September 22, 2023

Andrea Mojsoska

12th Grade

Nova International Schools

Introduction

From patterns to percentages, through skyscrapers and sunlight, math is all around us. And it has been for a while. Ages ago, the Ancient Greeks regarded this discipline as inherently beautiful, whereas Pythagoras and his followers viewed numbers as the center of our universe, placing emphasis more on their stringent rules than their larger, inherent beauty. The belief that mathematics can be both beautiful and practical has thus been shared by philosophers, mathematicians, and neuroscientists ad infinitum. As Bertrand Russel put it, “Mathematics, rightly viewed, possesses not only truth but supreme beauty.” As such, the scope of mathematics transcends pen and paper. It extends to situations that, at first glance, have nothing to do with neither numbers nor calculations. Among this wide array of mathematical applications lies the concoction of beauty and brains: cosmetology.

Skin Solutions

When we think of skincare, we usually think in terms of cosmetics and complexions. But underneath the mask of each face lies a hidden layer of mathematical operations. 

Cleanser, toner, and computational modeling: According to a research team at the University of Cincinnati, this is the formula for an effective skin-care routine. Their strategy is simple - instead of individually testing 30,000 products, they analyze a sample of 200 and develop predictive mathematical models based on the data they collect. In turn, they are able to foresee the effects of the remaining 29,800 compounds, saving both time and resources, as well as the environment. Thus, as more mathematical models advance, more skincare companies can start steering away from animal testing and leaning more towards efficient, ethical product-making. 

Apart from product testing, math is also present at the rudimentary, molecular level of skincare. That is to say, the ingredients in each skincare product coexist in different ratios, percentages, and pH values. Thanks to the wide applicability of mathematical functions and operations, every compound can be crafted so that it maximizes its desired effects, minimizes harm, and ensures quality and durability. 

So, the next time you see a cosmetic product containing 70% water, 10% vitamin C, 2% hyaluronic acid, and a pH of 5.5, remember: this isn’t a result of chance, but rather of deliberate calculations.

Detangling, Demystifying

Knots and split ends are among the main enemies of healthy hair. But the most dangerous of them all is an ineffective brushing technique. Luckily, mathematicians around the world have been working on a solution to detangle this issue. Among the first ones to do so was Harvard professor Lakshminarayanan Mahadevan, who was formerly “fired” from brushing his daughter’s hair. Along with two other authors, Mahadevan modeled a double helix of one pair of hair filaments. This model was pierced by a stiff rod (representing one tine of a hair comb) at its midpoint. The researchers were thus able to calculate and generate the force-extension curves associated with hair detangling. One of their main findings was that short strokes, which slowly move towards a tangled strand, successfully remove hair knots thanks to the topological quantity of link density. They also concluded that optimal combing strategies tend to vary from one hair type to another. 

Notably, their results and conclusions are currently being transferred to a variety of other contexts, including artificial intelligence and the development of robotic arms that can detangle hair with ease. They also utilized mathematics to study how hair reacts to humidity and different temperatures. This data can be used to design algorithms for robots that will continue to aid in cosmetology. And it is in this interdisciplinarity that the beauty of mathematics can be found.