Difference between revisions
quintic-insolvability
Status and infobox
- status:
—→ refuted - tier:
—→ V3 - kind:
—→ problem - year:
—→ 1550 - statement:
—→ Is there a formula in radicals for the roots of every polynomial of degree five?
Relations
- + related to inverse-galois: The original curation links this problem to Inverse Galois problem; the argument for the link has not been written yet.
Source +25 −0
+---
+title: Solving the quintic by radicals
+kind: problem
+status: refuted
+tier: V3
+year: 1550
+authors: after Cardano's cubic and Ferrari's quartic formulas
+statement: Is there a formula in radicals for the roots of every polynomial of degree five?
+space: algebra
+---
+There is not. Galois explained why: solvability corresponds to a property of the equation's symmetry group, and the symmetric group on five letters lacks it. Galois theory, the tool built to close this question, became one of the foundations of modern algebra.
+
+*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*
+
+Posed 16th century, after Cardano's cubic and Ferrari's quartic formulas. Closed 1824, Niels Henrik Abel (after Ruffini, 1799); explained by Galois, 1832.
+
+## Related problems
+
+- The original curation links this problem to [[related::Problem:inverse-galois|Inverse Galois problem]]; the argument for the link has not been written yet.
+
+## Sources
+
+- [Wikipedia: Abel–Ruffini theorem](https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem)
+
+[[Space:algebra|Algebra and groups]] · [[Continent:mathematics|Mathematics]]
Revision 51 as rendered
There is not. Galois explained why: solvability corresponds to a property of the equation's symmetry group, and the symmetric group on five letters lacks it. Galois theory, the tool built to close this question, became one of the foundations of modern algebra.
Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.
Posed 16th century, after Cardano's cubic and Ferrari's quartic formulas. Closed 1824, Niels Henrik Abel (after Ruffini, 1799); explained by Galois, 1832.
Related problems
- The original curation links this problem to Inverse Galois problem; the argument for the link has not been written yet.