Norwegian mathematician who, still in his early twenties and working largely in poverty, proved that the general quintic equation (and every higher degree) cannot be solved by a formula using only radicals, the Abel-Ruffini theorem, settling a question open since the sixteenth century solution of the cubic and quartic. He also did foundational work on elliptic and elliptic-related functions, including an 1827 result on dividing the lemniscate, the figure-eight curve, into equal arcs by straightedge and compass alone, a construction problem in the same family as Gauss's heptadecagon result three decades earlier. Recognition came only after his death from tuberculosis at twenty six; a professorship offer from Berlin arrived days too late.
Facts
BirthplaceNedstrand, Norway (then in union with Denmark) 2 Death PlaceFroland, Norway, of tuberculosis 2 Nationality / Culture Defining ContributionProved the general quintic (and higher) equation cannot be solved by radicals (Abel-Ruffini theorem); the 1827 division of the lemniscate by straightedge and compass. 2 Notable WorkMemoire sur les equations algebriques (1824); Recherches sur les fonctions elliptiques (1827) 2 Connections
Associated With
Source MacTutor History of Mathematics Archive
In Branch
Source MacTutor History of Mathematics Archive
Source MacTutor History of Mathematics Archive
Namesake Of
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the object's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Abel's Test, Theorems Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Proofs Credited
Source MacTutor History of Mathematics Archive
In the Other Atlases
- Also in Geography Atlas: Norway, nationality there.
Sources
1. Wikipedia: Niels Henrik Abel
WikipediaLead section, gender referenceQuote, Lead section, gender reference
His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals.
2. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and StatisticsAssociated With: Symmetry, https://mathshistory.st-andrews.ac.uk/Biographies/Abel/Quote, Associated With: Symmetry, https://mathshistory.st-andrews.ac.uk/Biographies/Abel/
Abel began working again on quintic equations and, in 1824, he proved the impossibility of solving the general equation of the fifth degree in radicals.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.