Your student has an assignment on Galois, a math history paper due, or an abstract algebra class that suddenly expects them to know what a "group" is and why it matters — and they need a clear, fast answer.

This TLDR guide tells the whole story: the short, turbulent life of Évariste Galois, the French teenager who reinvented algebra before he turned twenty-one, and the mathematics he left behind. Born in 1811 outside Paris, Galois grew up in the political upheaval of Restoration France, taught himself Lagrange and Legendre in a year, and then watched his manuscripts vanish in the hands of Cauchy and Fourier. He failed the École Polytechnique entrance exam twice, got swept up in the 1830 Revolution, went to prison, and died in a duel at twenty — leaving a frantic overnight letter that contained ideas mathematicians are still unpacking.

For anyone who has searched for a history of group theory explained simply, this guide delivers. Section by section, you get the biographical narrative first, then a plain-language tour of what Galois actually discovered: what a group is, what a field is, why the quintic equation has no general algebraic solution, and how that single insight seeded modern mathematics, physics, and chemistry.

This is a famous mathematicians short biography built for a student on a deadline — no bloat, no jargon left undefined, no filler. It is 15 focused pages written for high school and early college readers.

If you need to understand Galois tonight, start here.

• Understand what shaped Galois as a mathematician and a political radical in post-Napoleonic France.
• Trace the major events of his short life, from the lycée in Paris to the night before his duel.
• Grasp, in plain terms, what Galois theory actually says and why it transformed mathematics.
• Weigh the historical assessment of his legacy and separate the legend from the record.

1. 1. A Republican Childhood: Bourg-la-Reine, 1811–1823
   Galois's birth, family, and the political world of Restoration France that formed his character before he ever saw a math book.
2. 2. The Lycée and the Awakening: Louis-le-Grand, 1823–1828
   His entry into the elite Paris boarding school, early academic struggle, and the moment he discovered Legendre's geometry and Lagrange's algebra.
3. 3. Lost Papers and a Second Rejection: 1829–1830
   His first published work, the suicide of his father, the second Polytechnique failure, and the manuscripts that disappeared in the hands of Cauchy and Fourier.
4. 4. Revolution, Prison, and a Final Letter: 1830–1832
   Expulsion from the École Normale, two arrests, months in Sainte-Pélagie prison, and the frantic mathematical letter written the night before he died.
5. 5. What Galois Actually Did: Groups, Fields, and the Quintic
   A plain-language tour of Galois theory — what a group is, why the quintic equation has no general formula, and why this changed mathematics.
6. 6. Legacy: From Forgotten Manuscript to Foundation of Modern Math
   How Liouville rescued the work in 1846, how group theory became central to physics and chemistry, and where historians push back on the romantic myth.