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## 350-Year-Old Newton's Puzzle Solved By 16-Year-Old414

First time accepted submitter johnsnails writes "A German 16-year-old, Shouryya Ray, solved two fundamental particle dynamic theories posed by Sir Isaac Newton, which until recently required the use of powerful computers. He worked out how to calculate exactly the path of a projectile under gravity and subject to air resistance. Shouryya solved the problem while working on a school project. From the article: '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.'"
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## 350-Year-Old Newton's Puzzle Solved By 16-Year-Old

• #### That Moment (Score:5, Interesting)

on Sunday May 27, 2012 @08:38AM (#40127897) Journal

We all had that moment in school when a teacher would pose an "impossible" problem, thought to ourselves "Well, they've never faced ME before!", spent a few minutes toying with it and finally giving up. This kid...did not.

Kudos all around! The rest of your life will, unfortunately, now no longer live up to something you accomplished when you were 16.

• #### Re:That Moment (Score:5, Interesting)

on Sunday May 27, 2012 @08:48AM (#40127957)

There are two things impressive about this. One is the fact that you mention, that the kid did not give up until he had the solution and was smart enough to solve a problem that stumped every mathemetician for 350 years. The second is that people still try to solve difficult analytic problems at all instead of just turning it into a computing problem.

I don't know which surprises me more.

• #### Re:Explain the mind of a genius? (Score:4, Interesting)

on Sunday May 27, 2012 @08:48AM (#40127959)

Concepts of mathematics (calculus) are actually very simple.

Most confuse the trivia of solving problems (knowing many rules) and how to apply them with understanding of basic mathematical principles.

Teach your kid about 'x' and abstract thinking in relation to rates of change. The rest follows quite naturally. (IMO).

• #### Re:terrible article (Score:5, Interesting)

on Sunday May 27, 2012 @08:52AM (#40127977)

The article itself is mathless. It doesn't tell you what the solution was, or even present the exact problem that was solved.

And running a search for the kid's name turns up the same article fifty fucking times over. Google did some work on link farms... they need to do some work deduping / despamming press releases.

• #### Re:Specifics? (Score:5, Interesting)

on Sunday May 27, 2012 @09:10AM (#40128079)
The problem he solved is determining the exact path of a projectile, when accounting for air resistance. The drag coefficient for air resistance depends nonlinearly on velocity, so when it is included in the model the equations become difficult to solve (previously impossible, but apparently now done. Though I haven't found any links to his actual work). Here [aw.com] is an example of setting up the problem, and then solving it numerically.
• #### Re:are those problems NP? (Score:5, Interesting)

on Sunday May 27, 2012 @09:12AM (#40128089)
The problems he solved are not NP. They are essentially calculus, but they are both very nasty calc problems, and the traditional way to solve calc problems is using newton approximations until the answer is close enough to what you want. An analytical / precise way to solve these problems is extremely useful to the physics folks, as the solution will probably also lead to better models of particle motion.

-=Geoskd
• #### Re:Gotcha! (Score:5, Interesting)

on Sunday May 27, 2012 @09:13AM (#40128097) Journal

On a sad note, he only placed 2nd in the overall competition :(

• #### Re:Explain the mind of a genius? (Score:2, Interesting)

on Sunday May 27, 2012 @09:14AM (#40128103)

I'll bet you that any 6 year old can solve the problem of where a ballistic projectile will be, even accounting for air resistance, in real time without a computer.

Don't believe me? Toss them a ball. The rest is just notation.

• #### Re:That Moment (Score:5, Interesting)

on Sunday May 27, 2012 @09:23AM (#40128141)

Germany still produces some rays of light.

To be accurate... he was born in India and moved to Germany with his family at age 12. He did not speak a word of German when he arrived.

While credit must be given to the German school system, I think most of his accomplishment comes from him and possibly his family.

And maybe from not being in Europe or the western world the first twelve years of his life, adopting beliefs or creating a mental attitude that stuff like this cannot be done. And I'm not criticizing the Germans.

• #### Fermat & Poincaré (Score:5, Interesting)

on Sunday May 27, 2012 @09:27AM (#40128165)
Andrew Wiles solved Fermat's Last Theorm with paper only, as he despised the use of computers in writing mathematical Proofs. Another famous example is Grigori Perelman who solved the Poincaré Conjecture - with hundreds and hundreds of pages of mind-numbingly dense mathematics vs computer search.
• #### Re:Gotcha! (Score:5, Interesting)

on Sunday May 27, 2012 @09:51AM (#40128297)

Number one cured cancer AND solved the world's energy problem. That's hard to top. :)

• #### Re:Fermat & Poincaré (Score:5, Interesting)

on Sunday May 27, 2012 @09:54AM (#40128309) Homepage

Another famous example is Grigori Perelman who solved the Poincaré conjecture - with hundreds and hundreds of pages of mind-numbingly dense mathematics vs computer search.

Perelman's three primary papers ("The entropy formula for the Ricci flow and its geometric applications" http://arxiv.org/abs/math.DG/0211159 [arxiv.org], "Ricci flow with surgery on three-manifolds" http://arxiv.org/abs/math.DG/0303109 [arxiv.org], and "Finite extinction time for the solutions to the Ricci flow on certain three-manifolds" http://arxiv.org/abs/math.DG/0307245 [arxiv.org]) on modifying Hamilton's Ricci flow program to deal with singularities and proving Thurston's geometrization conjecture only span 68 pages, with the actual proofs/meaningful remarks comprising about 45 pages of that.

by Anonymous Coward on Sunday May 27, 2012 @09:57AM (#40128331)

I also had been told, "This problem cannot be solved analytically" in school, and even propagated this myth to my students for several years. Then I found a solution in an old dynamics book. Think of it as an "urban myth" that projectile motion with air resistance cannot be solved without a computer. Still, congratulation to this kid for working on a very tough problem which he believed to be unsolvable, and sticking with it through completion. Assuming of course that he solved it!

• #### Re:Explain the mind of a genius? (Score:5, Interesting)

on Sunday May 27, 2012 @10:05AM (#40128379)

I was not a prodigy, but a really smart kid who was in many environments with prodigies or near prodigies.

My experience has been that most pre-teen children with this history don't understand the material very well, and there tends to be a lot of exaggeration about it. Smart kids are good at mimicking things and that is all that is really need to "do" the first year or two of college math.

Occasionally, but very occasionally you get someone really young who later goes on to do decent, or even more rarely great things, like Norbert Wiener or Terry Tao. But I would like to hear those people give their opinions of the depth of their understanding at that age.

I knew Nadine Kowalsky, who in HS would essentially just remember everything she heard in class and got 100 on every exam. (She wasn't the only one though. I knew a number of other people like that though that didn't do as well as Nadine did.) She later went on to get a Ph.D. from Chicago and published her thesis in the Annals of Math. That is a journal most mathematicians can't get a paper in. Like publishing in Nature or Science. Nadine was the real deal, but sadly she died of cancer not long after finishing her Ph.D. But I don't believe that Nadine was doing calculus until she was 15. And that was certainly on purpose. She, and her parents apparently, knew what was a good idea to do, and not to do, with a super smart kid. (This last sentence is conjecture on my part.)

But I think most cases of pre-teens you hear about are really not what they are made out to be. Once you get to 12 or 13 those, I think things do change a lot.

• #### Re:Explain the mind of a genius? (Score:4, Interesting)

on Sunday May 27, 2012 @10:34AM (#40128561)

The principles of differential equations are also simple and there are many simple physical systems that can be used to demonstrate them in a way that is easy to grasp. Even by relatively young children.

The idea is not to confuse the understanding of principles with their applications, as those can be (and are) horribly complex.

Math is not hard. Math is very elegant and simple. Much like language, the same words that are in children's books also comprise the classics.

• #### Re:That Moment (Score:3, Interesting)

by Anonymous Coward on Sunday May 27, 2012 @10:57AM (#40128677)
If he solved it, then WHAT IS THE SOLUTION?! There is no link, no nothing, and we are apparently to trust this lame emotional article with no factual content. I'm surprised nobody else raised this point.
• #### Re:That Moment (Score:5, Interesting)

on Sunday May 27, 2012 @12:05PM (#40129053) Journal
Also he solved it without mooching off a company for 2 months (and still having nothing to show for it) or asking for \$500,000! [slashdot.org] No \$\$\$\$ up front and he still brought results! This 16 yr old will go far, I would happily donate to this kid's next .... whatever he wants to do, since he's already earned it in my opinion.
• #### Re:Explain the mind of a genius? (Score:5, Interesting)

on Sunday May 27, 2012 @12:25PM (#40129169) Homepage Journal

Exactly. As a kid, I had a dog that understood when I threw a ball up on the roof of our garage, which caused it to disappear from her sight, that it would roll along the slope of the roof and and reappear further down the roofline. She actually got fairly good at predicting where the ball would reappear, repositioning herself along its path over time so she would meet it at its eventual drop point. Does that mean my dog understood calculus, or solved Newton's problem? Well, she recognized a pattern and was able to apply a repeatable solution.

That tells me that the brain is capable of recognizing complex patterns around us, and is actually already very capable of deriving and applying practical solutions. ("So easy a dog could do it.") Applying abstract mathematical models to them, however, is not so easy.

What I'd be most interested in in this whole saga is "what methods did his father use to teach him math?" Obviously they were highly effective.

• #### Re:Gotcha! (Score:4, Interesting)

on Sunday May 27, 2012 @01:18PM (#40129457) Homepage

Doing a reply-to-self because I checked my interpretation using a numerical simulation. I wrote some python 3 code, which does a reasonably realistic simulation of a baseball being hit for a home run. Slashdot's lameness filter wouldn't let me post it, so I put it here: http://ideone.com/yeP4y [ideone.com]

The results:

u= 36.86184199300463 v= 25.810939635797073 Ray= 0.07075915491208162 KE+PE+heat= 147.825
u= 30.646253624059415 v= 12.467830176777555 Ray= 0.07075939744839914 KE+PE+heat= 147.82340481003814
u= 26.608846983666997 v= 1.6625489055858707 Ray= 0.07075957710355621 KE+PE+heat= 147.8224303518585
u= 23.559420165753 v= -7.761841618975968 Ray= 0.08597247439794412 KE+PE+heat= 147.82171310054588
u= 20.86163826256129 v= -16.094802395195508 Ray= 0.10413207421166563 KE+PE+heat= 147.82115230900214
range= 120.88936569485678 , vs 194.17117929504738 from theory without air resistance
u= 18.25141606403427 v= -23.242506129076933 Ray= 0.12066666645699123 KE+PE+heat= 147.8207286473949
u= 15.70673363979356 v= -29.088976584679852 Ray= 0.1353850869274781 KE+PE+heat= 147.8204307883206
u= 13.30143766684643 v= -33.65200048062784 Ray= 0.14867603720136566 KE+PE+heat= 147.8202356199746
u= 11.11267911406159 v= -37.07517115834146 Ray= 0.16096016949002218 KE+PE+heat= 147.8201144079141
u= 9.186200956690504 v= -39.564763699985484 Ray= 0.17255826567110216 KE+PE+heat= 147.82004160975018

The notation is that u and v are the x and y components of the velocity vector, "Ray" is the expression that Ray seems to be claiming is a constant of the motion, and the final column is the total energy, which should be conserved.

I tested my code two ways: (1) Energy is very nearly conserved. (2) If I turn off air friction, the range is very nearly as calculated by theory.

Let R be the expression that Ray says is a constant, under my interpretation of his variables. Then dR/dt appears to be very nearly zero early on in the simulation. However, later on it starts to drift upward. So I suspect that one of the following is true: (1) Ray is wrong; (2) my interpretation of his notation is wrong; or (3) my simulation doesn't use good enough numerical techniques to demonstrate with good precision that Ray is right.

Anyone who's got Runge-Kutta, etc., on the tip of their tongue want to try a better simulation of this?

• #### Re:Specifics? (Score:4, Interesting)

on Sunday May 27, 2012 @05:01PM (#40130699)

Here's a post where someone determined what the original equations were and verified Ray's answer (in the picture of him holding a solution) in Maple:

• #### Re:That Moment (Score:4, Interesting)

on Sunday May 27, 2012 @07:58PM (#40131455)

I suspect you're thinking of the brachistochrone problem, posed by Johann Bernoulli in 1696, and solved the next day by Newton (also by several other mathematical giants of the time, very quickly).

If it happens once, it's a bug. If it happens twice, it's a feature. If it happens more than twice, it's a design philosophy.

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