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16 year old solves 300 year old problem set by Isaac Newton 
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#1
May2712, 08:47 AM

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mobile.news.com.au/breakingnews/world/germanteenshouryyaraysolves300yearoldmathematicalriddleposedbysirisaacnewton/storye6frfkui1226368490521
m.heraldsun.com.au/news/breakingnews/germanteenshouryyaraysolves300yearoldmathematicalriddleposedbysirisaacnewton/storye6frf7k61226368490521 I am still trying to figure out what the original problem was. Any thoughts on this? 


#2
May2712, 09:40 AM

P: 538

I find it hard to believe a problem like that "stumped" mathematicians (and physicists too, I guess) for this long, only to be solved by a 16 year old kid.



#3
May2712, 09:48 AM

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Whatever it was, it won him 2nd prize in a competition and it has been published  but I don't read German well enough to spend time finding any more. http://en.wikipedia.org/wiki/Shouryya_Ray



#4
May2712, 10:00 AM

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16 year old solves 300 year old problem set by Isaac Newton
The article's only citation is to an Indian news website which repeats the claims of the British tabloid The Daily Mail. This is not a reliable source. —Psychonaut (talk) 11:23, 27 May 2012 (UTC) 


#5
May2712, 10:02 AM

P: 2,179

The problem is to calculate the trajectory of a body thrown at an angle in the Earth's gravitational field and in a Newtonian fluid. His paper claims to be the first analytical solution to the problem.



#6
May2712, 11:12 AM

P: 406

Arnold claims that the 1st order equation which the system reduces to is soluble by the method of variation of parameters, but when he says something like this you always get the impression he's ducking out. But what do you know, Wolfram alpha solves it so I assume the method must work eventually. Maybe the solution here is for more complicated force laws, or for a particle which perhaps has angular momentum or something? Of course, it's also possible that everyone (outside of Russia) simply forgot that the solution had ever been found. 


#7
May2712, 01:31 PM

P: 18

How do they know he figured out the actual solution if it has stumped mathematicians for so many years? That said, things like this have happened. There was a woman who, purely by random chance, figured out how to solve some kind of mathematical color theorems that had stumped mathematicians for many years.



#8
May2712, 02:40 PM

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#9
May2712, 04:34 PM

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Mathematica does solve this equation down to an integral which probably cannot be evaluated analytically. 


#10
May2712, 04:41 PM

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While the computer translation in AlephZero's post is a bit funny, it contains everything relevant. The actual problem and the solution are not given. 


#11
May2712, 07:10 PM

P: 2

I've also been searching high and low for his paper, to no avail, though I did run across one photo of him holding his equation, which looked quite simple for such a vicious problem. (The drag on a projectile is a function of the velocity squared (with caveats), and the velocity decreases based on the drag. The current method of solving the problem is iterative interpolation using data from standard reference projectiles.)
From some other references, I gather he approached it as a damping problem, mentioning attempts at it by Hertz and Stokes. 


#12
May2712, 08:14 PM

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I'm having deja vu  this just happened a few months ago.



#13
May2712, 09:01 PM

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If he has achieved anything significant on the contact/impact problem, I would be professionally interested in seeing it. Modelling this numerically as part of a larger mechanical system is usually a PITA. 


#14
May2712, 09:38 PM

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Here is the correct solution: http://www.wolframalpha.com/input/?i...cos%28a%29%3D0. Note that the solution contains a definite integral. What about that definite integral? As an indefinite integral, Wolfram alpha just gives up . http://www.wolframalpha.com/input/?i...x%29%5Ek%29*dx As a definite integral it times out. 


#15
May2712, 10:23 PM

P: 1,583

It seems like either something important (I'm not sure what) has just happened, or this is just another baseless tempest in a teapot manufactured by the media. But see here. They're claming that a 16year old kid named Shouryya Ray just solved a problem posed Newton centuries ago, concerning the trajectory of a particle in the Earth's gravitational field subject to air resistance. They're also claiming that in the course of his work, he solved a problem of linear damping in a Newtonian fluid posed by Stokes in 1850 and another linear damping problem concerning collision of a ball and a wall posed by Hertz in 1858. Apparently for this work he won 2nd place in the national high school science competition in Germany.
Here's the abstract or description of his work (via Google Translate): 


#16
May2812, 12:15 AM

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#18
May2812, 12:36 AM

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My main point still stands: Wolfram alpha (Mathematica) occasionally makes some absolute howlers. It assumed [itex]\frac{du}{da}[/itex] meant [itex]\frac{\partial u(k)}{\partial a}[/itex]. It then assumed that since u is a function of k that this means [itex]\frac{\partial u(k)}{\partial a}=0[/itex]. That is a howler. 


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