Student solves ancient math problem

  • Thread starter Monique
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  • #26
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so really it's nothing to raise an eyebrow about
 
  • #27
matt grime
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No, not in the manner that has been implied by many writers. Galois theory is correct. It is easy to learn and one of the nicest parts of pure mathematics there is, and it is not hard to show that in general polynomials do not have roots that are expressible algebraically in terms of the coefficients. Anyone who claims otherwise ought to take a step back.

It may be that htis student has found a *good* numerical approach (I have yet to see the student making any claims about contradicting galois theory; surely he'd've put that in the abstract if he actually thought that was what he was doing). As it only works for finding zeroes of polynomials there should be something useful about it, to make it different from the other methods of fidning zeroes of more general function, other wiase I don't even see why he'd have written it down.
 
  • #28
Ethereal
A quick question:
Does anyone know of any good web sites which contain a large collection of mathematical proofs? It's a little frustrating having to search the Web with Google only to find nothing.
 
  • #29
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Ethereal said:
A quick question:
Does anyone know of any good web sites which contain a large collection of mathematical proofs? It's a little frustrating having to search the Web with Google only to find nothing.

Try Google :smile:.

On this site you will find a large collection of mathematical proofs: http://list-of-mathematical-proofs.wikiverse.org/ [Broken] (there are a lot of sites containing the same list, so sorry if this is a list you have already found). A little less advanced mathematics: http://www.cut-the-knot.org/proofs/index.shtml .

Some mirror sites of the first site mentioned:
http://encyclopedia.thefreedictionary.com/list of mathematical proofs
http://www.campusprogram.com/reference/en/wikipedia/l/li/list_of_mathematical_proofs.html
http://www.book-spot.co.uk/index.php/List_of_mathematical_proofs
 
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  • #30
Ethereal
Okay, thanks for the links!
 
  • #31
970
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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 equasion 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.
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/ [Broken]
http://en.wikipedia.org/wiki/Symmetric_group
 
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