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Next great mathematical invention

  1. Jan 23, 2013 #1
    Hi , I was thinking about this , as you know calculus was used many years before the explicit work of both Newton and Leibniz , it was used the hard way , unrecognized , scattered and buried among unrelated formulas and topics.
    The golden question is ; what if there is another revolutionary mathematical "principle" "tool" "method" (call it what you want) lurking on the orizon and living incognito inside the works of mathematicians ?!
    Do you have some insights on what would it be like ?
    Everyone who works with math , experiences sometimes the "aha" feeling when meeting with some beautiful pattern or similarity or a connection between unrelated stuffs , that would be a great hint for this subject.
     
  2. jcsd
  3. Jan 23, 2013 #2
    Maybe it is there, just yet to be discovered
     
  4. Jan 23, 2013 #3

    jedishrfu

    Staff: Mentor

    Research from the P vs NP problem if its determined that P = NP will revolutionize computer technology since so much depends on search algorithms.
     
  5. Jan 23, 2013 #4
    It won't really revolutionize anything; knowing that P = NP doesn't give you any useful tools or algorithms. The truth or falsity of the statement has severe implications, but knowing the truth or falsity doesn't really do anything for you.
     
  6. Jan 23, 2013 #5
    P=/=NP probably. It's hard to prove but most of the computer scientist have a lot of reasons to think that.

    It's hard to tell if there is some area of mathematics that will get very important in the future. If we knew we would probably concentrate mostly on it.
     
  7. Jan 23, 2013 #6

    jedishrfu

    Staff: Mentor

    Sometimes the mechanics of the proof lead to new methods of computation.
     
  8. Jan 23, 2013 #7
    While doing physics problems, I wonder if we're doing it the hard way, when in reality there's some mathematics that we haven't developed or discovered that is much simpler and perfectly suited for all problems we encounter.
     
  9. Jan 23, 2013 #8
    It corresponds well with my line of thinking.
     
  10. Jan 23, 2013 #9
    Guess and check... Works every time, eventually.
     
  11. Jan 23, 2013 #10

    jedishrfu

    Staff: Mentor

    Yeah, I ran into that when I learned Lagrangian mechanics wondering why didn't they teach us this instead of Newtons way. The funny thing now is that I still remember Newton but nothing of Lagrange. the things you learn last are the things you forget first.
     
  12. Jan 23, 2013 #11
    If you think about it , calculus gives us a systematic way of doing some tasks that otherwise would be as painful as guess and check , so if we revise our current methods for resolving certain problems we may get insights about a new systematic way ....
     
  13. Jan 23, 2013 #12
    That is exactly the job of mathematics. To abstract things and find systematic ways to solve different but related by something problems. In the future there might be some easy way find solution of the things that seem impossibly hard to us but it would probably require a massive amount of knowlege.

    If you think about proving the formulas for area of circles volume of spheres, cones, pyramids without knowing calculus ( like ancient coltures did it and in school) it's realy painful because you just try different aproaches for every case and they don't aways work. Sometimes they require a lot more effort. With calculus this is very easy job. You can do it in less than a minute with very small efforts.
    But if you think about it in order to get there you need to prove many other theorems and statements about derivatives, integrals, limits... You are not actualy gaining all this for free.
     
  14. Jan 23, 2013 #13
    About ten years ago, I looked at Stephen Wolfram's "A New Kind of Science." It's a huge tome with thousands of computer generated patterns based on a limited number of simple rules for combining cells of cellular automata (either white or black or 0,1). The idea is that complex patterns seen in nature might be explained by a tractable set of simple rules of combination. His work is not original and his claims are controversial. A review by mathematician Rudy Rucker seems to give balanced view of his work. I'm not qualified to say whether mathematics as we know it will be replaced by purely computational methods for the hard problems of present and future science.

    www.rudyrucker.com/pdf/wolfram_review.pdf
     
    Last edited: Jan 24, 2013
  15. Jan 24, 2013 #14
    I am pretty sure that natural scientists (vs math guys) would be the first to find something when facing an out-of-place phenomenon ; just as Newton and Leibniz were Multidisciplinary men of science.
     
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