历史与综述

The singular value decomposition is arguably one of the most fundamental results in linear algebra. While rigorous proof of this result is of importance, equally important is the motivation in the applied settings. We provide a lively and…

Kolmogorov's Calculus of Problems is an interpretation of Heyting's intuitionistic propositional calculus published by A.N. Kolmogorov in 1932. Unlike Heyting's intended interpretation of this calculus, Kolmogorov's interpretation does not…

What happens when mathematics realizes infinity. When are mathematical definitions actually useful?

There has been an increasing trend of females performing better than males academically across the mathematical engineering courses. To confirm this assumption, final marks of two independent samples of students from Calculus courses across…

In Boole's famous 1854 book {\em The Laws of Thought\/} the mathematical analysis of Aristotelian logic was relegated to Chapter XV, the last chapter before his treatment of probability theory. This chapter is Boole's tour de force to show…

We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community.…

Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…

This paper offers what seems at first to be a minor technical correction to the current practice of computing indefinite integrals, and introduces the idea of a "Kahanian constant of integration". However, the total impact of this minor…

This memorial paper tells the story of the beginning of Boris (Boaz) Trakhtenbrot's long and rich life path, full of unusual and sometimes tragic events. This path led a boy from a Jewish settlement in Eastern Europe to be recognized as one…

To an extent, the 1966 congress was a hole in the iron curtain. At least that how a young Soviet mathematician saw it.

Looking at MacLane's thesis on proof theory in the light of combinatory logic

Starting from the well-known and elementary problem of inscribing the rectangle of the greatest area in an ellipse, we look at possible, gradually more and more complicated variants of this problem. Our goal is to demonstrate to an average…

A brief account of the development of the concept of the gravitational constant and the debate around in in Britain at the end of the 19th century.

The eighteenth century saw a flourishing of scientific and philosophical thought throughout Scotland, known as the Scottish Enlightenment. The accomplishments of prominent male figures of this period have been well documented in all…

SOS is a game similar to tic-tac-toe. We study a variety of variations of it played on a 1-by-$n$ rectangle. On our journey we change the target string to SOO, then study all target strings containing SSS, then go back to finite strings and…

This article discusses the reasons for the choice of the sexagesimal system by ancient Sumerians. It is shown that Sumerians chose this specific numeral system based on logical and practical reasons which enabled them to deal with big…

Ultimate Tic-Tac-Toe is a variant of the popular Tic-Tac-Toe game. Two players compete to win three aligned "fields," with each field constituting its own miniature tic-tac-toe game. Each move determines which field the next player must…

Alternative set theory was created by the Czech mathematician Petr Vop\v enka in 1979 as an alternative to Cantor's set theory. Vop\v enka criticised Cantor's approach for its loss of correspondence with the real world. Alternative set…

Review/essay of Ananyo Bhattacharya, The Man from the Future: The Visionary Life of John von Neumann.

This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…