Can high school students know calculus better than Newton?

[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.