The Calculus Controversy

Today, calculus is one of the most important fields of mathematics. However, two men claimed to be its inventor - Isaac Newton and Gottfried Leibniz. The ensuing dispute would embroil Europe in the greatest mathematical controversy of all time.

[@bm-br3go]

The reason why I'd be on "team leibniz" is that after Newton published the Principia, he basically just quit. He essentially said, "I'll never top this so I'm going to quit while I'm ahead." He then proceeded to try and defame leibniz for the rest of his life. But leibniz ignored Newton and his constant defamation attempts (this is after so long of course, leibniz also tried to defame newton but eventually quit) and continued to research mathematics. That's a real mathematician in my book.

[@Nothing_serious]

That's because Newton's purpose on creating calculus was simply scientific. He wanted to understand the universe especially when things like accelerations are instantaneous. He used it to derive some of his equations like his second law, he just used it to prove Kepler's law etc. so when he's done it he had no other purpose on continuing it.

[@Nothing_serious]

Um...ok?

[@JohnSmith-ys4nl]

Newton spent most of his time studying and writing about Arianism (a Christian sect). He was a very weird guy, by all accounts. And, yes, he wasted his genius on such trivial nonsense.

[@bryandiaz1044]

Newton invented calculus and most of the classical mechanics of physics so.... Wasted genius? Definitely not

[@JohnSmith-ys4nl]

I know that. He and Leibniz invented it concurrently. The problem is Newton wasted a lot of time on nonsense. He should have focused all his time on math and physics, not weird esoteric cults.

[@oliverrainer5771]

They pushed the "limits" of human comprehension

[@VVeltanschauung187]

Leibniz is incredibly underrated. He actually knows what he talks about, most likely borrowing from the Hermetic tradition

[@StdsRbop1]

This is just dead wrong. Leibniz stole the core idea of Newton, and while he made significant contributions, implementing the groundbreaking ideas of Newton and calling it his own is in fact fraud in my opinion. Look at the contents of Epistola Prior that Newton sent to Leibniz in the 1660s before Leibniz did calculus, it literally lays out the core idea of calculus.

[@Mutantcy1992]

Leibniz's notation is so much better than Newton's because it easily allows you to jump to multivariable calculus without any confusion.

[@anthonyhui1322]

YES!

[@CWSOF]

I agree. f'(x) is very poor, it doesn't show the main idea behind the calculus like the rate of change. But Df(x)\dx is just beautiful, elegant and special. It shows much more what a derivative really is. lim f(x) - f(x)\ (x - x) x--> x Is much closer to Df(x)\dx than f'(x). I never use Newton's notation.

[@DD-vc7fq]

@@CWSOF f'(x) is not Newtons notation. I believe that is from Lagrange.

[@CWSOF]

@@DD-vc7fq Just google ''Newton calculus notation'' and find out it yourself

[@DD-vc7fq]

@@CWSOF I did. I don't see that Newton used this notation. This is what I've got: "Newton's earliest use of dots, to indicate velocities or fluxions [i.e. derivative with respect to time] is found on a leaf dated May 20, 1665. Newton never used 𝑓′. Lagrange in his Theorie des fonctions analytiques (1797) introduced the new symbols : 𝑓′𝑥 for the first derivative, 𝑓″𝑥 for the first derivative of 𝑓′𝑥, and so on .."

[@pivottech8881]

Leibniz gets my respect more now, He done stuff in electronics which I like, developed more or less the language for electronics (binary) has a brand of biscuits for himself, and played a role in calculus. Totally underrated.

[@Torzadio]

This was great! I'm writing a big essay on Leibniz and his mathematic contributions to the modern world, and this really helped alot! Creds to you! :D

[@blakeschreckenbach679]

Leibniz' notation is what is used today

[@mohbehnia]

Great video!! I've been watching dozens of vids for my math project, but not many had made sense until now. Very clear and easy to understand.

[@najmlion7129]

This video was amazing Bro. Well done. It does speed volumes how back in the day the invention of calculus was one of the biggest controversies.

[@mosesvelasco5229]

Thanks for this video. Really shed a little bit of light on my view of the entire dispute.

[@karotix5]

I invented Calculus

[@assmane999]

All hail the immortal math God, William Morgan the Turd!!!!

[@amirkb7206]

Ironicly assertion alone is enough for most people to believe xD

[@assmane999]

Amir Fisher Yeah, it worked for Trump

[@MrFunnyHandsInYourPants]

samlawhorn ooooooo citing Wikipedia! Shoulda just said that without the wiki link and let ppl research that on their own.

[@makerKID5]

Thanks mate!

[@maikenzupancicdanko9377]

I just wish the audio was better, but other than that, the cartoons look awesome, and this was funny and very informative. Awesome!

[@samuellacher6423]

As for what everyone's saying about you talking too fast... You have good pacing, and the script as a whole was great, but you tend to rush some parts of sentences out, like halfway through saying them you think "Oh, screw it, I just wanna be done with it.". Looking over your lines and recognising where the syllable breaks are and if they are stressed or unstressed could help with that. At any rate, thanks so much! I'm working on a project that ties a bunch of major mathematical discoveries together in a giant web, but I didn't quite know what to put in regards to the comeabout of calculus. You've cleared up all the questions I've had up very straightforwardly. Nice job!

[@galileomoment]

Very interesting! Quite enjoyed this. I'll have to read more about this controversy, and the associated theories. Thanks!!! Etranger

[@bitchslapper12]

It did take a while, but it's crucial to understand Liebniz's notation in higher mathematics such as single/multi-variable Calculus

[@ssoko]

This video is very understandable and very well explained the dilemma. Great job!

[@XenoContact]

the question of "who made it" is a relic of a time long gone. Now what matters is how can we develop it further.

[@harderhscmaths]

Love the intro music. Great trip thru the history of the calculus.

[@ninjabreadgirl]

Awesome video, mate!! I like your sense of humour.

[@njabulomasina4180]

To me this proves one thing, which is that mathematics is the language of the universe or as Galileo put it, "the laws of nature are written in the language of mathematics". The fact that 2 guys in 2 different parts of Europe came to the same conclusions (using different notations) about the same mathematical concept is astounding.

[@DD-vc7fq]

I get what you are saying, but Newton and Leibniz actually communicated with each other through couple of letters discussing this matter. It is possible that one got the idea from the other and managed to develop it.

[@eu1043]

@@DD-vc7fq Read the book called "The war of calculus" (i don't know if the book is called like that in english)...In that is the explanation about the history of calculus.

[@archivesoffantasy5560]

@@DD-vc7fq “Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.” - Leibniz Perhaps his own quote indicates to us who inspired who.

[@StdsRbop1]

It's not astounding -- it's because Newton and Leibniz were both working off of Newton's core ideas of calculus that Newton expressed to Leibniz in a letter years before Leibniz "discovered" calculus. Leibniz merely implemented Newton's groundbreaking ideas. So in a sense Leibniz is a fraud for taking credit for "discovering" calculus

[@QMPhilosophe]

Let us not forget that the vast majority of Newton's writings were on Alchemy and Biblical Chronology. In addition, Newton's metaphysical claims in the Principia are muddle-headed at best.

[@archivesoffantasy5560]

“Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.” - Leibniz Also, look up the story of Newton’s lion claw, in a single night he solved a problem Leibniz and others wanted months to complete.

[@nadeemshaikh7863]

What does that have to do with anything?

[@StdsRbop1]

@QMPhilosphe Newton created modern science from literally nothing, and idk if you know this, but Leibniz was also super into theology. Additionally, Newton literally explained the core ideas of calculus to Leibniz in a letter years before Leibniz "discovered" calculus -- so Leibniz is a fraud in the sense he took credit for calculus when in reality the scope of what he did was implementing and putting to paper newton's groundbreaking ideas

[@kgprasad100]

Madhava of Sangamagrama discovered Taylor and Leibnitz series , differentiation , term by term integration and the theory that the area under a curve is its integral.

[@jimdogma1537]

Super cool vid, mon. Please make more.

[@chriscoooley]

5:30 "pressured" bernoulli, was that intentional?

[@joshcaz9735]

Leibniz's 1) calculus 2) differential equations 3) logic and mathematical logic/ discreet mathematics 4) topology 5) calculus application Newton's: 1) calculus based and calculus applied physics 2) some of calculus application 3) mathematics of fluxions ( now differential calculus )

[@gogetasaiyan5756]

The best part was of Charles Darvin after Newton's Book lol XD

[@Brianlane2]

4:02 Both men's calculus work had problems *Only names what Newton lacks... :-)

[@ayoopdog]

Great final note by the way, I couldn't agree more. It's pathetic when people take sides on this issue.

[@TehFingergunz]

Great video, thanks for making this.

[@srenjensen1205]

I was wondering if you have any links where I can find this story? The story of Enland banesing Liebnitz's metod? :D

[@jesusbermudez6775]

Thank for enlightening me on this controversy. It was well presented and unbiased.

[@QueenHolly832]

Very interesting video, nice job with the explaination

[@floatingpointerror55]

leibniz also invented a mechanical calculator

[@jasonevanbaldwin9922]

Fluxions (BY IT, $ dime ; ) were central to the Leibniz-Newton calculus controversy, when Newton sent a letter to Gottfried Wilhelm Leibniz explaining them, but concealing his words in code due to his suspicion. He wrote: I cannot proceed with the explanations of the fluxions now, I have preferred to conceal it thus: 6accdæ13eff7i319n4o4qrr4s8t12vz The gibberish string was in fact an enciphered Latin phrase, meaning: "Given an equation that consists of any number of flowing quantities, to find the fluxions: and vice versa".

[@christinelaferriere9412]

how resourceful and pleasant your are about your intellegence/you are alright thank you

[@danalain4126]

Without exception, the calculus that all students learn in schools is Leibniz’s calculus. That makes Leibniz the world’s calculus teacher. I have never seen Newton’s fluxion in any textbooks. In England they teach Leibniz’s calculus in schools.

[@drosha9314]

this is a really nice video. thankyou

[@thejameskan]

very interesting video thanks

[@MrAkashvj96]

Good video but one thing that should be clarified - the reason Newton didn't publish any of his papers till much later in his life was not because he wanted to keep his discoveries to himself but because he didn't have the money to publish them.

[@mikev4621]

@@leibniz5460 He was still a professor at Cambridge at the time of the Principia- Halley paid to have it printed

[@phandinhthanh2295]

Newton had always been wealthy. Who in the world would think he was poor.

[@RickCostello]

Well done. Good video.

[@atelectro1]

Both men were genius. However Leibniz produced more materials in all subjects and was much more prolific.

[@stevenbollinger9776]

Yes. Also, Leibniz was a much, much nicer person. If Newton had never attacked him, I don't think there ever would have been a calculus controversy. Leibniz found it easy to share credit and recognition. Newton found it impossible.

[@eu1043]

@@stevenbollinger9776 However a Man called Kaill attacked Leibniz and show Newton a Anounimus difamation writed by Leibniz, then Newton became so angry Because this.

[@archivesoffantasy5560]

“Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.” - Leibniz

[@archivesoffantasy5560]

@@stevenbollinger9776 Leibniz wrote anonymous letters criticising Newton’s work, and when called out on it lied that he had not been the author

[@make739]

This is like asking which sole person created a particular language.

[@tjentertainmentstudio]

no shit, mathematics is a language of patterns to describe the universe

[@HopDavid]

Barrow, Fermat, Descartes, Cavalieri, Barrow and others had laid the foundations of calculus in the generation before Newton and Leibniz. Neither should be called the father of calculus. Building this branch of mathematics was the collaborative effort of many people over many hyears.

[@RockerProf]

Today we use the elegant and compact notation of Leibniz, which does not reference any of Newton's convoluted fluxion derivations. I guess being head of the Royal Society has its perks.

[@The.Chiefman]

Thanks for this great bit of history

[@jjhjjff]

Awesome! Thank you so much! I think Newton's physics is what has made him way more recognized than Leibniz.

[@KpopOrigami]

Great video. i love the little comments the mathematicians make!

[@ashidilkhan]

why dont you use 3D studio or MAYA

[@amberuidenich5477]

Thank you!

[@bjo885]

One thing - Newton's "dot notation" is not the same thing Lagrange's "prime" notation. The dot notation puts dots above the dependent variable instead of using function notation.

[@emmanuelontiveros8446]

I use both methods when I write derivatives. Depends on if it's a time derivative.

[@factorylad5071]

You will find the dot notation is more plausible if you are dealing with Serrais Frenet and using TNB vectors.

[@jayejayeee]

brilliant video

[@joejoe722]

great job!

[@halonothing1]

Why is this so loud at the begining?

[@sharjeelkhan5584]

Somethings to point out here, first, contemporary political circumstances greatly favored Newton as GB was a unified nation while german speaking world was divided into smaller less influential states with no concept of pangermanism. Secondly the following era was even more favourable to newton as GB was to become a super power with dominant culture and political influence. Thirdly how can we trust the mathematical intuition of people, thats is the anglosphere of concerned time, who had rejected a superior system proven by time.

[@factorylad5071]

And what is time ? Haha

[@ber2bkyrs]

Thank you! Well done!

[@leonfe26]

I´m from Veracruz Mexico and I make in a video about Calculus, I talk about Newton and Leibniz, and wander if I can use some of your cartoons to illustrate my video, the video has no economical intentions, is to make clear some of the concepts. Your cartoons are very fun,

[@NoOne-yw6pr]

Brilliant effort, thank you gotthegist

[@NadaII]

"Taking mathematics from the beginning of the world to the time of Newton, what he has done is much the better half." - Gottfried Wilhelm Leibniz

[@hansdeguzman889]

Sources please?

[@jmfriedman7]

The cookies were a continuation of the controversy. Both Fig Newton's & Leibniz Keks were first made in 1891. It is a question whether one of the names was given to one of the cookies to offset the fact that the honor had been given to one but not the other of the two mathematicians. (In fact, Fig Newtons were named after the town, Newton Massachusetts and so only indirectly to Sir Isaac.) The bottom line is that if you devise a new branch of mathematics, you can end up with a cookie named after you.

[@darnell8897]

Eulers sound like they'd be greasy as hell.

[@factorylad5071]

And is that why every single copy of the Principia is sold by Berkeley State University?

[@factorylad5071]

@darnell try going Non Eularian then'

[@HeeysamH]

Source please?

[@langstonrichardson3828]

Great is the gravity of this controversy

[@samarthdelhi]

Gottfried Leibniz was the founder of Calculas. He used the signs of integration & Differentiation.

[@MrsCantey]

This is great!! Love it!

[@hanniffydinn6019]

They both did, but Newton was known to be a complete and utter bastard.

[@HarryKhan007]

Leibniz did something much worse to Newton: With his Monadology, he objected Newton's axiom "actio = reactio". He said there is no reactio. For example, if something moves, it does so because this was imprinted in it, as a "prestabilized harmony". Leibniz did have a point, and his monadologic view is legit because it is free of any inconsistencies, but in the end we will have to concede 50% of being right to each of them.

[@Machammerballs]

Calculus is easy, it's the trig and algebra that trip me up! Though, Calculus was when math REALLY got fun for me!

[@jordanharrison1394]

I enjoyed calculus far more than precalculus. I teach calculus and physics now!

[@D5614Red]

The key point is that these two geniuses worked together (inadvertently) through their correspondence, and building upon the works of those who came before (e.g., Pascal), discovered calculus independently - each approaching the work from his area of interest. The moral of the story is that a "careful analysis" of papers led to solving the controversy: always go to the primary source if you want the truth. Read the autobiography before the biography.

[@factorylad5071]

There are no morals in math only paradoxes.

[@davidrodgersNJ]

Newton's wig was way cooler

[@louise789]

Thank you

[@FExpiate]

Can someone name all the people named in the video? i am having a hard time figuring them out.

[@SonGoku-gj8xj]

+FExpiate Archimedes, Antiphon, Aryabhata, Parameshvara, Pierre de Fermat, Blaise Pascal, Isaac Barrow, Isaac Newton, Gottfried Leibniz. (also mentioned later on: Johann Bernoulli, René Descartes)

[@phiAndpi]

"Quite honestly, I don't even know who Sir Joseph Swan is!" Inventor of the light bulb :)

[@phiAndpi]

Continued In fact Swan went into litigation against Edison who lost the court case, as it was Sir Joseph Swan’s design. In the end the pair come to an agreement and set up the Edison Swan Electric Co, in London.

[@stephencarlsbad]

The level of mathematics that we develop and use is limited by our ability to perceive higher dimensions. If we were able to see and perceive in higher dimensions, then the level of our math would reflect that reality.

[@ordiv12345]

Newton is to physics as Leibniz is to mathematics.

[@DD-vc7fq]

No. Leibniz is to mathematics what Newton is both to physics and mathematics.

[@yuvrajbhagotra7134]

Whilst I think this is a great video and gets a lot of the fundamentals across. I think theres a key thing that needs to be discussed here. Newtons 'Principia' actually did not have any calculus in it and actually was very sparse in methodology (perhaps mirroring the ancient Greek way of keeping one's method to himself- we know he read the likes of Pappus and Euclid so this could be a reason as to why he didnt publish much of his earlier work until much later.) Leibniz's work was published "first" but at this point Leibniz and Newton had conversed via letter about calculus (see Newton's coded message to Leibniz) which is the true origin of the priority dispute. [you can see the stuff about Newton and the Greeks in Guicciardini's work in 'the Oxford Handbook of the history of mathematics'. Note this is not to dispute Newton's importance to calculus, I'm just very pro both of them being credited lol

[@JrJ2016]

aryabhatta of india does not use acrhemedies work on tangent at all. in fact his work is the first one which directly relates to calculus.

[@sidewaysfcs0718]

6:01 that's not Newton's dot notation, that's the Lagrange notation

[@Monochromicornicopia]

sidewaysfcs0718 Lagrange took his notation from Newton.

[@MrAkashvj96]

+sidewaysfcs0718 No that notation was also introduced by Newton. In fact one of the problems with Newton was that although he was a great thinker, arguably the greatest there ever was, his choice of notation was rather inconsistent & frustrating. Even in the principia, there is no standard notation (probably because he was never planning to publish it anyway).

[@DD-vc7fq]

@@MrAkashvj96 www.jstor.org/stable/pdf/1967725.pdf There is not a single part in this pdf file that claims Newton ever used this notation. It clearly states it came from Lagrange

[@apburner1]

Awesome!

[@janmejayapharande1843]

I donot like as we can not download videos directly we need to struggle hard to it

[@goshiluvarchie]

Really interesting :)

[@dcrw8878]

You tell em' bro.

[@EveningT]

Your presentation does indeed make clear that Newton & Leibniz were links on a line of evolution in mathematical understanding, but you did unwittingly slip into crediting "discoveries" (of that which has always been) as "inventions". As implied in the video itsel, no-one invented Mathematics, they discovered it, then developed useful notation & codification for its full expression. Same as with any other branch of knowledge, which is universal.

[@dAvrilthebear]

Thanks, enjoyed it! :)

[@suvrotica]

Loved it ❤

[@margarett.newman7574]

Thanks, really neat! Nice!

[@kyfegte827]

Newton typifies the anglosaxon way of dealing with problems (the same as we see today in England's attitudes towards modern Europe): far from the gentleman's approach, it is the approach of the boxing ring. By deceit and bullying it tries to get its way, and foolhardedly persists on long past-their-sell-by-day methods.

[@factorylad5071]

Wasn't Hitler a bit of a bully then?

[@martinsanchez4827]

Same way Germans were like during the Austrian painter's reign.

[@GrayBlood1331]

Man, I got short of breath just listening to this guy.

[@sandmann6851]

Das war großartig. Sehr schön.

[@ArthurvanH0udt]

Leibniz Integral Rule: Pupularised by Feynman and now called Feynman's trick. Also it is my unerstanding/opinion that Leibniz had a much greater and deeper understanding of the calculus techniques than Newton had. And hence his techniques were and are much more comprehensible than Newton's flux theories.IMHO Newton derived on some techniques he needed for his planetary calculations. Leibniz was doing math "inventions". On a large scale the same, but on technique level a lot more refined.

[@Arpit.singh.]

We Indians have contributed so much is field of science but we never get shout out for that.

[@hjalmarschacht2559]

There ought not be any "controversy" here. LEIBNIZ invented calculus and differential equations as we know them today, and as they are taught today, including the notations we use. The Newton crowd should get used to it.

[@043mehdi]

LEIBNIZ keks part was hilarious :D one of my favorite biscuit here in Germany

[@gogetasaiyan5756]

Sir!!II Is your debate will Newton over by now lol.

[@ARKHAMxMaverick]

Didn't think it was possible to think I was any dumber, then I watched this video.

[@chegrane]

Good video, you forget to mention Alhazen (Ibn_al-Haytham) who also contribute in this. At the beginning of the video you mention the ancient greek, the indian, then the european. But you forget Alhazen. { Alhazen (c. 965 - c. 1040 ce) derived a formula for the sum of fourth powers. He used the results to carry out what would now be called an integration of this function, where the formulae for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid. } en.wikipedia.org/wiki/Calculus#History en.wikipedia.org/wiki/Ibn_al-Haytham

[@chetangolconda5339]

why they discovered

[@EveningT]

I realise the calculus historical you present is not meant to be an exhaustive one, but you might have mentioned the Persian/Arab polymath Ibn al-Haytham, the first person thought to have integrated a 4th degree polynomial, in the 11th century.

[@billyrupin]

The naturally occurring relationships "that had always been" were indeed discovered. However, mathematics consists of entirely human created systems, and as such calculus and all of mathematics is invented, not "discovered".

[@empemitheos]

Leibniz visited England and had many pieces of information that he likely based calculus on, come on, you really think 2 people by coincidence discovered the same thing within just a few years of each other, that no one else came up with in thousands of years of human mathematics? It's just like when the Wright Brother's wing designs got stolen or when some of Tesla's inventions were stolen, there are only some rare cases of the same invention or technique being done at the same time, but because we have a backwards peer review system that prioritizes who published first, Leibniz got credit for it, recently some notes have been discovered that directly show how Leibniz used Newton's work to create his version of calculus