Teenager solves 300 year old Newton puzzle

[mr friendly guy]

outstanding

German teen Shouryya Ray solves 300-year-old mathematical riddle posed by Sir Isaac Newton


A GERMAN 16-year-old has become the first person to solve a mathematical problem posed by Sir Isaac Newton more than 300 years ago.
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.

Mr Ray won a research award for his efforts and has been labeled a genius by the German media, but he put it down to "curiosity and schoolboy naivety".

"When it was explained to us that the problems had no solutions, I thought to myself, 'well, there's no harm in trying,'" he said.

Mr Ray's family moved to Germany when he was 12 after his engineer father got a job at a technical college. He said his father instilled in him a "hunger for mathematics" and taught him calculus at the age of six.

Mr Ray's father, Subhashis, said his son's mathematical prowess quickly outstripped his own considerable knowledge.

"He never discussed his project with me before it was finished and the mathematics he used are far beyond my reach," he said.

Despite not speaking a word of German when he arrived, Mr Ray will this week sit Germany's high school leaving exams, two years ahead of his peers.

Newton posed the problem, relating to the movement of projectiles through the air, in the 17th century. Mathematicians had only been able to offer partial solutions until now.

If that wasn't enough of an achievement, 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.

Both problems Mr Ray resolved are from the field of dynamics and his solutions are expected to contribute to greater precision in areas such as ballistics.

Firstly, outstanding.

Secondly, how will this actually influence things like ballistics. Does air resistance really makes that much of a difference to missiles?

[Surlethe]

I wish they'd actually said what the problems are, and how he solved them. Or at least given a link to an arxiv paper or something.

Is this relevant? http://www.jufo-dresden.de/projekt/teil ... theinfo/m1

[Dave]

Secondly, how will this actually influence things like ballistics. Does air resistance really makes that much of a difference to missiles?

I got the impression this was solely for objects on a ballistic path, not powered flight. But yes, air resistance does significantly affect the path of projectiles (including missiles).

Our approximations of the effects of air resistance presumably get us pretty close to the 'correct result' (you know, in the "6-7 decimal range that is entirely adequate for engineers but drives the mathematicians nuts" way). However, I expect these results only hold for very short amounts of time, and you have to re-run the calculation for each tiny piece of the trajectory. If the trajectory is changing (either because of turbulence, or because air resistance didn't do exactly what you approximated, or you're thrusting in one direction or another), you have to re-run all those calculations again, over and over again, as the variables change. (But we can do that cheaply, because we have cheap, fast computers now. It didn't used to be that way.)

My almost entirely un-informed opinion is that this will probably lead to some minor improvements in ballistics (allowing us to model more of the trajectory for less computational time before real-life shakes things up again and we have to re-approximate), but there may be other gems in the model that have applications to aerodynamics.

EDIT: Someone on Reddit found the following image of the discoverer and some of the math: https://www.jugend-forscht.de/index.php ... /6038.4568

[Colonel Olrik]

I wish they'd actually said what the problems are, and how he solved them. Or at least given a link to an arxiv paper or something.

Is this relevant? http://www.jufo-dresden.de/projekt/teil ... theinfo/m1

Yes. I'll translate the important bits for you.

The title of his presentation is analytical solution of two fundamental Particle dynamics physics problems. The first is the analytical solution for the trajectory of a ballistics all in Newtonian free flight in the presence of newtonian fluid resistance. The second is the solution for the impact of a ball on a wall with linear damping And hertz collision force.

To those wondering if this has an impact in missile or aircraft development, right now I think that the answer is no, or not very significant. We can perfectly compute the trajectory of a missile travelling at high Mach numbers with the required precision with the help of approximation algorithms and aerodynamic draft and lift tables. Besides, at this speeds the flow is not Newtonian and the projectiles usually have 6 degrees of freedom, i.e. are not balls. I'll love to read his papers, though.

[Surlethe]

Thanks. I wonder if his solution is closed-form. As far as computation, I guess the only reason this would be useful is if the solution has an expansion that converges faster than the approximation algorithms.

[Sarevok]

Would this mathematical achievement be more useful practically if it came earlier, say during 19th century ?

[CaptainChewbacca]

Would this mathematical achievement be more useful practically if it came earlier, say during 19th century ?

A bit, but I don't think his solution works in an environment where air density varies (i.e. outdoors). Still, someone get this kid a Fields Medal.

[Winston Blake]

It seems impressive. However it's hard for me to tell whether this problem went unsolved for 300 years because (a) the greatest minds of every era grappled with it and walked away broken men or (b) it just isn't very interesting or useful. There was a time when the survival of nations depended on the power of their battleship fleets, a significant element of which was fire control. So if it was 'interesting' it should have been studied madly by ballistics experts yonks ago.

Still, even if the solution is useless, I still wish I had found it.

[PeZook]

However, if the kid wants to, he has an open career path laid bare before him, and might go on to develop lots and lots of very useful things in his lifetime

[Surlethe]

Here is a Math.StackExchange question-and-answer on the problem he solved. The first answer is particularly descriptive.

[ChaserGrey]

http://www.reddit.com/r/math/comments/u ... ng/c4szzld is linked off of the post Surlethe linked to, and in turns leads to a paper on the subject published in 1977. Basically, the guy back then got most of the way to the solution, but ended up with a really hairy integral and approximated a solution rather than solving the problem. Ray actually solved the problem out. Not Fermat's Last Theorem by any means, but as everyone else has noted it's still damn impressive for a 16 year old. I strongly suspect we've not heard the last of Mr. Ray.

Edit to add: Frankly, I don't think it's that important whether the problem was "mostly" solved or not, because it doesn't sound like Ray was aware of the 1977 paper. Independently re-deriving and extending the work is just as impressive. I know I could never do it.

[Eternal_Freedom]

I may well be barking up the wrong tree on this here, but if this "unsolvable" problem has been now solved, does this raise the possibility that other unsolvable might actually be solvable?

[Grog]

I may well be barking up the wrong tree on this here, but if this "unsolvable" problem has been now solved, does this raise the possibility that other unsolvable might actually be solvable?

There was nothing particularly unsolvable about this problem. It might have been unsolved before, there are lots of unsolved problems in math that become solved. It is what mathematicians do.

[Ziggy Stardust]

Maybe I am misunderstanding some of the details in the link Surlethe provided (I am skimming it, not reading it thoroughly), but it seems to me that this problem wasn't unsolved because it was particularly impossible, but that nobody had ever really bothered to work it through all the way.

I mean, the breakdown of the derivation/solution doesn't seem to contain any unusual tricks or clever moves, it all seems like pretty basic math, just being applied to a complex equation. Not that it isn't impressive, I could never do it, but it seems more like just a matter of everyone else that saw the problem just said, "Man, I do NOT feel like doing all THAT work."