## The Most Romantic Mathematician and His Language of Symmetry

On the morning of May 30, 1832, a single shot fired in a duel fatally wounded one of the most brilliant, and certainly the most romantic mathematician — Évariste Galois. The following day, his last words to his weeping brother were: “Don’t cry, I need all my courage to die at twenty.” Figure 1 shows Galois at about age 15, as drawn by a classmate.

Figure 1. Galois in about 1826, drawn by a classmate. This image is in the public domain. It was possessed by Nathalie-Théodore Chantelot, his older sister, and her daughter Mrs. Guinard. The image was released by Paul Dupuy, École Normale Supérieure professor of history, with his article “La vie d’Évariste Galois,” in 1896.

This young genius achieved nothing less than inventing the mathematical language that describes all the symmetries of the world. Whether one analyzes symmetries of shapes, in music, or in particle physics, the same formalism — Group Theory — applies.

What is a mathematical “group”? Take as an example the whole numbers, positive, negative and zero, and the simple operation of arithmetic addition. You’ll notice the following properties:

1. When you add two whole numbers, you get another whole number. For example, 3 + 6 = 9; -7 + 15 = 8.
2. If you add three whole numbers, it doesn’t matter how you group them. For example, (9 + 3) + 5 = 9 + (3 + 5).
3. There exists one whole number that when you add it to any other whole number, it leaves the latter unchanged. This is, of course, the number zero. For instance, 13 + 0 = 13.
4. For every whole number, there exists another whole number such, that if you add then together you get zero. For example: 8 + (-8) = 0; (-17) + 17 = 0.

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