Elena Hadzieva’s column explores the captivating relationship between mathematics and art, highlighting the aesthetic beauty found within mathematical concepts and their influence on various forms of art. Her journey reflects how mathematics can be perceived as a source of supreme beauty, fostering a deeper appreciation for the subject.

The inspiration for the title of this popular article stems from Stewart’s quote: “The best mathematics is like literature – it brings a story to life before your eyes and involves you in it, intellectually and emotionally” (Ian Stewart, mathematician, 1945- , [2]).

When I first read this quote in 2022, I realized that at that point in my career (I was a teacher and researcher in mathematics for 22 years), mathematics had intensely involved me intellectually and emotionally. It had fully immersed me with its intellectual challenges, absolute truth, exactness, balance, order, abstractness, smooth transitions from simple to complex concepts, and even more complex concepts and spaces. Moreover, all of these qualities of mathematics had produced a plethora of feelings in me, such as admiration, excitement, happiness, thankfulness, curiosity, respect, and relaxation.

Unlike many, my journey with mathematics did not commence in early education; it was instead just one of many subjects. In primary and secondary school, I effortlessly grasped mathematical concepts, spending minimal time on assignments. In 1995, when I enrolled in mathematics studies at the University “Ss. Cyril and Methodius”, Faculty of Natural Science and Mathematics, Institute of Mathematics in Skopje, Macedonia, I was in a group with many confirmed young mathematicians with an important competition history behind them. Being in such a strong group of students, I didn’t expect much of myself. However, I soon emerged as one of the top students in the group, which apparently triggered my future strong involvement with mathematics.

Soon after graduation, I started working as a teaching and research assistant in the field of Mathematics at the Faculty of Electrical Engineering and Information Technologies at the same university. A period of diligent preparation for tutorials, solving numerous problems, and crafting practical pedagogical approaches followed. I worked day and night to solve 100 problems and deliver 10-20 in a class. Simultaneously, I was progressing with my education. I earned a master’s degree in 2004, followed by a Ph.D. degree in 2009. The harmony of my role as both educator and researcher reached its peak in 2019 when I was honored with the title of full professor.

After this election, my perspective on mathematics expanded to encompass its distinguished aesthetic beauty. In 2022, a curiosity-driven exploration led me to delve into diverse definitions and descriptions of the term “mathematics”, resulting in a review article titled “A Review of the Definitions of the term “Mathematics” [3]. The personal perspectives of renowned mathematicians, physicists, engineers, and philosophers highlighted dimensions of mathematical beauty that I wasn’t fully aware of. I encountered many sayings in which mathematics is considered not only from an intellectual aspect but also as a supreme beauty in the world of sciences. A few such quotes follow:

- The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. (Aristotle, philosopher and polymath, 4th century BC [5])
- Mathematics is, in its way, the poetry of logical ideas (Albert Einstein, 1879-1955, theoretical physicist, [1])
- Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty. (Archimedes, mathematician, engineer, inventor, 3rd century BC)
- The pure mathematician, like the musician, is a free creator of his world of ordered beauty. (Bertrand Russell, philosopher and mathematician, 1872-1970, [4])
- Mathematics is the most beautiful and most powerful creation of the human spirit. (Stefan Banach, mathematician, 1892-1945, [6])

Having all these beautiful thoughts in mind, I was inspired to discover new viewpoints of mathematical concepts. I could notice beauty in different mathematical content every day. This newfound appreciation prompted a presentation titled “Mathematics is Beautiful,” delivered to mathematics teachers. I enjoyed presenting the inevitable connection between mathematics and art, expressed in architecture, painting, music, and design, incorporated in visually pleasing compositions. The main aim of the presentation was to motivate teachers to bring creative interactions between mathematics and art into the classroom, highlighting how this integration can enhance the students’ understanding and appreciation of both subjects. It was a pleasure to observe the audience’s admiration for the newly revealed aesthetic side of mathematics and motivation to continue spreading beautiful feelings stimulated by mathematical ideas.

A few examples of the entwining between mathematics and art follow:

- Kandinsky’s paintings (Wassily Wassilyevich Kandinsky, 1866-1944, Russian painter). Kandinsky often incorporates geometric shapes and symmetrical compositions, demonstrating his understanding of mathematics and striving for visual harmony and balance. He includes the golden ratio, symmetry, and diverse mathematical relationships between elements.
- Escher’s lithographs and prints (Maurits Cornelis Escher, 1898-1972, Dutch graphic artist). Escher’s art is renowned for its intrinsic patterns, optical illusions, and mathematical themes, made with astonishing mathematical precision. His paintings are eminent examples of the interplay between mathematics and art that stimulate viewers to appreciate the beauty and complexity of these two disciplines.
- Fibonacci sequence converted into melody. Mathematics and music share a profound and harmonious relationship that spans centuries. It is not a new idea to assign digits to a musical scale and a sequence generated in some determined way to be transformed into a melody. One such piece of art can be found in the video “Encoding the Fibonacci Sequence Into Music,” arranged and performed by David MacDonald. The ten digits are assigned to the E major scale, and then the music is created according to the digits generated by the Fibonacci sequence elements. The video can be found on the following link: https://www.youtube.com/watch?v=IGJeGOw8TzQ.

These and other enchanting artworks are the reasons why I was emotionally involved with mathematics. I couldn’t resist this “supreme beauty” reflected in the interactions between mathematics and art. Beyond being a set of tools for problem-solving, mathematics apparently has a unique role in creating visually pleasing artworks spanning from ancient civilizations to the present day. Can this perspective bring back the shine that mathematics deserves? Can mathematics be perceived as beautiful and not cold and austere by introducing this perspective into a classroom nowadays?

### Elena Hadzieva

University of Information Science and Technology “St. Paul the Apostle, Ohrid, N. Macedonia

Editor of the article: by Elham Ghaedi

## References:

[1] Albert Einstein Quotes. (n.d.). BrainyQuote.com. Retrieved May 28, 2022, from BrainyQuote.com Web site: https://www.brainyquote.com/quotes/albert_einstein_106697[2] Courant R., Robbins H., revised by Stewart I. (1996),*What is Mathematics?*, second edition, Oxford University Press.[3] Hadzieva E. (2022),

*A review on the definitions of the term “mathematics”*, Monografia wieloautorska pod redakcją naukową Anny Klim-Klimaszewskiej, Sabiny Wieruszewskiej-Duraj, ISBN 978-83-66597-51-8, WN IKRiBL, Siedlce.[4] McMaster University, Quotations from Bertrand Russel, https://www.mcmaster.ca/russdocs/brquotes.htm, Accessed: 18 May 2022.[5] St. Andrews University, Mac Tutor Quotations from Aristotle, https://mathshistory.st-andrews.ac.uk/Biographies/Aristotle/quotations/ Accessed: 18 May 2022.[6] Stefan Banach Quotes. (n.d.). BrainyQuote.com. from BrainyQuote.com, https://www.brainyquote.com/quotes/stefan_banach_311403, Accessed: May 28, 2022.

## About the column:

The column is well-written and provides a personal perspective on the beauty of mathematics and its connection to art. It effectively conveys the author’s journey in the field of mathematics and how their appreciation for its aesthetic aspects grew over time. The inclusion of quotes from renowned figures and examples of mathematical concepts in art adds depth to the narrative. Overall, it offers a compelling argument for the importance of recognizing the beauty of mathematics beyond its utilitarian aspects.