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Thread: Next great mathematical invention

  1. #1 Next great mathematical invention 
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    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.


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  3. #2  
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    This isn't likely.

    In the old days, (And I do mean old) knowledge was greedily possessed, nothing like how it is shared today.

    The details are lengthy, and I'm going away now so maybe I'll type on this later. That one line sums it up pretty directly, though.


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    Meh anyway... In the old days, for example, the age of the Library of Alexandria, and the days of Nobles and royalty - Higher education was reserved for the wealthy and the elite. The common (And by far, the majority) of people simply did not have access to higher education or usually, even mid level education.

    On a side note, this is where those guys that jump on science forums saying things like, "A hundred years ago, scientists thought the Earth was flat!" clearly demonstrate a lack of knowledge of their history. Eratosthenes had pretty accurately calculated the circumference of the Globe about two thousand years ago.
    This also relates to the Christopher Columbus story: They all knew that the Earth was a globe. Except some ignorant sailors, maybe, but they are not relevant to this story.
    Columbus' claim was not that the Earth was round, but that the calculations of the circumference of the Globe were wrong and that the Earth was smaller than believed. This allowed for a trip west from Europe- around the globe and landing in India in a much shorter time by Columbus' calculations of the Earths circumference than currently believed. Well, these claims were clearly in error and most of those Columbus approached did not fall for his claims. For whatever reason, Ferdinand and Isabella of Spain did.
    Some, (Self included) suspect that Columbus was well aware that the calculations he presented were fudged- but that he needed an excuse to hit the lands the Vikings wrote about. Columbus knew there was Great Wealth there... not in the form of Gold- that was secondary.
    In the form of Slaves... So, he cooked up a scam. I don't know... I said I suspect.

    Anyway, so we've established that the scientists knew that the Earth was a globe. They also were taught mathematics, such as algebra, geometry and later, calculus.
    But again, such knowledge was deemed, "too dangerous" in the hands of the common peasant. Education and knowledge was jealously kept for the Upper Class.

    There was a paradigm shift in our history, that public education was important and that the common man could be trusted with knowledge. What this allows for is the inevitability that you will come across the concepts of higher learning and education, even if not formally educated beyond high school.
    While in an age past, knowledge was denied to the general population, today it is encouraged. Companies and governments will even pay for promising students continued education.
    Peer review allows for constant comparing and sharing of knowledge.

    And now with this datburned newfangled interweb, even old fogies like me cannot keep up with all this sharing and free knowledge, what with the Wikipedia and the Google and th' puddin' pops...
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  5. #4  
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    Quote Originally Posted by mryoussef2012 View Post
    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.
    A recent example of this phenomena would be Category Theory, which showed a deeper structure and meaning to many seemingly disjoint construction types. Before that we Lie group symmetries showing the deep relationship between group theory and the solvability of differential equations. This unified many rather ad hoc solution methods into a coherent whole.

    There are some hints at a greater theory lurking here and there - the Monstrous Moonshine Conjecture and proof hint at some strange relationships between discrete and continuous structures for example.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  6. #5  
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    IMHO breakthroughs in mathematics happen all the time. How “revolutionary” they are depends not only on their relevance to the areas they are applied to but also to the extent to which laymen could readily understand what the breakthrough is all about.

    For instance, Andrew Wiles’s proof of the Taniyama–Shimura conjecture was “revolutionary” not only in establishing the relation between elliptic functions and modular forms but also in enabling the long-standing Fermat’s last theorem to be proved. But just as “revolutionary”, if not more so, was the classification of finite simple groups. Yet the former is much more well known, simply because of the concepts involved. Fermat’s last theorem is simple enough to understand: There are no nonzero integers x, y, z satisfying for any integer n > 2. Anyone with an elementary knowledge of mathematics can understand this equation. On the other hand, it is not likely that anyone who has not done any university-level mathematics would know what simple finite groups are, or the purpose of classifying them.

    At the moment I believe the biggest unsolved conjecture in mathematics is the Riemann hypothesis. The next “revolution” in mathematics, if or when it does come, will, I suspect, be in this area.
    Last edited by Crimson Sunbird; January 29th, 2013 at 10:18 AM. Reason: Make signature show
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  7. #6 I think probability is a rich field. 
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    Quote Originally Posted by mryoussef2012 View Post
    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.
    I'm not as much a guru as the other folks here, but from what I've seen when you really get beneath the hood with probability theory that are a whole lot of unexplored and interesting regions dealing with how it relates discrete areas, and areas where the expected behavior, if you assume the whole continuum from calculus, just doesn't hold up to the real world. I believe this is the ballpark of the next breakthrough.

    The main issue is that all the fantastical genius of math up to the end of the 20th century was developed for platforms of computation which consisted basically of pencil and paper. In a historical context, we are still young in the computer age, and haven't fully adapted our reasoning systems entirely to the possibilities that computers present us with. As a result, we still use mathematical systems which gloss over some very interesting (but computationally expensive) paths of inquiry.
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    Quote Originally Posted by TridentBlue View Post
    The main issue is that all the fantastical genius of math up to the end of the 20th century was developed for platforms of computation which consisted basically of pencil and paper.
    In applied mathematics, perhaps. Not in pure mathematics.
    “Don’t fear change. Change fear.”
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  9. #8  
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    Quote Originally Posted by Crimson Sunbird View Post
    Quote Originally Posted by TridentBlue View Post
    The main issue is that all the fantastical genius of math up to the end of the 20th century was developed for platforms of computation which consisted basically of pencil and paper.
    In applied mathematics, perhaps. Not in pure mathematics.
    My comment was intended to mean that math which was developed before computers was fundamentally restrained by the computational limitations of working mathematicians...But now that we have all this computational power, its a fairly unexplored domain.
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  10. #9  
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    To bolster TridentBlue's assertion, the 4 colour problem immediately springs to mind.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  11. #10  
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    Do you appreciate inventions that can save you money, time and even your life? If so, here are some forthcoming instances of future tech that will satisfy your inner futurist.
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  12. #11  
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    Quote Originally Posted by vanmill View Post
    Do you appreciate inventions that can save you money, time and even your life? If so, here are some forthcoming instances of future tech that will satisfy your inner futurist.
    Is this a sales pitch ?
    .
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  13. #12  
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    I'm guessing spammer and the forum software has removed the link he intended to go with the blurb...
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  14. #13  
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    The next great math breakthrough will be that somebody will finally discover 0.999... differs from 1.0 by an infinitessimal amount!
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  15. #14  
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    Some crank will discover that relativity is wrong...
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  16. #15  
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    My cousin studies psychology so maybe it will be a relative who discovers what's wrong with cranks...
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