Évariste Galois: The Passion That Transformed Algebra Forever

A Young Mind Discovers Galois Theory

1823. Paris. A 12-year-old boy from Bourg-la-Reine enters the Royal College of Louis-le-Grand. His teachers see a humanist in him: brilliant translations from Greek, a calm disposition. But inside Évariste Galois, a different passion is already taking root — mathematics.

He dreams of the École Polytechnique — the defining institution for engineers and republicans alike. At the entrance examinations he solves every problem and… fails. The committee believes the young man is “skipping” important steps. Galois is convinced they are self-evident.

Rejection and the Road to a New Path

A year later, he fails the exam again. According to legend, an infuriated Galois hurled a blackboard eraser at the examiner, permanently closing the door to that university.

But no one could close the door to mathematics. The following year, Galois enrolled in another prestigious institution — the École Normale Supérieure.

The Breakthrough That Defined Galois Theory

Galois accomplished what mathematicians had debated for three centuries: he derived a criterion for determining when an algebraic equation can be solved using radicals — and when it cannot. Like all great mathematical minds, he looked at familiar equations in a completely new way.

What matters is not the formulas themselves, but the structures. Specifically, the structure of the group of permutations of an equation’s roots — it is precisely this group that reveals whether a solution can be expressed through radicals.

A Short Life, an Eternal Legacy

Galois died in a duel at the age of 20, yet his ideas became the foundation of a pivotal branch of mathematics: algebra. Within a few decades, Galois theory had emerged — a language that explains why fifth-degree equations cannot be solved by radicals, how permutation groups describe the roots of polynomials, and why finite fields are structured the way they are.

Galois became one of the founders of group theory, transforming algebra from an art into a science.