Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in…

Many physics learners take the specific mathematical representations they are using as part of their learning and doing physics for granted. The paper addresses this problem by highlighting two goals. The first is to show how a historical investigation from history of science can be transformed into a concrete lesson plan in physics, in a physics…

The language of physics is mathematics, and physics ideas, laws and models describing phenomena are usually represented in mathematical form. Therefore, an understanding of how to navigate between phenomena and the models representing them in mathematical form is important for a physics teacher so that the teacher can make physics understandable…

The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in…

In his influential 1960 paper "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Eugene P. Wigner raises the question of why something that was developed without concern for empirical facts--mathematics--should turn out to be so powerful in explaining facts about the natural world. Recent philosophy of science has…

In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and…

The prevailing view is that Mathematics and Poetry have nothing in common. However, if we look below the surface and dig a little deeper into two of the most important human activities throughout recorded history, surely we will discover kindred elements and similarities unseen at first glance. The poetry of Odysseas Elytis will help us to bring…

For more than a century the notion of a pre-established harmony between the mathematical and physical sciences has played an important role not only in the rhetoric of mathematicians and theoretical physicists, but also as a doctrine guiding much of their research. Strongly mathematized branches of physics, such as the vortex theory of atoms…

The relationship between physics and mathematics is hardly ever presented with sufficient clarity to satisfy either physicists or mathematicians. It is a situation that often leads to misunderstandings that may spread quickly from teacher to student, such as the idea that mathematics is a mere instrument for the physicist. In this paper, we…

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we…

This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the…

I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a…

Before the 19th century the idea of more than three dimensions was exceptional. During the 19th century, however, geometry was revolutionized and new branches were developed. This revolution also created the idea of the possibility of a n-dimensional geometry or space; flatland, i.e. n = 2, was a consequence of this new thinking. In 1884 the…

Osmotic pressure proves to be a useful topic for illustrating the disputes brought to bear on the chemistry profession when mathematics was introduced into its discipline. Some chemists of the late 19th century thought that the introduction of mathematics would destroy that "chemical feeling" or "experience" so necessary to the practice of…

The treatment of pendulum motion in early 18th century Newtonian textbooks is quite different to what we find in today's physics textbooks and is based on presuppositions and mathematical techniques which are not widely used today. In spite of a desire to present Newton's new philosophy of nature as found in his "Principia" 18th century textbook…