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Modern Mathematical Debates?

  1. Aug 19, 2009 #1
    Hey guys,

    For my university application I've been told I have to investigate a modern mathematical topic on which there is currently a debate (i.e. some people who agree with the concept and others who disagree). The level of the topic should be about A level to first year degree kind of standard.

    I'm really stumped for ideas, and was wondering if anyone would be kind enough to suggest a good topic which has plenty of free online resources I can look at avaliable?

    Thanks very much in advance,
  2. jcsd
  3. Aug 19, 2009 #2
    It seems kind of strange as most modern mathematics is way beyond A level. If there is dispute it means that the problem is not properly understood by leading mathematicians so it would be hard for a high schooler/freshman to write anything novel about it. Anyway I guess I would look at some of the following conjectures:
    - http://en.wikipedia.org/wiki/3x%2B1" [Broken] (easy to understand).
    - http://en.wikipedia.org/wiki/P_vs_NP" [Broken] (requires a bit of knowledge of complexity theory. May not qualify as math, but CS).
    - http://en.wikipedia.org/wiki/Riemann_hypothesis" [Broken] (requires a bit of analysis to understand).
    - http://en.wikipedia.org/wiki/Classification_of_finite_simple_groups" [Broken] (requires a bit of group theory. Not really a conjecture, but there is some controversy about the proof).
    - http://en.wikipedia.org/wiki/Abc_conjecture" [Broken] (understandable using high-school math I think).
    Alternatively you may want to talk about the use of computers in theorem proving such as the use in the http://en.wikipedia.org/wiki/Four_color_theorem" [Broken].
    Last edited by a moderator: May 4, 2017
  4. Aug 19, 2009 #3
    Thank you so much for the speedy reply :)

    You've given me some good ideas - I see at least 2 or 3 i'd like to have a look at for fun if not as part of my project!

    Thanks so much again,
  5. Aug 19, 2009 #4
    What about the four color theorem? The computer-generated proof (which is too long to be checked by humans) generated lots of discussion whether or not the proof was valid. Google for "four color theorem controversy" (without the quote marks) for more information.
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