历史与综述

We present a set of lectures on topics of advanced calculus in one real and complex variable with several new results and proofs on the subject, specially with detailed proof-always missing in the literature - of the Cissoti explicitly…

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

Using an adaptation of Qin Jiushao's method from the 13th century, it is possible to prove that a system of linear modular equations a(i,1) x(i) + ... + a(i,n) x(n) = b(i) mod m(i), i=1, ..., n has integer solutions if m(i)>1 are pairwise…

Pebbles (calculos in Latin) are the "bits" used in the Ancients' four function calculator / computer. The Ancient Computer's normal mode is to work with numbers in what we would call exponential notation. Decimal numbers can have up to 10…

In this article we study some geometric properties of a non-trivial square tile (a non-trivial square tile is a non-constant function on a square). Consider infinitely many copies of this single square tile and cover the plane with them,…

The early Renaissance artist Albrecht Durer published a book on geometry a few years before he died. This was intended to be a guide for young craftsmen and artists giving them both practical and mathematical tools for their trade. In the…

We give a brief overview of the area of Banach algebras, intended for a general mathematical audience.

The non-standard identity concept developed in the Homotopy Type theory allows for an alternative analysis of Frege's famous Venus example, which explains how empirical evidences justify judgements about identities and accounts for the…

The classic Edgar Allan Poe story The Gold-Bug involves digging for pirate treasure. Locating the digging sites requires some simple trigonometry.

We present a method to compute the volume of a solid of revolution as a double integral in a very simple way. Then, we see that the classical methods (disks and shells) are recovered if this double integral is computed by each of the two…

In the celebrated Theaetetus 147d3-e1 passage Theodorus is giving a lesson to Theaetetus and his companion, proving certain quadratic incommensurabilities. The dominant view on this passage, expressed independently by H. Cherniss and M.…

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.

This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…

This paper aims to provide an overview of recent researches studies on Camille Jordan's early works (1860-1870). We especially shed new light on the relation between Galois and Jordan by discussing the collective dimensions of Jordan's…

We found a solution of the star puzzle (a path on a chessboard from c5 to d4 in 14 straight strokes) in 14 queen moves, which has been claimed by the author as impossible.

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of…

We construct a number of sculptures, each based on a geometric design native to the three-dimensional sphere. Using stereographic projection we transfer the design from the three-sphere to ordinary Euclidean space. All of the sculptures are…

Supportive attitudes can bring to a blossoming science, while neglect can quickly make science absent from everyday life and provide a very primitive view of the world. We compare one important Greek achievement, the computation of the…

This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.

The paper is proposing a short discussion on the ancient knowledge of Platonic solids, in particular, by Italic people.