Related papers: Infomathic
We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
The impact of the computer on present and especially future mathematics is illustrated by means of the iconic example of WZ theory.
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…
One of the main uses of computers is to do statistical analysis of data. But, so far, the theory of statistics, and its noble mother, Probability theory, were all discovered and developed by lowly humans. No more! Computers can also develop…
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…
An information service for mathematical software is presented. Publications and software are two closely connected facets of mathematical knowledge. This relation can be used to identify mathematical software and find relevant information…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
What would you teach if you had only one course to help students grasp the essence of computation and perhaps inspire a few of them to make computing a subject of further study? Assume they have the standard college prep background. This…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…
Papert's (1980) work with Turtle Geometry offered an early and provocative vision of how digital technologies could be used with young learners. Since then, research on digital technology use has focused on the middle and high school…
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…