Mathematics
The term Gibbons conjecture is widely used in connection with symmetry results for the Allen-Cahn equation. However, its origin is less transparent than its frequent citation suggests. In this note, we revisit its emergence, tracing it to a…
In one of his posthumous papers, conserved in G\"ottingen, Riemann considers the derivatives of $\log\zeta(s)$ at the point $1/2$, giving explicit values for them. Around 2010 we shared Riemann's value of the second derivative with some…
We extend a property of Mazzola's theory of cadential sets in relation to the modulation between minor and major tonalities from triadic to tetradic harmony, using the PLRQ group of Cannas et al. (2017) as the analogue of the classical PLR…
In this paper, we explore the connections between Christiaan Huygens and Niels Henrik Abel through the tautochrone problem. The problem -- determining the curve along which a particle descends under gravity in the same time, regardless of…
This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…
We trace a conceptual genealogy from Abraham de Moivre's derivation of the normal curve (1733) to the modern distributional approach to statistics. De Moivre's Approximatio ad Summam Terminorum Binomii gave the first systematic derivation…
We partially update Grossman's 2005 survey of patterns in mathematical research using a sample of 401 profiles from MathSciNet. The mathematical landscape has changed substantially: single-paper authors have reduced from $43$ \% to $32.42$…
This paper investigates the connections between combinatorial design theory and the creation of new forms of poetry through a specific combinatorial structure called Steiner triple systems. We introduce five original poems constructed using…
In this expository article we show explicitly how to compute Gamma(p/q) in terms of Beta function values which in turn are Kontsevich-Zagier Periods.
The capabilities of generative AI in mathematics education are rapidly evolving, posing significant challenges for research to keep pace. Research syntheses remain scarce and risk being outdated by the time of publication. To address this…
This paper is about a forgotten function and a forgotten mathematician. The double gamma function is now an important special function, which appears for different reasons in many branches of mathematics and in mathematical physics, as it…
We describe and axiomatize finite solitaire puzzles and zero sum sequential games graph theoretically. Zermelo's theorem telling that there is a win for one of the players or a draw follows from the definitions. The god number is a…
This essay argues that Alice Ambrose precedes key elements later critiques by Quine, first of Truth by convention (Quine 1936) and later of the analytic-synthetic distinction (Quine 1951). I demonstrate how Ambrose identifies in writing as…
Drawing primarily on her early work (1931-1934), I argue that Alice Ambrose develops a philosophical project centered on preserving the rigor of extensional logic while rejecting the metaphysical and epistemological endorsements of logicism…
We solve the following problem of W.H. Besant using a formula for the coefficients of an ellipse inscribed in a quadrilateral, $Q$: \enquote{If an ellipse be inscribed in a quadrilateral so that one focus is equidistant from the four…
A Pythagorean scale is a mathematical encoding of a musical scale as a finite list of numbers of the form 3^b/2^a. Previous work of the first author discussed the 2-step property as a way to measure which Pythagorean scales are the most…
The Koch snowflake is a classical example of a planar curve with infinite perimeter enclosing a finite, positive area. Although such examples are well known individually, classical treatments typically analyze each construction in isolation…
These are my memories of moments with Dick and Liz Askey in Russia, Wisconsin, Arizona, and abroad. Dedicated to the Askey family, these recollections span over 40 years and encompass many dramatic changes in the world. Due to this, it is…
Public universities in the US must now meet digital accessibility (DA) standards under 2024 updates to Title II of the ADA. For math instructors, course materials must be screen-reader parsable, which standard LaTeX-to-PDF workflows cannot…
The Bologna Process has substantially reshaped higher education systems across Europe, including the structure of mathematical studies in Poland. One of the increasingly visible consequences of these transformations is the relatively low…