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Student solves ancient math problem

  1. Sep 9, 2004 #1


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    A dutch student from Eindhoven, G. Uytdewilligen, solved an ancient mathematical problem: after two years of struggling he came up with a formula that describes the zero-points (where the function crosses the y-axes) of polynomals of ANY degree.

    Only during the Renaissance did Gerolamo Gardano (1501-1576) solve the equation for 3rd degree polynomals. Ferrari (1522-1565) solved the 4th degree equation, Galois (1811-1832) classified the 'unsolvable' 5th degree polymals with his grouptheory.

    Noone was able to come up with an answer for higher-degree polynomals, but this student just wrote a formula that solves it for ANY polynomal :surprised :biggrin:
  2. jcsd
  3. Sep 9, 2004 #2
    This is a great info Monique ! Thank you very much.

    However, what happened to Galois' theory ? I doubt...
    See : pdf on arXiv
    I am going to read it when have time. Please somebody comment...
  4. Sep 9, 2004 #3


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  5. Sep 9, 2004 #4
    considering me ignorant if you like, but i was just wondering ...if there is no formula to find the roots of high degree polynomial ...then how can the graphing calculators do it (i mean like how was it programed to find the roots)??
  6. Sep 9, 2004 #5
    that's great..
    i tried once.. i focused for a while..
    i tried to solve the high-degrees polynomials functions..
    i have some notions..
    but i dont think they're enough
  7. Sep 9, 2004 #6
    I could not help reading it :wink:
    Alas, I was not able to understand it yet. I think such an important would require a higher quality paper. I would advise this student to write a better review.
    I am eager to see mathematicians response.
  8. Sep 9, 2004 #7


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    Yep, I'm having real problem trying to understand exactly the steps he took, as the pape'rs not very well written. Hoepfully Matt Grime can take a look at it, but the more I read of it the more skeptical I become.

    Out of interest where did you get the story from Monique?
  9. Sep 9, 2004 #8
    Could one become more skeptical after reading ? Galois is among the greatest mathematicians of all time.

    Just a thought : maybe there is no method for general polynomials, but one can prove that an algorithm works for a dense subset in the polynomial space. That would be useful.
  10. Sep 9, 2004 #9

    I think the answer to your question is numerical analysis...

  11. Sep 9, 2004 #10


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  12. Sep 9, 2004 #11

    This Galois, isn't he the guy from the finite fields in Algebra. Stuff like GF(2) where you need to calculate every number modulo 2. So only 0 and 1 are valid numbers.

    That's very nice because you get crazy results in such algebraic structure like the Moulton-plane or the Hilbert-plane. When you work with kar2 (modulo 2) the line y = x is PARALLEL to y = -x since 1 and -1 are equivalent
    (-1 = 1 mod2).

    nice, isn't it ???

    Last edited: Sep 9, 2004
  13. Sep 9, 2004 #12
    I was referring to incidence-geometry in my last post

    mon cher ami humanino

  14. Sep 9, 2004 #13
    Hey Marlon !
    I am not too sure about everything you wrote. But yes, he is the guy from the finite fields in Algebra.

    Some people (including me) think that if he did not die so young, math would be totally different today. He was an extraordinary genius, and such a compliment is even unfair to him... His work is really difficult to grasp, I tried and did not fully succeded. His life is fascinating.

    Mon cher Marlon, j'aimerais pouvoir vous faire l'honneur de vous repondre dans votre langue :shy:
  15. Sep 9, 2004 #14

    Je parle néerlandais :surprised , mon cher humanino, mais aussi le français :blushing: et l'italien :cool: .
    Duncque puoi scegliere tu...

    Trust me, it is no joke what I wrote about these modulo-things. We studied it in college... :devil:

  16. Sep 9, 2004 #15
    Yes I trust you. We probably don't have the same notations/semantics that is all. In France, fields are called "corps" (bodies) for instance. This avoid possible confusion between math fields and phys. fields. Of course, such a confusion is very unlikely to happen to somebody knowing the context.

    EDIT Sprechen Sie nicht Deutcsh ? ... oder ähnlich Sache :shy:
  17. Sep 9, 2004 #16


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    Has this been disproved yet?

    Sorry to be so sceptical but the paper is awful and doesn't look like ground breaking mathematics to me. In fact reading that over again it doesn't even seem to prove anything.
  18. Sep 9, 2004 #17


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    To put this into perspective:

    Abel's theorem is that for any n > 4, there is no formula for the roots of a general n-th degree polynomial that uses only the coefficients of the polynomial, arbitrary integers, +, -, *, /, and k-th roots.

    Furthermore, one can find explicit polynomials (I think x^5 + 4x + 2 is one) whose solutions cannot be expressed in terms of integers, +, -, *, /, and k-th roots.
  19. Sep 9, 2004 #18
    I was sure they would not even bother trying to search where it goes wrong, because it is too obviously wrong.

    right, we should have thought about that earlier.
  20. Sep 9, 2004 #19


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    Last edited by a moderator: Apr 21, 2017
  21. Sep 9, 2004 #20
    Look for my "Booda Theorem" on my website, below. It involves a simply stated, nontrivial, and original proof involving cubic polynomials - but nothing to change the world.
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