Search results
Results from the WOW.Com Content Network
Abel–Ruffini theorem refers also to the slightly stronger result that there are equations of degree five and higher that cannot be solved by radicals. This does not follow from Abel's statement of the theorem, but is a corollary of his proof, as his proof is based on the fact that some polynomials in the coefficients of the equation are not ...
By 1823, Abel had at last proved the impossibility of solving the quintic equation in radicals (now referred to as the Abel–Ruffini theorem). However, this paper was in an abstruse and difficult form, in part because he had restricted himself to only six pages in order to save money on printing.
The case of higher degrees remained open until the 19th century, when Paolo Ruffini gave an incomplete proof in 1799 that some fifth degree equations cannot be solved in radicals followed by Niels Henrik Abel's complete proof in 1824 (now known as the Abel–Ruffini theorem).
1905 Emanuel Lasker's original proof of the Lasker–Noether theorem took 98 pages, but has since been simplified: modern proofs are less than a page long. 1963 Odd order theorem by Feit and Thompson was 255 pages long, which at the time was over 10 times as long as what had previously been considered a long paper in group theory.
Download as PDF; Printable version; ... (this is the Abel–Ruffini theorem). This is the case, for example, for the Bring ... by the fundamental theorem of algebra, ...
However, there is no algebraic expression (that is, in terms of radicals) for the solutions of general quintic equations over the rationals; this statement is known as the Abel–Ruffini theorem, first asserted in 1799 and completely proven in 1824. This result also holds for equations of higher degree.
ATS theorem (number theory) Abel's binomial theorem (combinatorics) Abel's curve theorem (mathematical analysis) Abel's theorem (mathematical analysis) Abelian and Tauberian theorems (mathematical analysis) Abel–Jacobi theorem (algebraic geometry) Abel–Ruffini theorem (theory of equations, Galois theory) Abhyankar–Moh theorem (algebraic ...
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikimedia Commons; ... Abel–Ruffini theorem; Søren Georg Abel; Abel's identity;