Related papers: The AMC -- What It Is and Why It Matters
This article contains a selection of problems from the American Mathematics Competitions.
We provide an historical overview of how advances in technology influenced high school and university mathematical competitions in the United States and at the International Mathematical Olympiad. While students are not allowed the usage of…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
We present the problems and solutions to the 50th Annual USA Mathematical Olympiad.
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
A few remarks on how mathematics quests for freedom.
A review is given of some mathematical contributions, ideas and questions concerning liquid crystals.
Academic challenges comprise effective means for (i) advancing the state of the art, (ii) putting in the spotlight of a scientific community specific topics and problems, as well as (iii) closing the gap for under represented communities in…
We present the problems and solutions to the 12th Annual USA Junior Mathematical Olympiad.
The situation surrounding the Olympiads is paradoxical. On the one hand, considerable resources are spent on the Olympiads. On the other hand, there are widespread arguments about the harm of the Olympiads, often very strange ones. For…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at…
This is a brief overview of some turning points in the history of infinitesimals.
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…