Today, I am just over twenty, close to finishing my bachelor’s. Looking back, I have mixed feelings about the subjects I have taken; most are fond memories, while only a few forgettable. But they all have one thing in common, their abstract names: Algebra, Linear Analysis, Optics, Calculus… There is only one exception, the only course named after a person: Galois Theory.
Students worldwide study this course at roughly the same age he died. A coincidence that feels strangely poetic. With that in mind, I invite you to discover the story of the young rebel behind that name, a man who faced his era with unyielding conviction. He challenged authority and paid a high price for his ideals: Évariste Galois
⚔️Duel
May 29th, 1832
Évariste Galois knew it was the last night of his life. The young, fiery, and rebellious mathematician knew that, by the next day, he would probably be dead at the age of twenty. He had agreed to face a Captain of the Guard in a duel, and, fully aware of his inferiority and the fatal consequences, he spent the last night of his life writing letters to his relatives.
“Show my work to Jacobi and to Gauss”. -His last letter, to his friend Chevalier
The duel wasn’t born of calm reflection. It was an example of the pride and devotion to duty that marked Galois’s short life. He had a gift for making enemies. The reasons that drove this brilliant student to a duel on the outskirts of Paris still remain a mystery; it may have been a romantic affair or a political act.
The following day, the weapon of the Captain of the Guard, whether a bullet or a blade, tore through the abdomen of Évariste Galois. That mind, as insolent as it was ingenious, was extinguished at 20 years old on that dark morning of 1832. Far too soon.
“Don’t cry, Alfred! I need all my courage to die at twenty” -His last words.
🛡️A man under siege
If I had to define Évariste’s life, I would do so with a single word: Insolence. After his father’s suicide, he inherited a passion for politics and joined the Republicans who overthrew King Charles X in favour of Philippe of Orléans. Unsatisfied with the new king, he offered a very peculiar coronation toast: raising his glass in one hand, brandishing a dagger in the other. Charged with sedition, he was sentenced to six months in prison.
This clash with authority became a recurring theme in his short life. Despite starting out as a promising student, he was eventually expelled from school for his behaviour. Thus, he had to dedicate his life to mastering algebra on his own, relying on nothing and nobody but his inner brilliance.
Frustration marked his path to higher education. Twice he attempted to enter the prestigious École Polytechnique, the heart of French science, and twice he was rejected. It wasn't for lack of knowledge, but a clash of temperaments: Galois solved the complex problems in his head, skipping the intermediate steps that his examiners demanded. Frustrated by what he saw as their mediocrity, he reportedly threw a blackboard eraser at one of them. To the academic elite, he was just an insolent student whose ideas were as incomprehensible as his attitude was unbearable. His arrogance often overshadowed his genius.
He was always a man of conviction. After failing in his academic career, he redirected his intellectual energy toward the revolutionary cause. He unsuccessfully attempted to enlist in the army as part of Poland’s Voluntary Revolutionary Legion.
“Examiners are machines who only know how to ask questions, but do not know how to listen to answers”. -Evariste Galois
🧩The problem
Galois solved a problem that had resisted mathematicians for centuries, and did so with a complete and elegant solution.
He proved that there is no general formula to solve equations of the fifth degree or higher, a mystery that had baffled the greatest minds since the Renaissance. To achieve this, Galois looked beyond the numbers themselves; he focused on the underlying symmetries of their roots. In doing so, he laid the foundation for what we now call Group Theory, changing the landscape of algebra forever by demonstrating that the limits of mathematics are defined by its internal structure.
His work opened entirely new directions in mathematics. Today, the ideas he introduced help describe the behaviour of elementary particles in the Universe and, at the same time, explain the symmetries found in the floors and walls of the Nasrid Palace in the Alhambra of Granada.
