Imagine that you want to learn painting, and they explain to you how beautifully and well to paint a fence, instead of showing paintings by Van Gogh, Picasso or other great artists, and do not even tell you that they exist. Unfortunately, the study of mathematics in schools sometimes resembles the process of observing how the paint dries and cracks on a wooden board. In this book, the famous mathematician Eduard Frenkel reveals hitherto hidden aspects of mathematics, allowing us to see in it the beauty and elegance that are characteristic only of the greatest masterpieces. “Mathematics,” he says, “is a portal to the unknown world, the key to understanding the deepest secrets of the Universe and ourselves.” The great mathematician invites us all to this mysterious world.
Chapter 2. The essence of symmetry
In the minds of most people, mathematics is inextricably linked to numbers. Mathematicians for them are people who spend whole days sitting around calculations and operating with numbers: large numbers, huge numbers, numbers with unusual, extravagant names. I also thought so - at least until Yevgeny Evgenievich introduced me to the concepts and ideas of modern mathematics. One of them turned out to be the key to detecting quarks. It was a concept of symmetry. What is symmetry? On an intuitive level, we all know this very well. At first glance, we recognize the symmetry in the objects around us, without requiring additional explanation. If you ask a person to give an example of a symmetrical object, then he will remember a butterfly, a snowflake or indicate the symmetry of the human body.
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