Related papers: Mathematical Monsters
Chaotic iterations have been introduced on the one hand by Chazan, Miranker [5] and Miellou [9] in a numerical analysis context, and on the other hand by Robert [11] and Pellegrin [10] in the discrete dynamical systems framework. In both…
A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions allowing one to transform a set of automata into one automaton. We revisit some language…
Arising out of an attempt at a new foundations of mathematics, in which relations are more primitive than sets, and out of the theoretical physicists' concept of underlying causes of empirical phenomena, the idea of a purely mathematical…
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…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
This article presents an overview, and recent history, of studies of gender gaps in the mathematically-intensive sciences. Included are several statistics about gender differences in science, and about public resources aimed at addressing…
We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…
The monster tower is a tower of spaces over a specified base; each space in the tower is a parameter space for curvilinear data up to a specified order. We describe and analyze a natural stratification of these spaces.
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
"The hardest logic puzzle ever" presented by George Boolos became a target for philosophers and logicians who tried to modify it and make it even tougher. I propose further modification of the original puzzle where part of the available…
The definition of who is or what makes a ``mathematician" is an important and urgent issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered…
A review of the development of the concept of dark matter is given. I begin the review with the description of the discovery of the mass paradox in our Galaxy and in clusters of galaxies. In mid 1970s the amount of observational data was…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
The mathematisation of the socio-economic sphere, where mathematics actively constructs social reality, presents a challenge for studies on ethics in mathematics and its education. While existing scholarship on ethics in mathematics offers…
The distribution of the sizes of clusters is not continuous, but rather has local maxima. The numbers of atoms of those maxima distribution is called magic numbers. Two methods of determining magic numbers are firstly introduced, followed…
Since the mathematicians of ancient Greece until Fermat, since Gauss until today; the way how the primes along the numerical straight line are distributed has become perhaps the most difficult math problem; many people believe that their…
Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the…
A perplexing problem in understanding physical reality is why the universe seems comprehensible, and correspondingly why there should exist physical systems capable of comprehending it. In this essay I explore the possibility that rather…
J. Hadamard's ideas about the correct formulation of the problems of mathematical physics have been analyzed. In this connection various interpretations of the directly related Banach theorem about the inverse operator has been touched. The…
Phys and Math are two colleagues at the University of Sa{\c c}enbon (Crefan Kingdom), dialoguing about the remarkable efficiency of mathematics for physics. They talk about the notches on the Ishango bone, the various uses of psi in maths…