Motivation

“A physicist must know mathematics even more than a mathematician.” I heard it from a Professor at the very first year of my study in Physics. He was right; You need a much deeper understanding of a theory when it comes to application. And physics is to see the very obvious yet hidden phenomena around us with an analytical mind, to extract orders out of a seemingly chaotic world; And no order can be built without a foundation of mathematics. In fact, the shortage of clarity and rationality in physics has been always overcome by the power of mathematics.

“At present, I occupy myself exclusively with the problem of gravitation and now believe that I shall master all the difficulties with the help of a friendly mathematician here [Grassmann]. But one thing is certain: in all my life I have labored not nearly as hard, and I have become imbued with great respect for mathematics, the subtler part of which I had in my simple mindedness regarded as pure luxury until now. Compared with this problem, the original relativity is child’s play.”, wrote Einstein when he was working on the theory of gravitation. The power of mathematics, however, is beyond the borders of physics.

Background & Mission

For me, the practical power of mathematics was first revealed when I was working on my master thesis. A particular equation (diffusion equation) and function (so-called Bessel function), used in a particular form of material (cylindrical glass substrate), made it possible to anticipate and design a strategy for fabricating an optical lens. Later, when I was working on my Ph.D. thesis, I realized to my amazement that many molecules, e.g., proteins, are capable of doing their functionality only in special forms (so-called secondary structures). As a result, I came up with this conclusion, that perhaps we are living in a geometrical world and that everything, as far as it is aimed to perform a well-defined function, should exist in an especial form. Forms and functions, hidden in the basic principles of nature, are the obvious signs of existing a mathematical foundation for our world. Making ourselves familiar with these forms and functions not only is a step toward a better understanding of the world around us, they can also be extraordinary models for designing artificial materials with similar functionality.

Exploring the practical power of mathematics and in particular, the geometrical forms in the context of special functionalities and corresponding applications, is our aim here. If you are a student, wondering whether those sophisticated functions you must learn in the courses of mathematics might be ever useful anywhere, you will find the answer here. Following me in this website will get you to this point that no matter what you want to do in the future: engineering, basic science or even something completely outside the scientific realm like art or sport, you better work on your analytical skills because the best practitioners are those who know how to analyze the situations and design a good strategy.

I will first take you through forms and functions in optics, the most beautiful of all science: the science of light. Then we will discover how those mathematical principles and functions used in optics can specifically solve problems in biochemistry and medicine. We will do it also the other way around; We will investigate the forms and functions in nature and see how they can be applied for designing artificial structures that can be especially used in optics. We learn how to use mathematics while we are not a mathematician. Easy-to-understand contents make this website useful for everyone. However, it would be most interesting for those who are passionate about science and interested to see the practical face of basic science.

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