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Swedish Student Partly Solves 16th Hilbert Problem
An anonymous reader writes "Swedish media report that 22-year-old Elin Oxenhielm, a student at Stockholm University, has solved a chunk of one of the major problems posed to 20th century mathematics, Hilbert's 16th problem.
Norwegian Aftenposten has an English version of the reports."
You solved the whole thing or you got an F.
I'm still trying to figure out the 15th Dilbert cartoon ...
"A door is what a dog is perpetually on the wrong side of" - Ogden Nash
Uh, sorry. Thought I was on fark for a second.
Seriosly though, a hot Swedish mathematician? That's so much like my dreams it's scary.
Jurisprudence Fetishist Gets Off On A Technicality --theonion.com
And you thought
An infinite number of monkeys will eventually come up with the complete works of
Yeah, and he had this group of construction worker buddies he would hand out in bars with. He had a great mind, but he was abused as a child and couldn't express intimate emotions. He solves this problem on the board, and the next hting he knows the math professor really wants him to work on problems together. Then Robin Williams shows up and...oh, wait a minute.
Just kidding ... these are perfectly reasonable stories. But I'm still a bit surprised. But then, slashdot readers don't disappoint. They immediately honed in on Turing's sexuality and the student's physical attributes. Math, what math?
Mencken had it right. So glad that's old news.
Looks like the 20th century FAILED IT!!!!
Awww crap, did I say that out loud?!!! I'm gonna get a karma burn for that!
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
I think that story is an urban legend, but if you've ever used Huffman coded data, Huffman himself used to tell this story:
He was flunking information theory at MIT, and his prof told him he'd pass if he solved mimimal redundancy coding. So he did, and invented Huffman codes.
<HUMOR>
Of course, as his students at UCSC, we used to believe that his roommate solved it, and Huffman killed him for the solution (and hid the body)...
</HUMOR>
The only reason we have the rights we have is that people just like us died to gain those rights. -- Cheerio Boy
the caption below the photo says "Elin Oxenhielm pointing to the second part of Hilbert's 16th problem on her web page"
looks like a chalkboard to me...
oh well.
They've got cute mathematicians, terrorist beavers, psychopathic elves and I've got friends over there. That's it, I'm moving to Norway.
It is by the juice of the coffee bean that thoughts acquire speed, the teeth acquire stains. The stains become a warning
Click.
Legend: A student arrives late to math class and finds two problems written on the chalkboard. Assuming they're homework problems, he jots them down in his notebook and works on the equations over the next few days before turning his solutions in to the instructor. Several weeks later, the professor turns up at the student's door with the student's work written up for publication. The two problems were not a homework assignment; they were problems previously thought to be unsolvable which the instructor had used as examples in his lecture that day.
Origins: This has to be one of the ultimate academic wish-fulfillment fantasies: a student not only proves himself the smartest one in his class, but also bests his professor and every other scholar in his field of study.
As far as we know, this legend is based upon a true incident. (That is, a version of this legend that antedates a known true incident has not yet been discovered). George B. Dantzig, then a graduate student at the University of California, Berkeley, arrived late for a statistics class one day and found two problems written on the board. Not knowing they were examples of "unsolvable" statistics problems, he solved them as a homework assignment. Dantzig, who later became a staff mathematician at Stanford University, recounted his solving two "unsolvable" problems in a 1986 interview for College Mathematics Journal, and his solutions to the two problems can be found in the journal articles listed in the Sources section below.
Whatever it is I'm complaining about, I'm sure the Republicans did it. This is
I'm impressed by the sweedish girls at Stockholm University.
:)
:)
One
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Enjoy
Norwegian Aftenposten has an English version of the reports."
Uh..can anybody translate the english version into moron for me?
Mod me down with all of your hatred and your journey towards the dark side will be complete!
Here's a description of the problem from
http://aleph0.clarku.edu/~djoyce/hilbert/toc.html
snip...A thorough investigation of the relative position of the separate branches when their number is the maximum seems to me to be of very great interest, and not less so the corresponding investigation as to the number, form, and position of the sheets of an algebraic surface in space...
Can someone please post graphical, dumbed down representation of this problem so we can better understand it?
Dada ended art.
It's a chick who solved it
Math chicks always get me hot. And she is one hot math chick.
I'd love to estimate the area under her curves.
Opinions on the Twiddler2 hand-held keyboard?
> not only that... but it's like she's showing off the ring too!!
Yeah, and it's like the writing on the blackboard is her boasting about her guy...how does it make you feel, huh? Angry, right? So angry you've just got to do SOMETHING...you're not going to let her get away with it, are you?
Based on the photo alone. I would say she is engaged or even *gasp* married. Yup, when your single and on the prowl...the "ring finger" is the first thing you look at. Why bother wasting hers and your time?
Life is not for the lazy.
That was pretty nice, leading us down a primrose path and then throwing that 4th babe in there. Wasn't expecting that fine piece of crumpet. You bastard.
To hell with estimating, I'd rather have a firm grasp on the number.
Endless arguments over trivial contradictions in books written by ignorant savages to explain thunder in the dark.
I believe it'll remain imaginary for you...
Well (after being through myself) I tend to disagree with your oversimplification (even if there is a tiny teeny-weeny truth in you assesment):
/. had an article about how most researchers have major breakthroughs before their 30s. That article offered several ideas why is that, like (simplified): need for show-off, extra time because of lack of families, etc...
1. It was her job. (she is a grad student and a teaching asst, therefore has a JOB even if it way underpaid).
2. Just the other day
3. She is not a "college kid" as you put it, but a PhD student (she does not fit into the same drug-imbibing, all-night partying picture)
Code poet, espresso fiend, starter upper.
However, Andrew Wiles, who solved Fermat's last theorem, spent seven years in his attic to do so.
I guess broad generalizations don't work so well, eh?
In other word's, problem no 16 is still unsolved besides special cases.
Special versions of fermats theorem were already proofed by fermat himself. But it took 300 years until Andrew Wiles and one of his students proved it generally. If You look at the history of famous mathematical conjectures (ie fermats, poincares) You'll see: prooving a special case will probably not really help prooving the general case. If You are very lucky, You get a hint how to solve the "real" problem.
I wonder how many people read the article only because of this post here.
I know I did.
Computer Go: Writing Software to Play the Ancient Game of Go
Yes. Broad generalizations never work well.
Hi, I'm Elin. Let's see if you can figure this out...
:)
Imagine that my bra size is 30B, dress size is 8, and pants size is 30, and I'm changing clothes on a train going from New York to Stockholm at 80 mph that leaves at 8pm local time. Meanwhile another train going the oppisite direction at 70mph leaves Stockholm at 6am local time the same day with you inside. If my boyfriend who is infinitely hotter and smarter than you leaves Chicago on a flight to Stockholm at 7pm local time and takes 10 hours to get there, what is the area of naked skin under my clothes, and what are your chances of ever getting sight of it as our trains pass one another, taking me to heaven in the arms of Jean-Claude and you to hell in the bowels of Slashdot trolls? Show your work with your answer.
(Yes, that's a joke, I'm not Elin)
I wanted to read the responses to this article because I thought that maybe one Slashdotter could give a qualified explanation of Hilbert's 16th problem, and maybe even explain something about the partial solution. That was possible back when Andrew Wiles proved his theorem, you know.
And look at this, not a single post even gets started on the subject! At least not when you browse at +2, like I do. But we're all standing around slobbering over the thought of a hot Swedish math babe! And so am I!
Hey Taco, can we get this gal for an Ask Slashdot interview? She could explain her theorem, and tell us something about her lingerie.
Always keep a sapphire in your mind
What are you an idiot?!? Haven't you seen any teen love movies? Geek chicks always turn out super hot!! All you need to do is take of the glasses, let down her hair and unbutton her shirt a little.
Glasses? check
Long hair in bun? check check
Dowdy, boyish outfit? check check eheck!!!!
She is the trifecta! MAN SHE IS RIPE FOR THE TAKING!!!!
If you can't see that, well, then that's just sad.
Arbitrary sig
I know that this is Slashdot and that around here the looks of a mathematician are more important than her work, but if anyone is interested, here are a few pointers to get to know more.
First, a short description of Hilbert's problems at Wolfram: Hilbert's Problems -- from MathWorld.
Then, a link to a text of Hilbert's original lecture in Paris in 1900.
Next, a quote of the 16-th problem as laid out by Hilbert. (Sorry, no fancy LaTeX here.)
Finally, I'll quote the abstract from Miss Elin Oxenhielm's article On the second part of Hilbert's 16th problem :
To get the full text of the article you must apparently have a subscription of pay a $30 fee. It is easily available if you follow the directions from the author's page as I did.
Hope this helps
Now allow me for a few comments: solving one of Hilbert's problem is a huge achievement, even it's only part of one. What is even more stricking is that it's coming from a woman. Don't get me wrong, I'm no sexist, quite the contrary. What I mean is that only very few women made it to be recorded in the history of the mathematical science at large: other than Hypatia of Alexandria; Maria Gaetana Agnesi; Sophie Germain; Ada Byron, Lady Lovelace; Sofia Kovalevskaya; Emmy Noether, not many names come to mind. It would be really nice to add another one, to begin, and then work up from there.
Xavier
Do I make sense? Please report if not.
"This has to be one of the ultimate academic wish-fulfillment fantasies"
It has to be pure fantasy. In the real world, the math prof would quietly take credit for the solution himself.
Reading Hilbert's lecture and a couple other sources, here is what I THINK Hilbert is asking in his 16th problem. Take this with a grain of salt.
The first part of Hilbert's 16th problem asks about the relative number and position of the components of a curve of order n. In other words, if we look at the graph of an equation of nth degree in the plane, what might the graph look like? We can describe it fairly easily for small n.
If n=1, the first order equations are precisely the linear ones, so the curve always consists of a single unbounded component (the straight line).
If n=2, the general equation of the 2nd order is Ax^2+Bxy+Cy^2+Dx+Ey+F=0, also known as the equation of a conic section. Depending on the coefficients, the graph will be a point, a line, a parabola, two intersecting lines, an ellipse, or a hyperbola. Geometrically, all of the cases but the last are only a single component. Therefore an equation of the second order has at most two branches. When there are two branches, they both are unbounded.
The case n=3 is much more complicated, and involves the study of what are known as elliptic curves. Beyond that, it just gets worse.
What Hilbert wished to have investigated was the geometry of the branches in the case of the curves with the most branches. As it turns out, you can't just have any orientation. If n=6, for example, the greatest number of branches is 11, but if the curve has 11 branches then one of the branches will always lie completely inside another branch. The 16th problem asks what similar restrictions are required for other n, and what happens if we look in higher dimensions than the plane.
A related problem that Hilbert referred to in his problem was that of curves defined by differential equations instead of polynomials. Here the objects of interest are boundary cycles of first order (featuring no derivatives higher than the first) differential equations. I have not encountered this term before, but if I had to guess I would say a boundary cycle was a closed, limiting path of a function satisfying the differential equation (so, for example, a boundary cycle of the second-order differential equation given by gravitation would be a planet's orbit after it is sucked in the system). The same sort of question is asked: how could these cycles be placed relative to one another in the plane? It is this question that may have been answered by the student in the article.