历史与综述

We study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the circle on the third side as diameter. In particular, we find…

This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…

We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math.

This article deals with peer-assessment in the context of higher education teaching in mathematics, and examines the nature of student activity when assessing work produced by peers. After an overview of research on peer assessment, we…

At the start of the higher education curriculum, the conceptualization of local approximation objects of a function requires the articulation of knowledge and skills from Functional Analysis and Topology. In the study of functions, a number…

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…

The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called "Plato's problem," in line with the program of a philosophy of mathematical practice. It then provides a sketch of a…

New formulas for the construction of Pythagorean triples and generalizations to equations of higher powers. Application of formulas to some problems, in particular Fermat's equation with n=4.

In this paper we offer a reconstruction of the evolution of Leibniz's thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassignability and syncategorematicity, and the closely related…

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…

A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…

We study properties of certain circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the arc of a circle erected internally on the third side.

In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…

We show arithmetic triplets of Gaussian squares are in 3-to-1 correspondence with Pythagorean triples thereof. This correspondence would transform a solution to the Magic Square of Squares puzzle into a larger structure of perfect Gaussian…

We consider a classial case of irrational integrals containing a square root of a quadratic polynomial. It is well known that they can be expressed in terms of elementary functions by one of three Euler's substitutions. It is less known…

This is an overview of the life and works of Pavel Florensky, an important and singular figure of the period rightly described as the \emph{Silver Age of Russian mathematics}, with a substantial overlap with the \emph{Silver Age of Russian…

We describe the development of the mathematics of Helmut R. Salzmann (3. 11. 1930 -- 8. 3. 2022) and the main difficulties he was facing, documenting his lifelong productivity and his far reaching influence. We include a comprehensive…

In classical geometry, there is no such well-known and much-studied topic as the construction of conic sections (or briefly conics) from its five points. Its importance in many applications of mechanical engineering, civil engineering and…

In this paper, we chronologically recount several situations that have contributed to the development and formalization of the objects known as imaginary or complex numbers. We will begin by introducing the earliest documented knowing for…

Wythoff's game is a modification of the well-known game of ``nim." Wythoff's game, which does not resemble the Fibonacci sequence, has direct relation to the Golden ratio. We will explore the sequence behind this surprising relationship,…