Student solves ancient math problem

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SUMMARY

G. Uytdewilligen, a Dutch student from Eindhoven, has developed a formula that claims to solve the zero-points of polynomials of any degree, a feat not achieved since the Renaissance when mathematicians like Gerolamo Cardano and Évariste Galois addressed lower-degree polynomials. The discussion reveals skepticism regarding the validity of this claim, particularly in light of Galois's theorem, which states that there is no general solution for polynomials of degree five or higher using radicals. Participants express concerns about the clarity and rigor of Uytdewilligen's paper, suggesting it may not contradict established mathematical principles.

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Galois Giant...

Evariste Galois (1811-1832), a French mathematician, proved that it is not possible to solve a 'general' fifth (or higher) degree polynomial equation by radicals. Of course, we can solve particular fifth-degree equations such as x^5 - 1 = 0, but Abel and Galois were able to show that no general 'radical' solution exists.
Galois's Theorem:
An algebraic equation is algebraically solvable if its group is solvable. In order that an irreducible equation of prime degree be solvable by radicals, it is necessary and sufficient that all its roots be rational functions of two roots.
Evariste Galois was 21 years old when he died.[/color]
Abel's Impossibility Theorem:
In general, polynomial equations higher than fourth degree are incapable of algebraic solution in terms of a finite number of additions, subtractions, multiplications, divisions, and root extractions. This was also shown by Ruffini in 1813 (Wells 1986, p. 59).
Abel-Ruffini theorem:
...states that there is no general solution in radicals to polynomial equations of degree five or higher.
In the modern analysis, the reason that second, third and fourth degree polynomial equations can always be solved by radicals while higher degree equations cannot is nothing but the algebraic fact that the symmetric groups S2, S3 and S4 are solvable groups, while Sn is not solvable for n=>5.
Reference:
Calculus - (Larsen, Hosteller, Edwards) - Fourth Edition - pg.238
http://mathworld.wolfram.com/GaloissTheorem.html
http://mathworld.wolfram.com/AbelsImpossibilityTheorem.html
http://en.wikipedia.org/wiki/Abel-Ruffini_theorem
http://c2.com/cgi/wiki?FermatsLastTheorem
http://proofs-of-fermat-s-little-theorem.wikiverse.org/
http://en.wikipedia.org/wiki/Symmetric_group
 
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