On the night of May 29, 1832, a 20-year-old French student sat by candlelight, convinced he would die in a duel at dawn. Instead of a will, he furiously scribbled mathematical equations, laying the foundation for an entirely new branch of mathematics in his final hours.

This deep dive tells the deeply human story of Evariste Galois: prodigy, political radical, and tragic outsider. We trace how a brilliant mind was repeatedly failed by rigid institutions and a chaotic France, how his father’s political suicide and his own imprisonment fueled his rebellion, and how the work he left behind eventually transformed modern algebra, physics, and cryptography.

• Reading Legendre’s geometry like a novel at 14 and mastering Lagrange by 15
• Two failed Polytechnique exams and lost manuscripts handled by Cauchy, Fourier, and Poisson
• Radicalization into a Republican artillery unit, a provocative toast, and imprisonment
• How he proved the quintic equation has no general solution by radicals, founding group theory
• Why his papers sat unread for a decade until Liouville published them in 1846