Can high school students know calculus better than Newton?

[arildno]

A simple test to verify your assertion is to see how many theories have been written by graduate students in the last 20 years that are comparable to the output of Bohr, Einstein, Newton, Leibniz, et al.

Or just produce something groundbreaking youself, Jose.

Oh, dear!
I had forgotten all about that idiot.
It's probably Jose in a new disguise..

Have you proved the Riemann hypothesis by means of asymptotic series expansions yet, dear?

Done another pointless function transformation to get a worthless integral expression?

 

[Klaus_Hoffmann]

Don't know who is this 'eljose' you are talking about.. no idea.

If Quantum Gravity and RH were soo easy involving only calculus or Fourier series is 100% sure it would have been discovered many years ago

 

[Gib Z]

If possible i would like to write some arguments supporting my ideas

1) Upto 1800 (but some exceptions) many math problems involved Calculus II or Algebra (without groups and similar) as you will have seen through the forum many users claimed having 'discovered' identities involving $$\zeta (s)$$ and prime-generating functions.. many of them proved by Euler or others, --> If a problems involves 'simple' math anyone can give the solution)

2) Many recent theorems or proofs of 'Poincare Conjecture' (Perelman) or 'Fermat theorem for every n>3' (Wiles) involved hard math , that is not avaliable for many of us, however the math at Newton's time was easier to understand and work with, you and me can understand reading a book the Zeta regularization (Ramanujan sum), or Borel resummation.. but i really believe that there will be only a few people understanding Cohomology, Diff. Geommetry or C*-Algebra and Functional Analysis.

3) Are Newton an Einstein really GENIUSES?.. calculus had been previously defined and invented by others such us Fermat ( a lawyer ¡¡) Leibniz,Gregori,Descartes... and SR was also 'invented' by Poincare, Lorentz, MInkowski, Hilbert himself even derived Field equation with a Variational principle

1) Re discovery is not pointless and IMO, actually can show signs of mathematical insight. If someone is able to rediscover a certain theorem and prove it, without knowledge of the theorem, then they have 'original' though, using the word in the sense of using new ideas to the student.

2) What basis do you have to make your comments? In Newton's time, Calculus would definitely have been a daunting concept for the people of the time. (This point is good because it relates to the thread). The only reason it seems easy to us now because of so many people making the calculus more rigorous etc etc. The concept of a limit would have been difficult back then, as would operations with differentials and a seemingly unintuitive Fundamental Theorem of Calculus, especially with the integral not even being defined properly yet.

3) Genius is opinion, but there is so much else wrong with that point. Since when did Fermat invent and define Calculus? Fermat contributed to certain ideas that are now linked with Calculus, but so did the Islamic Scholars, Ancient Greeks, Descartes, Kepler, Roberval, Hudde and Sluse. (The last 3 names are not really known because their methods of finding tangents were for specific cases and complex, soon to be made obsolete by Calculus). However it was Newton and Leibniz who related all of these problems back to one field of mathematics, and did even more. (I believe Leibniz did develop it independently, but definitely later than Newton).

And Special Relativity was not invented by those people..Lorentz definitely made his transforms, but Pioncare contributed to differential geometry. Just because that is used in SR does NOT mean he contributed to the Theory. Not to mention, you make it obvious you just shove out any names you can think of when you hear SR, as Minowinski only invented the convenient co-ordinates to work with in SR, which is not inventing SR. Also, he did after SR was published. And the whole theory is not based on a single Variational principal, so Hilbert did contribute but not as much as you wish to make it seem.
PS. To your last Post, you don't sound too believable mate. No one mentioned an "eljose", just Jose...

And Yes, QG and RH require more powerful mathematical tools than previous theories. But It seems to me you know nothing of physics..which requires physical evidence and observation to bring about a need for a theory. QG is not purely mathematical, it needs physical observations which could not be made many years ago. Heck, we didn't even know about quarks 30 years ago.

And it surprises me that you know RH needs very powerful mathematical tools, because you still try to attack it with techniques that I can understand (which means its far too simple).

 

[arildno]

Don't know who is this 'eljose' you are talking about.. no idea.

If Quantum Gravity and RH were soo easy involving only calculus or Fourier series is 100% sure it would have been discovered many years ago

Hmm..if you don't know who "eljose" was, how could you know his username??

It has never been mentioned in this thread, eljose..

 

[ice109]

this discussion belongs in the lounge section, or philosophy, as there is no mathematics in it.

this is like asking whether mohammed ali would have beaten rocky marciano, it is endless, negative, and depressing. look where we are letting ourselves be led by this.

the answer is no.

everyone has ignored you but i on the other hand ignored everyone but you. personally i like the question of bruce lee v tyson better than ali v marciano. and yes this is a silly silly question that is more about ego than real discourse

 

[arildno]

I have not ignored mathwonk, but it is difficult to match his excellence in writing so I won't sully his comments with my pathetic excuses for replies.

 

[FrogPad]

I thought Chuck Norris invented calculus?

 

[turbo]

I thought Chuck Norris invented calculus?

No, he just honed it to the lethal study it is today.

 

[matt grime]

Klaus's point 2 is precisely the kind of thing that Jose would write. Notice the implication that mathematics is a closed shop keeping people out. Wiles's proof is freely available to all. Firstly because the Annals encourages posts to the arxiv, though I've not checked if they put Wiles's paper there. But that is immaterial because it now occupies a book that anyone can buy or order or obtain from their local library if they really wanted to.

More on point 2: many many more people know and understand cohomology than Borel resummation and zeta renormalization - I don't even know what those terms mean, nor would almost any mathematician I spoke to, but most of them would know what a cohomology group was. Hilbert knew what they were, if we're going for the classics. Even a 'high schooler' knows what they are, though they do not know it. Consider the maps of vector spaces

0-->V--f-->W-->0

the failure of f to be injective is measured by a cohomology group, the failure of it to be surjective is measured by the cohomology group. It is just the kernel and cokernel of the map, and the failure of a system of linear equations to have a unique solution is taught in high school - if there are infinitely many solutions then we're saying that the first cohomology group is non-zero (assume W is in degree 0).

Plus I'm not sure that I would ever believe a claim made by you to 'understand' what you'd read about Borel resummation or the like. Sorry, but you've not demonstrated any understanding of anything you've posted here.

 

[robert Ihnot]

Well, I am sure I understand the Calculus much better than Archimedes did. Is this something to argue over?

If your interested in what Newton knew, you can always get a copy of Principia in the library. Won't cost any thing there to look! And if your interested in Einstein, his 1905 paper is readily available on the internet.

 

[robert Ihnot]

Part of the confusion is over a "Name Theorem" such as Fermat's Little Theorem, which many--especially when he takes Number Theory and has the tools--might stumbled on. The student then has an chance to compare his ability with Fermat, but, of course, this is not what is really involved. Even so, the instructor may encourage such thinking.

Gauss, when a mere schoolboy and was asked to add up the first 100 integers, was able to do so immediately. This was very unexpected since the teacher hoped to leave the class alone for an hour or so.

I was under the impression, as it was explained to me, that Gauss actually was the first to discovered the formula for this sum; but, of course, it must have been know long before that. However, it is a nice to believe you can keep up with the great mathematician Karl Fredrick Gauss.

 

[duke_nemmerle]

As far as I can tell we should listen to mathwonk.

 

[Johan de Vries]

More on point 2: many many more people know and understand cohomology than Borel resummation and zeta renormalization - I don't even know what those terms mean, nor would almost any mathematician I spoke to

For physicists this is different. I think that a large minority of advanced theoretical physics students know what Borel Resummation means. The difference between physics and mathematics is that in physics you learn to actually calculate things.

Borel resummaton is a basic tool allowing you to resum the divergent tail of an asymptotic series. There are other tools for resummation like Pade methods etc. etc. Physics students are told told about such methods when they study statistical physics and field theory.

 

[arildno]

Part of the confusion is over a "Name Theorem" such as Fermat's Little Theorem, which many--especially when he takes Number Theory and has the tools--might stumbled on. The student then has an chance to compare his ability with Fermat, but, of course, this is not what is really involved. Even so, the instructor may encourage such thinking.

Gauss, when a mere schoolboy and was asked to add up the first 100 integers, was able to do so immediately. This was very unexpected since the teacher hoped to leave the class alone for an hour or so.

I was under the impression, as it was explained to me, that Gauss actually was the first to discovered the formula for this sum; but, of course, it must have been know long before that. However, it is a nice to believe you can keep up with the great mathematician Karl Fredrick Gauss.

The genius of Gauss lies of course in that he, as a mere, ignorant school-boy thinks out FOR HIMSELF how to do this sum.

It is totally irrelevant if Descartes or any other mathematician knew of this formula, since little Gauss didn't know any of their works.

It is the originality, individual creativity and independence that are the marks of genius not which type of problems is being solved.

 

[Klaus_Hoffmann]

About 'Calculus' there is a deep irony, 3 hundreds years ago Calculus (real variable) was the deepest tool to solve problems, in Physics we afford a similr problem too,.. functional integration could help solving many deep results in theoretical Physics but nobody knows how to perform it (excpet for Gaussian case).

And today 'originality' is very hard to find, almost any idea you or other people from the forum may have has ocurred to famous mathematician before, as an example (without critizying him) many of the methods by Ramanujan were 'invented' before him by Euler, Gauss or other.. of course I'm not saying he had no merit

 

[matt grime]

For physicists this is different.

Possibly. But we're all guilty of extrapolating what we know too far.

I think that a large minority of advanced theoretical physics students know what Borel Resummation means.

and they ought to know what cohomology is too, since it is a very common tool in large parts of theoretical physics these days, albeit often in disguise. Indeed it even comes in in engineering/applied maths very early: the fact that every conservative field in a simply connected domain is grad of something is a fact about cohomology, for instance. It is just saying that a certain homology group is trivial (the image of grad is equal to the kernel of curl).

 

[robert Ihnot]

Kummer: Mathematicians of today, stand on the works of Cantor/Kummer/Kronecker/Poincare/Hilbert... Those mathematicians stood on the works of Weierstrass/Galois/Abel/Riemann/Gauss... Those mathematicians stood on the works of Laplace/Lagrange/Legendre/Euler/Bernoulli/Fourier... Those mathematicians stood on the works of Newton/Leibniz. Those mathematicians stood on the work of Fermat.

I stop at Fermat because the era of Fermat and Descrate was the rise of the modern age of mathematics
Oh, but Fermat left his famous margin notes in Arithmetica of Diophantus.
Written something like 250 A.D.

Wikipedia says: The findings and works of Diophantus have influenced mathematics greatly and caused many other questions to arise. The most famous of these is Fermat's Last Theorem. Diophantus also made advances in mathematical notation and was the first Hellenistic mathematician who frankly recognized fractions as numbers.

 

[Kummer]

As far as I can tell we should listen to mathwonk.

Yes, we should, he is perhaps the most experienced coffee turning machine here.

So, the answer is "No".

 

[Haelfix]

I'd say the vast majority of physics grad students know what cohomology is, or at least remember where to look it up in their notes. Its fundamental in modern quantum field theory.. I can't imagine it not showing up in some shape of form somewhere in their studies.

 

[uiulic]

but I would say the person who invented the wheel is 'smarter' than the Chinese people who invented the rocket, or the Person who invented the mobile phone. Can you appreciate that?

Gib_Z : I suspect there is racialism in your statement.

 

[Gib Z]

>.< Thats actually quite funny but 64% of the people in my grade are Chinese or Korean, and a lot of them are my friends. I have nothing against them, I just happened to know that it is the Chinese who invented the Rocket. Anyway, how do you know the Chinese didn't invent the wheel?

 

[uiulic]

Gib_z,

1 I don't mean you, as a human being, have it. But your example (by chance or not) indicated it.

2 Your example "would say the person who invented the wheel is 'smarter' than NEWTON AND EINSTEIN" would be what you mean BETTER? A dog is "smarter" than a common human being in smell, you agree?

You are comparing what you can with what others can't.

3 "I just happened to know that it is the Chinese who invented the Rocket. Anyway, how do you know the Chinese didn't invent the wheel?"

WHAT IS THE POINT OF THIS QUESTION?YOU HAPPEN TO KNOW WOT?

 

[Gib Z]

1. Well I didn't mean it, sorry if you thought I did.

2. I don't seem to understand you, sorry.

3. I said that to show that if a Chinese person DID invent the wheel, there was no racialism in the statement. Since I don't rule of that a Chinese person did invent the wheel, It is further evidence that the statement was is no way intended to be racist..

 

[uiulic]

GIB_Z

First, you don't even know who invented rocket. HOWEVER you said it is the Chinese people...

Second, your "further evidence" is very funny. You seem to want to show this: the whole Chinese people invented rocket, but some Chinese invented the wheel;; since the whole Chinese includes a Chinese, the statement itself was not a reasonable statement. You know the difference between a people and a person? Your further evidence just makes the problem more complicated.

Third, I just want to point out the unreasonable logic which may exist in your current and old statements. And your further evidence turned out to confirm the illogic reasoning.

Finally, I won't respond further for this issue, as I don't want to ruin the original thread.

 

[Integral]

this discussion belongs in the lounge section, or philosophy, as there is no mathematics in it.

I agree.

Thread moved.

 

[Klaus_Hoffmann]

the 1000000$$ dollar question is.. if Einstein and others were sooo smart why are there still unsolved problem in physics ??.. I'd be also a genius if i had mathematician like Hilbert Poincare or similar working on my side ¡¡¡ .. Newton and Einstein were the LUCKIEST (at least speaking from scientific point of view) men in the history easy problems --(except GR of course but with a good mathematician you can understand almost everything) and easy solutions.

The main problem for us (physicist) is the vast complexity of actual theories.. you can deduce the Uncertainty relations for (x,p) and (t,E) from Fourier Analysis, but 'Standard Model' of particles need heavy courses of Group theory not to mention that 'Functional integrals' are impossible to solve and so on NO way :(

 

[Darkiekurdo]

There still are unsolved problems in physics because the mathematics to solve those problems is not (yet) created. I think.

 

[Jimmy Snyder]

Of course we know more than he did. We have the shoulders of a bigger giant than he had.