Newton vs Leibnitz

DiracPool

I wanted to start a thread to hear everyone's opinions over who they thought actually invented the calculus. I read "the calculus wars" a while back and have always been interested in the phenomenon of "simultaneous discovery." And the calculus debate is really a fascinating one. In short, I would put my vote to Leibnitz. Why? Well, again, in short I think Newton had a sense of the calculus but was too preoccupied with his physics and alchemy to really develop it properly. Leibnitz, on the other hand, was focused on the problem of the calculus specifically and operationalized his maths enough to get them published well before Newton. So there goes my vote, what about yours, and please give your reasons and make an argument.

zoobyshoe

I vote Newton because Newton gave some of his personal papers to someone at Cambridge to look at and that guy showed them to Leibnitz, who made notes. Later Leibnitz claimed he didn't copy the calculus parts. Right.

DiracPool

Yeah but...Newton in fact was a prima donna, so don't you think that if he actually had his stuff together he would have promoted himself more? After all, he was in a big tiff with Hooke over some optiks issues, I believe. I think calculus was a work in progress for him that was on the back burner and he got scooped by a more precient Leibnitz. Maybe Leibnitz did get some clues from a manuscript of Newton's, but that's like saying that any significant contribution to science today is only significant if the author doesn't quote any references, right?

Woopydalan

Is it possible that they both developed it independently?

zoobyshoe

Newton was actually incredibly secretive. His religious ideas were heretical, and his alchemical studies were too potentially big (in his mind) to go around shooting his mouth off about. He played his cards close to his chest in everything. He showed his private math papers to a guy he trusted and respected and whom he thought would appreciate them.

He showed his telescope to the Royal Society because it was non-controversial. Seeing the attention Newton was getting, Hooke claimed he'd already made a microscope on the same principle, that he should have credit for replacing the lens with a mirror. He was never able to produce this alleged microscope for inspection. Newton was suitably irrked. The whole time he was alive Hooke continued to claim, without evidence, he had somehow done everything Newton did long before. Hooke claimed he had given Newton every possible important insight that found it's way into the Principia Mathematica. Newton developed a complex about this: about people claiming precedence. By the time Leibnitz came along with his calculus, Newton's self-defensive reaction seemed like that of a Prima Donna.

Bipolarity

This is what I remember of the story:

Newton solved the problem of finding the slope of the tangent to a curve. He developed some of the differentiation rules but did not prove them very rigorously. He also developed the idea of limits which he applied to his differential calculus, but not rigorously (this was later done by Cauchy).

Leibniz approached the problem of finding the area under a curve. When he met Newton in Germany, Newton was struck by Leibniz's efforts and realized a strong connection between the tangent problem and the area problem, which later led him to develop the fundamental theorem of calculus.

If I remember correctly, both of them eventually developed calculus by themselves each using his own notation.

BiP

jtbell

For what it's worth, with the usual caveats about Wikipedia's reliability:

http://en.wikipedia.org/wiki/Leibniz...us_controversy

Sayajin

I personaly think that Newton actualy is responsible for the invention of calculus. His work in physics could not be done without calculus. He needed it very desperately. On the other hand Lebnitz was mathematician and philosopher. Mathematicians have a lot of other things to do that are not connected to calculus. Why would he suddenly try to do just this.

I mean the very basic concepts of calculus like derivatives and limits are very physical concepts and the first thing that you can apply them to is to describe velocities, accelerations and other kinds of mechanical things. Its true that you can do a lot more like analysing functions graphs finding areas under curves and volumes of figures but that comes after you defined the basic concepts and you realize that they can be used for this. After you study the subject more and more you see that there are even more things that can be solved using calculus and it becomes very very powerful tool. But who would be the first one to explore this path and see all those applications? A philosopher and mathematician or a physicist searching for the most natural definiton of speeds, velocities, acceleration and other rates of change of physical properties?

Ofcourse Lebnitz contributed a lot to the subject but I personaly think that Newton was the one who got the idea first.

BobG

The first was: Bonaventura Cavalieri

Okay, it would be a gross exaggeration to say Cavalieri invented calculus, but he did develop a couple of key ideas used in calculus even if he didn't develop it and formalize it as thoroughly as Newton and Leibniz.

The reason both Newton and Leibniz invented calculus about the same time independently was Cavalieri, plus Rene DesCarte's invention of Cartesian coordinates, which led to analytic geometry, linear algebra, and calculus among other things.

It wasn't an incredible coincidence that two men "invented" calculus on their own. One thing led to the other.

Newton developed his calculus first, but refused to publish (just another chapter in the Hooke-Newton feud). Whether Leibniz had read the little Newton had written on calculus is beside the point. If Newton wouldn't publish, why should everyone else sit around and wait?

russ_watters

If I invented a new branch of math [yawn] because I needed a tool to figure out a physics problem I'd probably let that go to my head too.

"I'm so much better than you at math that I invent new math as a sidebar to my physics study!"

That's like inventing the jet engine because you need a new propulsion system to power the airplane you also just invented.

Woopydalan

Why were they so secretive about their findings, did they not want to be scrutinized? Were they afraid that others would try to claim the work as their own? Newton afraid that Newton's Method would be called Leibniz's Method or something?

zoobyshoe

Newton was secretive because his primary interest was theological and his private beliefs were heretical at the time. He was also a serious alchemist, trying to turn lead into gold, and no one who thinks they're onto a new source of gold ever tells anyone else about it. His general need to keep his mouth shut just bled over into his math and physics, I think.

Leibniz was not secretive at all that I know of.

BobG

Newton was secretive about many things, but the main reason for not publishing his calculus was that he was offended by Robert Hooke's criticism. Newton didn't have limits (they were developed by Cauchy years later), so the idea of inventing some infinitesimally small number sounded like a crackpot method of dividing by zero. Or at least close enough that Hooke would find a way to use it to insult Newton.

Both had some sort of personality disorder or another and you had to take care when around either if you didn't want to offend them. And when both were in the same room?

At least Hooke had an excuse. He was incredibly ugly and practically a dwarf. He had a tendency to compensate by making others feel small.

Yet Newton probably did a lot stranger things. And he got into feuds with a lot more people than Hooke did.

And, of course, there was that cute little P.S. Newton included in one of his letters to Hooke: "If I have seen further, it is by standing on the shoulders of giants."

Just one of those passive-aggressive digs that left one wondering if he was complimenting Hooke or if he was really saying, "Obviously not by standing on the shoulders of dwarves!"

DiracPool

I want to state this here in Physics Forums for the record and have this quote petrified in history as what I, DiracPool, personally thinks, and here it is..."if I have seen further, then it is because I have stood taller than others." Thank you everyone.

DiracPool

IMO, this statement is really at the crux of the matter and has been echoed in a number of posts to this thread. Ostensibly, this is the argument for Newton being the principal founder of the calculus. But the question I think is one of recognition. How many examples do we have of ideas and technologies putatively conceived by some individual that didn't really recognize what they had? Many. My argument is that Newton may have had to develop some of these concepts of fluxions and derivatives as a consequence of deriving his foundational physics models, but it was Leibnitz that recognized the significance and purity of the maths. This is something that perhaps Newton did not recognize at the time, again, because he had several irons in the fire. Again, being the prima donna that he was, I think he would have formalized and published this if he did recognize it. Nobody, not even Newton int he 1600's is gonna sit on a winning lottery ticket and not cash it.

Woopydalan

Is it fair to say that no one really invented calculus singlehandedly? I mean what constitutes of whole of ''calculus'' is development by many individuals over a number of years. What is being argued here is who discovered the very first notions of what calculus is, right? In that case, could it be argued that there are people pre-Newton that made discoveries that could be counted as a concept of calculus?

zoobyshoe

If Leibniz appreciated it better than Newton, it still does not make him the inventor of it.