350-Year-Old Newton's Puzzle Solved By 16-Year-Old 414
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.'"
terrible article (Score:5, Insightful)
The article itself is mathless. It doesn't tell you what the solution was, or even present the exact problem that was solved.
Specifics? (Score:5, Insightful)
Can anyone actually find the problems in question somewhere? I've been scouring Google and the whole thing is very vague -- no story really goes into depth about the actual problem he solved and how.
Difference between Germany and the US (Score:4, Insightful)
German media praise math geniuses, while american media praise hollywood actors/actresses (read: human rubbish) and reality show weirdos. In the US a "genius" is someone who makes millions, especially with lower education and without being able to do anything. That's "free market economy", and "supply and demand", right?
"The land of the free and of the brave" (with some fat on the belly).
Re:terrible article (Score:2, Insightful)
With all due respect to this brilliant student, I wouldn't worry too much about that - the problem isn't actually solved until its been peer- reviewed and thd other mathematicians agree that his approach is correct.
Re:That Moment (Score:3, Insightful)
While credit must be given to the German school system
Must it? The school system could be garbage and still have the occasional intelligent person go through it. Perhaps it's not the school system that must be given credit, but something else (like the child himself, for instance).
Flash journalism (Score:5, Insightful)
Think about that for a moment. A story supposedly lionizing science lacking the most basic facts that would permit substantial verification, or falsification, of that science. This is just flash journalism at work.
Re:That Moment (Score:3, Insightful)
Computing tends to be a brute force analysis of all the possible inputs. That doesn't work well for NP hard problems and is often impossible with problems dealing with infinity... Not all problems are solvable by computers yet and instead need the analytical approach. Also computers may not find the most elegant solutions, for example there are problems which have been solved but required the invention of a new type of math to do so.
Re:Explain the mind of a genius? (Score:5, Insightful)
No. The problem is to determine the trajectory from the initial position and velocity. A human tracks the ball as it moves, which is a completely different problem.
Re:Explain the mind of a genius? (Score:5, Insightful)
I was doing advanced Geometry and Algebra at age 8, yes I'm a slow fool compared to this kid. but it's mostly the quality of teachers (his dad) and the willingness to keep giving a kid what they want and challenging them.
The american school system is designed to DISCOURAGE this. Smart kids are told to be happy with the A they got without trying. If they challenge their teachers knowledge they are told they are wrong. Mostly because Grade-High-school education in the USA is simply following a lesson out of a book and not teaching it from an expert. the Gym teacher teaches computer class, The English teacher teaches Chemistry, and all of it creates a ho hum boring as hell experience for the children.
Here in the USA we do NOT want geniuses, we want good factory and office workers. Mediocre will not challenge authority.
yes I am jaded at the education system here. I was one of them that got bad grades because the teachers were idiots. I challenged my math teacher who could not believe that a kid can do multiplication and simple geometry in his head. I proved it on several occasions, but I was given failing grades for not doing the busywork of writing it all out. Plus I refused to learn his technique. It sucked and was harder than what I was using that came from college text books. So I ended up being a pissed off moody kid hating the education system because all I saw was idiots and morons trying to tell me they knew more than Me and I knew that they were wrong. I was reading at a 14th grade level when I was 12 years old. I read 1984 and understood the concepts and hidden meanings. I was devouring Vonnegut with a passion. I was told that the books were "too grown up for me" Everyone talked down to me and all it did was piss me off.
Sadly I did not have rich parents, so I had to suffer through the waste of time that the American Public School system is. College I slept through and aced it, at least they were not morons requiring me to turn in worthless busy work. It was in college where I ran into real education, educators that actually knew what they were talking about and would actually hold a discussion with me and help me learn more.
This is the problem here in the USA. If you are smart, you have a sack put over your head to slow you down to match the rest of the other students.
Re:That Moment (Score:5, Insightful)
Analytic solutions are far superior to computed approximations. They are far easier to calculate--computers have made computed approximations far easier, but most of the time that doesn't mean that they're *easy*--only that they're now possible. Being able to obtain the answer in a small fraction of the time is still a big advantage. They are more precise and do not require initial parameters. And they provide much greater understanding and insight into the underlying phenomenon. There is no surprise at all that people are still looking for analytic solutions.
Re:Explain the mind of a genius? (Score:5, Insightful)
Here in the USA we do NOT want geniuses, we want good factory and office workers. Mediocre will not challenge authority.
I've shared this and I'll share it again (and again...) but when I was in third grade I had an asshole, authoritarian teacher who I believe was only at my school for a couple of years. He was a lazy, arrogant, abusive asshole. When one was done with one's work one was to literally lay one's head down on one's desk and wait quietly for the other children to finish. I was in trouble on numerous occasions for "looking at the other children". I wrote so many lines I had wrist problems before I ever owned a computer or even discovered masturbation.
Sadly I did not have rich parents, so I had to suffer through the waste of time that the American Public School system is.
I went to a private school for a couple of years, before my parents broke up and there wasn't enough money because my dad was a deadbeat. I was about to be learning algebra, I was learning Spanish (I had great retention back then, and I never forgot some of the words I learned back then... though "ferrocarril" does have a fantastic ring to it, no?) and so on. Then I was placed literally into kindergarten due to my age and went from actually learning at a satisfying pace to being told lies about American colonization, making flags out of construction paper and placing Dead-President's-Head's stickers on them, and the like. After a year of that I spent two weeks in first grade before being bumped up to second, where I was still doing work inferior to what I'd been doing in my previous school.
This is the problem here in the USA. If you are smart, you have a sack put over your head to slow you down to match the rest of the other students.
Especially if you are smart, but your parents are dysfunctional and can't teach you how to blend in because they know fuck-all about how social situations work.
College I slept through and aced it, at least they were not morons requiring me to turn in worthless busy work.
Alas, I discovered life about the same time I went to college for the first time and besides, by that time I was prejudiced against education. What really shat upon my educational aspirations at that time, though, was a counselor who suggested I take a fully practical case load and save my electives for later. If I could remember who that was, I would send them a picture of my asshole right now. Hated it. Made school just a big bore of a chore. Most counselors don't give one tenth of one fuck about you as a person or even as a student, you're just a convenient unit that can be used to fill out slightly empty classes. What, am I bitter? Why do you ask?
Now I have a two-year degree from going back to school much later, but it wasn't convenient for me to matriculate to a four-year at the time and now what do I do with this extra piece of paper? It's too crisp to be good bumwad.
Re:That Moment (Score:5, Insightful)
Computing tends to be a brute force analysis of all the possible inputs.
Hello? We've had symbolic computing ever since 1960's. There are many software tools today to assist mathematicians with creating and verifying proofs (e.g, Coq is probably the best known one). What's wrong with using them? Not to do that would be like using a pencil and paper instead of typing when you're preparing a publication – I'd think that brain power and time should be used constructively.
Re:Fermat & Poincaré (Score:3, Insightful)
If you're doing a half page proof that square root of 2 is irrational, then a computer would be pointless, but clearly you don't know that math is more complicated than that.
And to head off potential flames, I completely respect people who want to and are able to work through those derivations by hand, but to think doing it with a computer is pointless just shows your ignorance.
Re:Explain the mind of a genius? (Score:5, Insightful)
I have to agree with your comment about learning DE, I failed differential equations the first time I took the class (a D-grade) I was taking engineering course work at the time that required them - and what they actaully "meant" clicked in an electrical networks class - when I took the class again (my university had a 1 time grade forgiveness policy) I got an A - it seemed trivial and simple the second time around in a different context. I general I have mathematics makes mroe sense to me personally when I can relate it to a real world problem - Mathematics taught as rote learning is a horrible thing - some of us can't do it that way....
Re:Explain the mind of a genius? (Score:5, Insightful)
Exactly. And I tell you, is the same thing here in Brazil.
Re:Fermat & Poincaré (Score:4, Insightful)
This is why I read /.
Re:That Moment (Score:4, Insightful)
What's wrong with using them? Not to do that would be like using a pencil and paper instead of typing when you're preparing a publication – I'd think that brain power and time should be used constructively.
It's not a matter of the tool is wrong. It's a matter that assuming one tool is always best is wrong.
Your premise is based on: using a computer is easier and better for 100% of humans. That's not true. Allow me to introduce you to my parents. Allow me to introduce you to senior engineers who can craft new formulas on a whiteboard faster than juniors can wake their laptops.
Different areas of the brain are involved with the act of handwriting than with touch typing or pecking. Make LCARS speech recognition a reality and we have a winner. Solving problems that stump otherwise intelligent humans for *hundreds* of years, *clearly* requires some creatively alternate use of the brain, and not Microsoft Clippy. ("I see you're trying to solve an unprovable theorem, would you like to Quit without Saving?") I don't even need to cite sources that say poor UIs slow people down. That's how it is. Computers add cruft, otherwise there wouldn't be a market for applications that remove distractions when writing.
...like using a pencil and paper instead of typing when you're preparing a publication...
Poor analogy. Publication implies mass reproduction and distribution. An *author* can write however they want to form their ideas, the result is the same. How the idea gets distributed is irrelevant to the core point. (Also there are such things as shorthand.)
Re:That Moment (Score:5, Insightful)
Ha! Inventing a new mathmatical system in order to solve a problem is cheating! But it works.
Not only is it cheating, it's tradition. We have many great branches of mathematics because of it.
Re:Explain the mind of a genius? (Score:5, Insightful)
Teachers are doing this for your benefit, not theirs. If you can hand in your homework with just the answers and get them all correct, great, but if you hand in the homework and get some wrong, the teacher won't have any idea where you went wrong, whether you used the wrong method when solving it or if you just made a simple error with the arithmetic. 99.9% of kids, even the ones who think they don't need to show their working because they know to do it, will at some pointstruggle with something and need help.
The UK exam system drills this into you pretty early, only 1 mark out of 3 or 4 being awarded for the correct answer, the rest being awarded for the method used. By the time you get to A-level (High school) maths, you're even given the answer beforehand and asked to "show that x = 5".
Ultimately the working out is usually more important in maths than the answer. You won't win a Fields medal for "Fermat's late theorem : it was correct. The end"
Re:Fermat & Poincaré (Score:4, Insightful)
Half a page? If (x/y)^2 = 2, then x^2 = 2y^2, so x is even. Let z = x/2, now we have 2z^2 = y^2, so y is also even. Thus, any fraction that's equal to the square root of 2 cannot be expressed in lowest terms, so cannot exist. That's, what, three lines at most?
I agree with the main point, though; quite a few of the proofs I do are just boring churning through tens of possible cases. Up to 100 or so it's plausible to do it by hand, although tedious and it's easy to make mistakes; significantly beyond that, though, you're going to want to automate it.
Re:That Moment (Score:5, Insightful)
Analytic solutions are not necessarily easier to calculate.
Analytic solutions tend to involve special functions for which the computer can only compute an approximation anyway. Have you ever tried to write code to evaluate the error function over the entire domain of floating point numbers? (Yes, I know, it's now in the standard library; ten years ago, it wasn't.) That's one of the easier ones.
Even if there are no special functions, analytic solutions are still often harder to calculate if the problem is big enough. Think of solving systems of linear equations, one of the standard workhorses of numeric programming. We're talking really big ones; hundreds of thousands of equations in hundreds of thousands of unknowns or bigger. In the real world, this problem would almost certainly be solved using successive approximations, even though high school students know how to solve them analytically.
Finally, and most importantly, the problem statement is usually an approximation. Take the OP as an example. What this kid almost certainly solved was an analytic solution to the problem of a particle in a gravitational field with linear air resistance. Well, air resistance is not linear. At low velocities, and for projectiles with a sufficiently small cross-section, it's close enough. But it's still an approximation.
The advantages of analytic solutions are almost always not computational. What they buy you is understanding. The methods of obtaining the solution, and the form of the final equations, often reveal some deep insights about the problem. For many situations, that's far more valuable. And it's certainly something that no computer can give you.