Related papers: Dragons and Kasha
New understandings of the functioning of human brains engaged in mathematics raise interesting questions for mathematics educators. Novel lines of research are suggested by neuroscientific findings, and new light is shed on some…
A fascinating hypothesis is that human and animal intelligence could be explained by a few principles (rather than an encyclopedic list of heuristics). If that hypothesis was correct, we could more easily both understand our own…
We discuss the idea that computers might soon help mathematicians to prove theorems in areas where they have not previously been useful. Furthermore we argue that these same computer tools will also help us in the communication and teaching…
Many forcing notions obtained using the creature technology are naturally connected with certain integer games.
Adinkras are graphical tools created for the study of representations in supersymmetry. Besides having inherent interest for physicists, adinkras offer many easy-to-state and accessible mathematical problems of algebraic, combinatorial, and…
In this paper, we present a series of mathematical problems which throw interesting lights on flamenco music. More specifically, these are problems in discrete and computational mathematics suggested by an analytical (not compositional)…
This is the first chapter of an introductory text under construction; further chapters are available via the authors' web pages. Our aim is to provide an elementary access to Cox rings and their applications in algebraic and arithmetic…
Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by…
The purpose of this paper is to show the magic of physics by showing the physics of magic. What usually makes magic tricks interesting is that something unexpected occurs. Similarly, demonstrations are interesting inasmuch as they produce…
The main purpose of this paper is to study a concrete example of $\delta$-Koszul algebras, which is related to three questions raised by Green and Marcos in [3].
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…
The present work consisted in developing a plateau game. There are the traditional ones (monopoly, cluedo, ect.) but those which interest us leave less place at the chance (luck) than to the strategy such that the chess game. Kallah is an…
Large cosmological datasets have been probing the properties of our universe and constraining the parameters of dark matter and dark energy with increasing precision. Deep learning techniques have shown potential to be smarter, and to…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
Most if not all of today's revolutionary technologies have a common foundation, namely the intelligent use of information. It is clear that computers play a central role: but the contribution of mathematics, though less visible, is no less…
We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…
We encounter mathematical problems in various forms in our lives, thus making mathematical thinking an important human ability. In this paper, we present Bublz!, a simple, click-driven game for children to engage in and develop 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…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.