Related papers: Infomathic
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…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely…
Recent advances in computing have changed not only the nature of mathematical computation, but mathematical proof and inquiry itself. While artificial intelligence and formalized mathematics have been the major topics of this conversation,…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
Computers have already changed the way that humans do mathematics: they enable us to compute efficiently. But will they soon be helping us to reason? And will they one day start reasoning themselves? We give an overview of recent…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
Infographics are a form of data visualization combining data, information, and statistics. Over the last ten years, infographics have become a popular method for displaying concise information, where infographics are a useful tool for…
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…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
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…
The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry,…
"Is math useful?" might sound as a trick question. And it is. Of course math is useful, we live in a data-filled world and every aspect of life is totally entwined with math applications, both trivial and subtle applications, of both basic…
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…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…