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Georgia Teen Stumbles On New Theorem
dread minerva writes "Proof that the kids are alright: The Atlanta Journal-Constitution published the following article about Josh Klehr, who discovered a math theorem while sitting in study hall one day in eigth grade. The theorem is now known as the Klehr-Bliss Theorem and a paper on it is being published in The American Mathematical Monthly."
I'd love a citation on this.
I know you're just a bullshit troll, but I'm still calling you out on the bogus gender stereotypes.
Just so this isn't a one-sided game, here's an article from US News about how women now outnumber men in higher education. And here's a report from the US Department of Education's Education Statistics Quarterly that suggests that girls continue to excel in verbal skills relative to boys at all ages, and that there's no statistically significant difference in their achievment in math and sciences.
Kinda shoots down your central assumption ("girls do better than boys when younger, but worse later, in education").
Any response?
-Isaac
I am not a lawyer, and this is not legal advice. For Entertainment Purposes Only.
And some of the most obscure set theory stuff, the Banach-Tarski Theorems, which were thought to be completely abstract actually help describe the Eightfold way of quark theory.
/.'ers: Number theory was thought to be the "queen of mathematics", unspeakably pure. Of course, now it's the workhorse of crypto.
Other "useless" stuff, but of more interest to
General Relativity: Space-time tells matter where to go; Matter tells space-time what shape to be.
Don Knuth solved a math problem at the beginning of the school year in High School. He got an A on the course and was excused from any extra work.
That article reads like a story on the onion:
Geekboy average Joe grocery-bagger astounds mathematician PhD's with a doodle from study hour.
Squeezed in the margin of his geography text book under a crude replica of a Limp Bizkit logo, a weird triangle with intersecting lines gives hope to millions of parents that their kid might actually do something meaningful.. even if the kid doesn't fully understand what they've done.
Speak truth to power.
"Girls...have a higher boredom threshhold."
As a female, I tend to disagree with this.
....
Okay, I'm bored now.
Angry IT woman in big clompy boots. And talking lint!.
The school he goes to (Paideia) is actually quite cool. It is kinda a free form private school. From what I remember they really don't have many grades or announced tests. Kids are encouraged to learn at their own rate, and many gifted kids go their when they out pace their regular classes. It is kind of a neat place. They actually encourage creative thinking instead of kicking you out or arresting you!
You might be interested in Sudbury Schools, which are modeled more or less after the original Sudbury Valley School in Massachusetts.
The schools are run as a democracy, with students, parents and staff voting in the weekly school meeting on things including hiring and firing of staff. Students of all ages are able to mix freely, and there is no mandated curriculum. Never been to one, but they do seem to have more than a few good ideas.
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I guess I disagree on this point. Debunking quackery is a valid and valuable scientific service. It might not be as great as developing a new treatment, but it's important for people to know whether or not the treatment they're seeking is actually likely to help them. After all, if somebody decides to go to a quack, they may not seek help from somebody who can actually do them some good.
I think that you're really wrong here. The problem is that the advocates of theraputic touch have no science. There's no credible scientific evidence that theraputic touch has any positive health benefit. There are no peer reviewed, placebo controlled, statistically tested, double blind studies to determine the efficacy of theraputic touch. AFAIK there aren't even any lousy, uncontrolled studies, just a bunch of anecdotes. That's not science, it's just a bunch of pseudoscientific garbage with about as much scientific credibility as faith healing.
Now compare that to the tests that this girl and her parents carried out. You are quite correct in claiming that they set out with the single goal of debunking theraputic touch. What you miss is that any study that has a reasonable chance to debunk the theory also has a chance of turning up a reall effect. If the practitioners had actually been able to do what they claimed and detect the girl's energy field, they would have been able to produce a positive result and the study would have produced evidence in their favor- which is exactly what they need if they really want to get anywhere scientifically and medically. An interesting counterpoint is acupuncture; skeptics tried very hard to debunk it but couldn't. Eventually they became convinced that there was a real effect, figured out what caused it, and have helped to develop it as a theraputic technique. That's what science is about.
There's no point in questioning authority if you aren't going to listen to the answers.
Public schools are little more than federally funded daycare for working parents, and consumer indoctrination.
If you gave kids 3 hours of study hall, they'd hang out and socialize.
School voucher programs are bad because it imposes a blanket solution (vouchers vouchers everywhere) to a problem that only exists in certain areas (poorly funded inner city schools).
Plus, just because one genius kid shakes up the math world doesn't mean that the school was successful, just the kid. Schools' success shouldn't be measured based on how many geniuses they happen to have enrolled, they should be measured based on tests showing improvement in student knowledge and skills over time.
These are my friends, See how they glisten. See this one shine, how he smiles in the light.
Basically right, except you leave out the really important part, which is where Gauss explains his work and makes it accessible even to his teacher. How he did this was to argue that the sum of the numbers from 1 to n is half of twice that sum. Okay...we can go for that. But then he points out that this double sum can be written as n terms that combine the ascending and descending series like this:
(1+(n)), (2+(n-1), (3+(n-2), ... ((n-1)+2), ((n)+1)
Now, each of these terms has the sum (n+1), and there are n such terms since there are n terms in the original series. So the double sum is just n*(n+1), and the sum we want is just half of that.
And that is why he's Gauss, and you're not. :-)
Babar
Say what you will about this. But what amazes me about this story is that this kid took the initiative to check on whether the idea was novel or not. I think we can all learn a little from that.
The nine point circle includes:
o the midpoints of the three sides
o the feet of the three altitudes
o the midpoints of the lines joining the orthocenter (there the three altitudes meet) to the vertices.
The easiest way to find it is to simply take any of these three groups (say, the midpoints of the three sides) and find the circle that touches those three - the circle that circumscribes the triangle formed by those three.
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Vidi, Vici, Veni
Anybody know what the theorem actually states? The article was quite vague in that area, even for mainstream press. I'd really like to know some details of the discovery.
Bugrit! Millenium hand and shrimp!
He was not suspended, expelled, or arrested for "Thinking While In Highschool"!
I AM, therefore I THINK!
However, mathematics is, on the surface, a rigourously boring subject. What enables these children to see its inner beauty?
I think that mathematics is taught incorrectly in our schools. For pre teens, the education system is a Gradgrindish experience, and they are asked to remember many boring but worthy facts. This is a shame, because it happens at the time when they are at their most creative and curious.
Only later, when they are in their final years of school, are they taught in a creative and interesting way.
I think this explains why girls do better than boys when younger, but worse later, in education. Girls are good at doing routine tasks. It has been scientifically shown that they have a higher boredom threshhold. However, boys desire stimulation, and so the pre teen education system disadvantages them.
If only our schools education system saw learning as a voyage, a journey of exploration, rather than a means of inculcating our children in corporate dronery.
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The article notes that he attends a public school. This raises an interesting conundrum.
A successful school is, by definition, one that succeeds in engaging its students in academic pursuits and gives them the intellectual growth they need to succeed in the world. But education takes time and effort, as everyone knows.
If education monopolizes a student's time to the exclusion of all other activities, then he won't be able to develop these new and exciting discoveries. He'll be proficient in the knowledge of yesteryear, but he won't be able to look ahead to the future; for his nose will be constantly buried in a book.
This is why it's imperative for schools not to spend too much of students' time on homework. A half hour of homework per night and three hours of enforced studyhall periods would go a long ways towards giving students the time and the environment to make these wonderful discoveries. Some will spend it doodling, as the article noted, but that's the price we pay for a sophisticated environmentally-holistic educational approach.
Public schools are already making great strides in giving our students these opportunities, but private schools lag far behind (and public schools are starting to join them). This is why it's more imperative than ever that we oppose school-voucher programs. Students must be kept in the environments where we're already seeing successes like Josh's.
Here [http://www.csm.astate.edu/Ninept.html] is a more visual definition of a nine-point circle for people like me who are much more visually oriented.
THIS is the kind of news that should be reported, not "some guy shot some clerk on the other side of this state" or "it might snow in [distant state] tonight."
Use my userscript to add story images to Slashdot. There's no going back.
First and foremost, I don't think the theorem is actually called the Klehr-Bliss theorem. AFAIK it's the van Lamoen theorem, since he was the first to furnish a full proof. Lou Talman had a quicker (and simpler) proof that was purely geometric, but I believe it was found to be flawed. I was working on a brute-force algebraic manipulation, but Floor van Lamoen carried essentially the same technique to its completion before I was able to. You can read about his proof here.
Josh's conjecture was pretty accurately summarized in the article. The point E mentioned is actually the circumcenter, the center of the only circle passing through the three vertices of the triangle. Also, it is not exactly correct to say that the lines through A, B, and C intersect in "a point" inside the triangle. The three lines are concurrent (they all pass through a common point, a rare thing for three lines to do), but Josh's slope-reciprocal construction is really just a reflection about the line y=x in the coordinate plane, and changing the orientation of the coordinate axes relative to the triangle makes the point of concurrence wander around inside the triangle. The kicker that I noticed is that as it wanders, it stays on the nine-point circle, or Feuerbach circle of the triangle. I've actually found that there's a lot more to be said along these lines, and to my knowledge none of it has been published.
For the public/private thread... I think that Josh was and is attending a private school (Paideia, an excellent school by the way) though I attended a public one (Collins Hill... not too bad as public schools go).
Not only does the theorem have little to no practical value, it also is of little interest to mathematicians. I've always thought of it as simply a little ditty in triangle geometry. I haven't yet read van Lamoen's article in the AMM, but I believe he mentions it only in passing.
And yes, it is vitally important to have an encouraging mentor. Steve Sigur, Josh's teacher, is a great guy and an excellent math teacher. I don't mean this to trivialize Josh's accomplishment--it's also vitally important to have a creative mind and be willing to explore--but Mr. Sigur deserves the real praise here.
I'd also like to take this opportunity to shamelessly plug The Geometer's Sketchpad. It's a great piece of software that dynamically creates geometric constructions. It's excellent for visualization. I used it to see the generalizations I was after, and I think Josh was using it when he first made his conjecture. If you've any interest in geometry--or are willing to have some anew--you should check this out. You can download a free sample version.
Anyway, I just wanted to post and settle a few things... If anyone has any questions, you can post them here or email me (I'm abliss at freeshell.org). Thanks for your attenton!
http://home.wxs.nl/~lamoen/wiskunde/concur.html
The extremely vague statements in the article look similar to what is presented there...
Interesting. I always understood it better graphically:
...and so on up to 100 lines. Then you mirror it about the diagonal edge and get
1
22
333
4444
55555
666666
1666666
2255555
3334444
4444333
5555522
6666661
Hey - the width is equal to the height + 1! Multiply width and height, divide by two...
I find it far more likely that, in reality, this is how Gauss explained it. For something this simple, the equation usually comes after the concept.
I got my Linux laptop at System76.
Greetings
See you all at HAL 2001 http://www.hal20001.org/
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A slight correction. Emily Rosa did not prove that "theraputic touch" doesn't provide medical benefits. She proved that practitioners of it could not detect the proximity of another human due to the presence of their bio-electrical field (which definitly does exist, by the way). All her study showed was that the conscious human brain cannot reliable sense nearby electrical fields. It didn't prove or disprove that altering things in and near a human's electrical field have any other impacts on the human.
Think about this analogy. Even though I can't consciously tell how much Vitamin C is in the food I eat, the Vitamin C still affects my physical health. A study that shows people can't detect how many vitamins are in their food does not prove that vitamins are (or aren't) nutritionally helpful.
If people want to further study the bio-electrical field using scientific methods, great. Maybe we'll find better health that way and maybe we won't. This study just deals a blow to the nut-cases who don't use scientific backing for their therapy, but would they care about that study in the first place?
-Ted
I hope he gets an A in math for the rest of high school. How I would love to be in his math class and hear him say to his teacher "when you come up with law of mathematics on your own then you can tell me my math homework is wrong!"
I've hit Karma 50 and gotten a Score:5, Troll... I win!
Josh, if you're out there and just happen to be reading this, count your lucky stars, and thank that teacher of yours. My teachers would have either not cared or taken credit for themselves.