Is Calculus Really the Most Difficult Form of Math?

[uperkurk]

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 particle 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...

 

[Jimmy Snyder]

I learned calculus in high school.

 

[uperkurk]

I learned calculus in high school.

You completely missed the objective of my question...

 

[Jimmy Snyder]

You completely missed the objective of my question...

You completely missed the objective of my response ...

 

[leroyjenkens]

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.

 

[WannabeNewton]

So my question is Calculus is considered for the most part the most difficult form of math right?

No...

 

[Vorde]

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.

 

[hotvette]

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.

 

[Drakkith]

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.

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)

But when you're dealing with orbiting planets, motion of epic proportions how can you ever prove that your theory is correct?

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.

I also have the same problem when it comes to people who invented string theory and particle 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?

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.

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...

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.

 

[dipole]

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).

 

[Vorde]

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).

I would say it's straightforward looking back, I doubt it was the same back then.

 

[dipole]

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.

 

[Vorde]

I meant more when Newton, Leibniz and others were figuring it out, not us learning it today - for that I'd agree with you.

 

[Astronuc]

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.

. . .

Well, Newton didn't live in a vacuum.

. . . in 1667, Newton returned to Trinity College as a Fellow (professor), and 2 years later Dr. Isaac Barrow, Newton's teacher, resigned so Newton could become Lucasian Professor of Mathematics.

and

In developing the calculus, Newton used the method of "fluxions" (from the Latin "flow"): functions flowed and he considered their "rate of flow." He routinely dealt with "infinitesimal" (infinitely small quantities) and used dots above the variable functions to denote derivatives. The notations we use in calculus are primarily due to the other inventor of calculus, Leibniz. Newton and Leibniz both used an intuitive idea of "limit," but neither seemed to have a precise definition of it.

Ref: http://scidiv.bellevuecollege.edu/math/Newton.html

Isaac Barrow, Newton's teacher at Cambridge, was a competent and creative mathematician, who must have helped to raise Newton's interests. It is known that Barrow made contributions to the Fundamental Theorem of Calculus.

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.

 

[AlephZero]

If you want to see what Newton actually did when he was an undergraduate (and afterwards), go here: http://cudl.lib.cam.ac.uk/collections/Newton

 

[uperkurk]

No...

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.

 

[Drakkith]

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.

Underwater metric weaving.

 

[Best Pokemon]

Newton and Leibniz didn't invent calculus.

 

[SolsticeFire]

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.

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

 

[Astronuc]

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

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.

 

[mathsciguy]

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. random as the equations being taught at universities...

I've never been formally educated in Abstract Algebra, which I think is the heart of what you are calling Algebra (you mean Elementary Algebra right?). It's mind-blowing just thinking of how consistent that 'equation manipulation is'. I think, with mathematics you can define lots of things and derive lots of conveniently 'true' stuff to it, but I don't think that's an easy feat to do. If it was, there would be more mathematicians out there.

I might have hijacked the thread here, what I mean is, Algebra is just as amazing as Calculus.