitely many primes in arithmetic progressions was published in 1837, introduced L-series for the first time, and it is said to have started rigorous analytic number theory. Dirichlet uses Euler's earlier work on the…

By suitable examples we illustrate an algorithm for composition of inverse problems.

The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…

Zeno's paradoxes are explained as being the result of inappropriate combination of discrete and continuous mathematical systems. It is proposed that the source of this confusion lies in the course of development of the number system, which…

This article analyses some paragraphs of the Dissertatio de Arte Combinatoria (1666) where G.W. Leibniz considers the syntax of a language with a given number of primitive terms. We propose a new formulation which generalizes the…

There are many papers written on the Two Envelopes Problem that usually study some of its variations. In this paper we will study and compare the most significant variations of the problem. We will see the correct decisions for each player…

It is time to renew old ways of thinking about dimensional analysis. Specifically, more than $n-r$ invariants and more than one functional relation between invariants need to be considered simultaneously. Thus generalized, dimensional…

Once upon a time there was an esoteric and specialized notion, called "size of the Durfee square", of interest to at most 100 specialists in the whole world. Then it was kissed by a prince called Jorge Hirsch, and became the famous (and to…

In celebration of the distinguished achievements of Professor Tsuyoshi Ando in matrix analysis and operator theory, we conducted an interview with him via email. This paper presents Professor Ando's responses to several questions we gave…

We present an algorithm for constructing the fixed point of a general non-isometric similarity of the plane.

This article introduces and translates letters from T.J. stieltjes (1856-1894) to C. Hermite (1822-1891) regarding Stieltjes' published notes claiming to have solved B. Riemann's conjecture "it is very probable that all the roots [of the…

The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…

The original shipping strategy of FedEx is to fly all packages to a hub location during the afternoon and evening, sort them there, and then fly them to their destinations during the night for delivery the next day. This leads to…

We investigate the properties of the James function, associated with Bill James's so-called "log5 method," which assigns a probability to the result of a game between two teams based on their respective winning percentages. We also…

This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.

We provide an historical account of equivalent conditions for the Riemann Hypothesis arising from the work of Ramanujan and, later, Guy Robin on generalized highly composite numbers. The first part of the paper is on the mathematical…

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…

The paper approaches to the reader to topology with a curious example of topological classification by homeomorphisms applied to the letters of the alphabet viewed as subsets of Euclidean plane.

The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively. If we are using compass and ruler the way we construct new points is by first…

Carlos Grandjot (1900-1979) was a German mathematician, doctorate from G\"ottingen, who moved to Chile in 1929 and developed there his life and career. He was influential in the development of Chilean mathematics during the period 1930 to…