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Newton and Calculus

  1. Oct 29, 2012 #1
    So I read that at age 23 Newton went about inventing calculus, I've read different stories on who invented calculus but I'm not going into that here. So my question is Calculus is considered for the most part the most difficult form of math right? So how can a 23 year old invent it? I mean it's difficult enough for people to learn it at uni with qualified professional teachers and this guy in his early 20's, with no books, internet or anyone to guide him invented and taught himself calculus is just mind boggling.

    I've never studied calculus but when I think about Muhammad ibn Mūsā al-Khwārizmī inventing algebra, well it doesn't match anywhere near to calculus. I mean I can see how algebra is a pretty simple subject to invent and it's easy to prove with a pen and pad. You're literally just manipulating numbers. But when you're dealing with orbiting planets, motion of epic proportions how can you ever prove that your theory is correct?

    I also read that even today, Newton's calculations are so precise that when we shoot a probe right passed the rings of saturn, we use exactly the same equations that Newton unravelled in the 1600's. But how could he have possibly calculated for planets, suns ect?

    I also have the same problem when it comes to people who invented string theory and partical physics etc... how can you possibly write an equation for something so tiny you can't even see it? How would you even go about inventing some equation? I could sit in my room and just make up some random equations for string theory and they'd be just as random as the equations being taught at universities...
     
  2. jcsd
  3. Oct 29, 2012 #2
    I learned calculus in high school.
     
  4. Oct 29, 2012 #3
    You completely missed the objective of my question...
     
  5. Oct 29, 2012 #4
    You completely missed the objective of my response ...
     
  6. Oct 29, 2012 #5
    Newton was special. He invented and discovered a lot of things.

    And when you take calculus classes today, you're not just learning what Newton invented (discovered?), you're also learning things other people came up with.
     
  7. Oct 29, 2012 #6

    WannabeNewton

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    No...
     
  8. Oct 29, 2012 #7
    The equations 'being taught at universities aren't random', they are the result of some of the smartest people in the would looking at decades of experiments and, on the shoulders of hundreds of years of mathematical progress, deducing the equations to describe the real world.
     
  9. Oct 29, 2012 #8

    hotvette

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    I don't think there is any doubt that Newton was brilliant. From what I've read though, he didn't discover/invent calculus in a vacuum. There were bits and pieces already known at the time (e.g. formulas for integrating polynomials) from the work of others. What he did was unify the known information and filled in the blanks. Liebniz did similar work and there was a big political battle at the time as to who was the true father of calculus.
     
    Last edited: Oct 29, 2012
  10. Oct 29, 2012 #9

    Drakkith

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    What do mean? Newton had all kinds of books and had learned previous math from schooling. He had the knowledge of everyone before him to go off of, he didn't just invent it out of nothing. (Similar to Einstein's invention of Relativity)

    You watch what they do over long periods of time. But more to the point, calculus doesn't care whether it's a planet or a flea or a simple graph of something random I can't even think of at the moment, it's all just math.

    Again, by observing things, acquiring data, and figuring out how to make them all mathematically fit together into a theory and model that works. We aren't working blind here, we are building off previous math and previous scientific models.

    Nonsense. The equations at universities are accepted as being MEANINGFUL. They make sense within the model or theory that uses them. They are not at all "random" and people have overwhelming amounts of time of effort making sure they work and are consistent.
     
  11. Oct 29, 2012 #10
    Calculus is actually very easy and straightforward. At the high school level at least, it's just an extension of geometry from polygons to continuous curves (in some sense).
     
  12. Oct 29, 2012 #11
    I would say it's straightforward looking back, I doubt it was the same back then.
     
  13. Oct 29, 2012 #12
    Well no, even when I was first learning calculus everything made pretty good sense. Obviously learning how to do the actual calculations takes practice, but the basic concepts were always fairly straightforward to me.
     
  14. Oct 29, 2012 #13
    I meant more when Newton, Leibniz and others were figuring it out, not us learning it today - for that I'd agree with you.
     
  15. Oct 29, 2012 #14

    Astronuc

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    Well, Newton didn't live in a vacuum.

    and
    Ref: http://scidiv.bellevuecollege.edu/math/newton.html

    Ref: http://www.wfu.edu/~kuz/Stamps/Newton/Newton.htm

    http://www-history.mcs.st-and.ac.uk/Biographies/Newton.html

    A chronology of Newton's life and works - http://www.newtonproject.sussex.ac.uk/prism.php?id=15

    I suspect quite a number of PFers like myself started learning calculus during high school. I started studying it when I was about 14, and didn't have a formal class until I was 16 during my senior year in high school.
     
    Last edited: Oct 29, 2012
  16. Oct 29, 2012 #15

    AlephZero

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  17. Oct 30, 2012 #16
    So what math is generally considered the most difficult? I know everybody finds things easier than others but there must be a general topic that is just a pain in the *** to grasp.
     
  18. Oct 30, 2012 #17

    Drakkith

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    Underwater metric weaving.
     
  19. Oct 30, 2012 #18
    Newton and Leibniz didn't invent calculus.
     
  20. Oct 30, 2012 #19
    Functional Analysis was my Krypto. It's kind of a fusion between calculus and algebra. Go figure! :P

    I realized that there were some gaps in my knowledge so I used last summer to fill those gaps in. If you keep at it, you'll also make some profound discoveries! :)

    SolsticeFire
     
  21. Oct 30, 2012 #20

    Astronuc

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    The History of Calculus - according to some sites - "is often attributed to two men, Isaac Newton and Gottfried Leibniz, who independently developed its foundations."
    http://www.uiowa.edu/~c22m025c/history.html [Broken]

    There were many contributors:
    http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html

    http://www.mscs.dal.ca/~kgardner/History.html

    http://www.eng.utah.edu/~cs5961/Resources/calculus.pdf

    http://faculty.unlv.edu/bellomo/Math714/Notes/11_Calculus.pdf

    http://www.math.vanderbilt.edu/~schectex/courses/whystudy.html

    http://www.saintjoe.edu/~karend/m441/Cauchy.html

    It would be better for a mathematician to provide the definitive history.
     
    Last edited by a moderator: May 6, 2017
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