Student solves ancient math problem

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A Dutch student, G. Uytdewilligen, has reportedly solved an ancient mathematical problem by developing a formula that determines the zero-points of polynomials of any degree, a feat that has eluded mathematicians since the Renaissance. Historical figures like Gardano, Ferrari, and Galois previously addressed polynomials up to the fourth degree but could not provide solutions for higher degrees. The student’s claims have sparked skepticism among mathematicians, particularly regarding the validity of his paper and its implications for established theories like Galois's. Critics argue that the paper lacks clarity and does not contradict the known results about the insolubility of general polynomials. The discussion highlights the ongoing debate in the mathematical community about the nature of polynomial roots and the methods used to approximate them.
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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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