# 16 year old solves 300 year old problem set by Isaac Newton

by surajt88
Tags: isaac, newton, solves
P: 76
mobile.news.com.au/breaking-news/world/german-teen-shouryya-ray-solves-300-year-old-mathematical-riddle-posed-by-sir-isaac-newton/story-e6frfkui-1226368490521

 Shouryya Ray worked out how to calculate exactly the path of a projectile under gravity and subject to air resistance, The (London) Sunday Times reported. The Indian-born teen said he solved the problem that had stumped mathematicians for centuries while working on a school project.

m.heraldsun.com.au/news/breaking-news/german-teen-shouryya-ray-solves-300-year-old-mathematical-riddle-posed-by-sir-isaac-newton/story-e6frf7k6-1226368490521

 Mr Ray has also solved a second problem, dealing with the collision of a body with a wall, that was posed in the 19th century.

I am still trying to figure out what the original problem was. Any thoughts on this?
 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.
 Engineering Sci Advisor HW Helper Thanks P: 7,119 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
Emeritus
PF Gold
P: 16,091
16 year old solves 300 year old problem set by Isaac Newton

 Quote by AlephZero 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
Read the talk page. At this moment:
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)
yeah, I'm seeing this story everywhere but Can't find any details on the actual math involved.144.132.197.230 (talk) 11:38, 27 May 2012 (UTC)
Where is the maths problem and what was his solution? 220.239.37.244 (talk) 11:44, 27 May 2012 (UTC)
ha I guess I am not the only one looking for the problem. It's just annoying when you hear something like an unsolved problem in physics and they don't tell you the actual problem. — Preceding unsigned comment added by 76.197.8.154 (talk) 12:17, 27 May 2012 (UTC)
Page should be deleted and recreated some time in the future if the story turns out to be true. It's too soon and Wikipedia is not a news source. There should also be a verifiable citation of the nature of the two problems in question and that they actually were regarded as unsolven previously. 82.6.102.118 (talk) 14:02, 27 May 2012 (UTC)
 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.
P: 406
 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.
In "Mathematical Aspects of Classical and Celestial Mechanics", Arnold & co. claim that this problem was solved by Legendre for a wide class of power law resistance terms of the form $$c v^\gamma$$. The extract is attached.

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.
Attached Files
 extractmethods_classical_celestial.pdf (248.8 KB, 146 views)
 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.
Engineering
HW Helper
Thanks
P: 7,119
 Quote by AlephZero 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
 Quote by Hurkyl Read the talk page....
This seems to be the primary source for the story. http://www.jufo-dresden.de/projekt/t...r/matheinfo/m1 Computer translation:

 Category: Mathematics/computer science Supervisor: Prof. Dr.-ing. Jochen Fröhlich, Dr.-ing. Tobias Kempe Type of competition: Young researchers Prizes won: •2nd place in the State contest •National winner •Regional winner for the best interdisciplinary project Two problems of classical mechanics have withstood several centuries of mathematical effort. The first problem is therefore, to calculate the trajectory of a slanted raised body in the Earth gravity field and Newtonian flow resistance. The underlying power law was already discovered by Newton (17th century). The second problem, the goal is the description of a particle-Wall collision under Hertz'scher collision force and linear damping. The force of the collision was already in 1858 derived from Hertz, a linear damping force is known since Stokes (1850). This work is the analytical solution of this so far only approximate or numerically solved problems so to the objectives. First the two problems in the context of generalized solved full analysis, these are then compared with numerical solutions and finally starting inferred statements about the physical behavior of the analytical solutions.
Without seeing his actual competition entry, comparing it with any previous work is just speculation IMO. Perhaps the press is ignoring the second problem because it doesn't have an nice headline like "Indian kid is smarter than Newton".
P: 2,470
 Quote by ObsessiveMathsFreak But what do you know, Wolfram alpha solves it so I assume the method must work eventually.
Alpha solves it because it interprets your equation for u[k], rather than u[a]. Partial u with respect to alpha is zero, in this case, so naturally, solution is just the remainder of your equation, which is a non-differential equation. You really should never rely on Alpha to interpret your equations correctly. Always double-check. Better yet, skip Alpha and use Mathematica.

Mathematica does solve this equation down to an integral which probably cannot be evaluated analytically.
Mentor
P: 11,837
 Quote by CAC1001 How do they know he figured out the actual solution if it has stumped mathematicians for so many years?
Solving problems can be tricky - checking the solution is usually much easier.

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.
 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.
 Mentor P: 22,288 I'm having deja vu - this just happened a few months ago.
Engineering
HW Helper
Thanks
P: 7,119
 Quote by gturner6ppc From some other references, I gather he approached it as a damping problem, mentioning attempts at it by Hertz and Stokes.
I took the computer translation as meaning they were essentially two separate problems, the second one being Hertzian contact with the wall (including some model of energy loss during the impact).

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.
Mentor
P: 15,155
 Quote by ObsessiveMathsFreak But what do you know, Wolfram alpha solves it so I assume the method must work eventually.
It's always a good idea to check whether Mathematica made some amazingly dumb mistake. And it did.

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.
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 16-year 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):
 Two problems in classical mechanics have withstood several centuries of mathematical endeavor. The first problem is therefore to calculate the trajectory of a body thrown at an angle in the Earth's gravitational field and Newtonian flow resistance. The underlying power law was discovered by Newton (17th century). The second problem is the objective description of a particle-wall collision under Hertzian collision force and linear damping. The collision energy was derived in 1858 by Hertz, a linear damping force has been known since Stokes (1850). This paper has so far only the analytical solution of this approximate or numerical targets for the problems solved. First, the two problems are solved fully analytically generalized context, they then compared with numerical solutions and, finally, on the basis of the analytical solutions derived statements about the physical behavior.
P: 2,470
 Quote by D H Here is the correct solution: http://www.wolframalpha.com/input/?i...cos%28a%29%3D0. Note that the solution contains an integral equation. What about that integral equation? Wolfram alpha gives up on that. http://www.wolframalpha.com/input/?i...x%29%5Ek%29*dx
That's not an integral equation. That's just an integral.
My main point still stands: Wolfram alpha (Mathematica) occasionally makes some absolute howlers. It assumed $\frac{du}{da}$ meant $\frac{\partial u(k)}{\partial a}$. It then assumed that since u is a function of k that this means $\frac{\partial u(k)}{\partial a}=0$. That is a howler.