Évariste Galois
Mathematician · 1811-1832 · Mathematics, stage 3: Meet the mathematicians
Explained which equations can be solved by a formula, by attaching a group of symmetries to each one.
Overview
Galois died at twenty after a duel, having spent the previous night writing out his mathematics in a letter. His work attaches to each polynomial equation a group of permutations of its roots and shows that the equation can be solved by a formula built from arithmetic and radicals exactly when that group has a particular structure. This settles at once why no general formula exists for equations of degree five and above, a fact proved separately by Abel, and it explains why the formulas do exist for degrees two, three, and four. The method mattered more than the result: it introduced the group as an object of study and replaced questions about equations with questions about symmetry. His papers were rejected or lost during his life and were published by Liouville in 1846. Read a modern account before going near his own writing, which is compressed to the point of obscurity.
Where to start reading
Mémoire sur les conditions de résolubilité des équations par radicaux 1846
Written in 1831 and published posthumously, this is the paper that establishes the correspondence between an equation and its group of symmetries.
Part of
Sources
- Évariste Galois MacTutor History of Mathematics
- Évariste Galois Wikipedia
- Abstract groups MacTutor History of Mathematics
