“A tragic tale of mathematical brilliance.” That’s how many describe the story linked to Square Évariste Galois. Who was Évariste Galois?
This square commemorates Évariste Galois a French mathematician. He was born in Bourg-la-Reine near Paris. Galois made significant contributions to group theory. His work helped solve algebraic equations.
Évariste Galois was born in October 1811. His father Nicolas-Gabriel Galois was a respected citizen. Nicolas-Gabriel even became mayor. Évariste’s mother Adélaïde-Marie Demante educated him.
Galois entered the Collège Royal de Louis-le-Grand in 1823. His mathematical talent blossomed there. He studied Legendre’s geometry and Lagrange’s algebra.
Under teacher Louis Richard’s guidance Galois studied algebraic equations. Mathematicians had formulas for equations up to degree four. They struggled with higher degrees. Lagrange treated equation roots as objects. He studied their permutations. In 1824 Niels Abel proved the impossibility of solving quintic equations by radicals.
Galois sought conditions for solving algebraic equations by radicals. He analyzed admissible root permutations. His key discovery was brilliant. Solvability by radicals is possible only if the group of automorphisms is solvable. Solving quintic equations required a different approach. Galois used group concepts but lacked a formal theory.
While at Louis-le-Grand Galois published a minor paper. He submitted a memoir on algebraic equation solvability to the French Academy of Sciences in 1829. Cauchy lost it. Galois failed to enter the École Polytechnique twice. His father committed suicide in 1829 after political clashes. Galois enrolled in the École Normale Supérieure. He turned to political activism while continuing research.
In 1830 Galois had three short articles published. He rewrote the lost paper and presented it again. Fourier took it home but died. The manuscript disappeared again.
The July Revolution of 1830 disappointed republicans. Louis-Philippe became king. Galois wrote a pro-republican article. He was expelled from the École Normale Supérieure. He was arrested twice for republican activities.
In 1831 Galois presented his equation theory memoir for the third time. It was returned with a negative report. The judges could not understand Galois’s ideas.
The circumstances of Galois’s death in a duel remain unclear. He wrote a scientific last testament to Auguste Chevalier. He summarized his work and included new theorems. Galois was shot and died.
Galois’s manuscripts were published in 1846 by Joseph Liouville. Group theory became established in 1870.
Square Évariste Galois stands as a reminder. It marks the life of a brilliant mathematician. His innovative work continues to influence mathematics today. His life however was tragically cut short.