Related papers: The AMC -- What It Is and Why It Matters
Anyone who has tried to memorize a one-hundred-digit number can attest that the human brain acquires abstract information slowly. However, following a three-decade increase of results at memory competitions, the best competitors manage to…
We briefly review the history of Mach's principle and discuss its significance in the light of modern physics.
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
This is an essay about the value of mathematical and symbolic reasoning in the age of AI.
This paper provides some reflections on the field of mathematical software on the occasion of John Rice's 65th birthday. I describe some of the common themes of research in this field and recall some significant events in its evolution.…
A introduction to the syntax and Semantics of Answer Set Programming intended as an handout to [under]graduate students taking Artificial Intlligence or Logic Programming classes.
Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his…
We reflect on the life and influence of the academic journal, charting their history and contributions, discussing how their influence changed society, and examining how in death they will be mourned for what they initially stood for but in…
Modern society is full of computational challenges that rely on probabilistic reasoning, statistics, and combinatorics. Interestingly, many of these questions can be formulated by encoding them into propositional formulas and then asking…
We discuss several aspects of infinity in the history of mathematics.
The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent 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)…
A brief introduction into Idempotent Mathematics and an idempotent version of Interval Analysis are presented. Some applications are discussed.
This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the…
This paper offers a glimpse of the major contributions made by Arabs to mathematics in middle ages history period. Its purpose is to stimulate interest in an object based on mutual respect and understanding. We give a short list of the most…
This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a…
We illustrate the concept of mathematical proof.
Politics today is largely about the art of messaging to influence the public, but the mathematical theory of messaging -- information and communication theory -- can turn this art into a precise analysis, both qualitative and quantitative,…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously. As a case study, the story of Szemer\'edi's theorem is presented.