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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
Just somethingto think of.
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
College students are the ones who tend to have the time for it, just like college students are often the major contributers to open-source projects.
"They redundantly repeated themselves over and over again incessantly without end ad infinitum" -- ibid.
In this case the theory that it's to get chicks can probably be ruled out, as:
Link
... I read it first time as "Swedish Student Party"
Seemed to be an interesting image!!
in something only 10 slashdotters know anything about;
Her website is here.
The abstract for her paper is here.
And you thought
An infinite number of monkeys will eventually come up with the complete works of
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
Maybe you weren't expecting a sloven, coke-bottled, matted-haired geek like the rest of us apparently were.
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.
For about 1.7 seconds, I thought the headline said ... oh, nevermind.
"It's not your information. It's information about you" - John Ford, Vice President, Equifax
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
Proof?
If a 45 year old college professor solved it, would this be news?
I think it's pretty well-known that among mathematicians, the older you get, the less likely you are to do anything really important. In other words it's not really "funny" that a college kid would solve this; it's pretty much the norm.
There's a PBS documentary about John Nash that I recently saw where this is talked about a bit; the commentators liken mathematicians to ballerinas, and Nash himself said he felt his best years were behind him at age 30 (and not because of his mental illness - in fact, his mental illness may have in part been due to the stress he was feeling). It's on DVD if you want to look for it - A Brilliant Madness was the title, I believe.
In fact, you're in luck - I just Google'd it for you and there's a web site here that includes a transcript of the program.
I'm impressed by the sweedish girls at Stockholm University.
:)
:)
One
Two
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Four
Enjoy
what the hell is the answer?
90 posts already down the drain...
If you don't know what AltaVista is (was), get off my lawn.
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.
not only did he sneak a goatse into here and got people to look, but he even got a +1 informative out of it! moderators TRULY smoke crack.
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?
That is true. Also of note is the angle is inversely proportional to the mass of the ass.
I really hate Dan Patrick.
> 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.
Or the volume, in this case. ;-)
Karma: It's all a bunch of tree-huggin' hippy crap!
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.
Our mathematicians are busy dribbling^H^H^H^H^H^H^Hanalizing around the girl^H^H^H^Hproblem
sign(c14n(envelop(this)), x509)
More than mere navel gazing.
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.
Not to mention C. F. Gauss (1777-1855)
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.
It's sad, but I was more excited to see EverQuest Players Defeat 'Unkillable' Monster than the solving of a math problem. Makes ya wonder who's more geekier.
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
>
>Many, many times. All in the interest of science, of course. Hubba, hubba.
You're not a mathematician, you're a physicist. Not as bad as an engineer, mind you.
The picture of Elig proves that there exists at least one female mathematician for whom "I'd hit it". As a mathematician, that's good enough!
She was wearing a Tux shirt, but she told me it was her boyfriend's (sorry guys), and she didn't use computers much (just Mathematica on the SGIs).
The entire male membership of slashdot just went limp thanks to you Mr. Spoils-All-The-Fun!
GMD
watch this
I'd rather say it was Hardy's hypothesis, although from what I know of his character, he was probably not a sexist or prone to any other form of bigotry;
He was an atheist and [most likely] a homosexual, and was therefore very much an 'outsider' himself in his times)
There simply weren't very many women in math 100 years ago.
And while I'm on the topic, it is interesting to note that Stockholm University was one of the first universites to give a chair in mathematics to a woman;
The great Sonya Kovalevskaya.
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
This is apparently a true story. At least, I have Dantzig's account here in "History of Mathematical Programming -- A Collection of Personal Reminiscences." Two interesting side nodes:
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
It's sad to see how fast the posts went from "discussion" to almost pure sexism.
/. normally. Focus on the relevant part. She proved a part of an unsolved problem at the age of 22. Give her some respect. Kudos to Elin!
:)
Come on, what kind of people do you want us to be seen as?
So she's pretty hot, so what? I don't see a lot of "hot chick"-articles on
Wish we were all as smart her, here in southern Sweden as well.
Yay Vidarh ! At least someone around here has a perspective ... but it seems to me that someone that solves boundary cycles for polynomial differential equations should get some respect on /.
I tend to not like differential equations let alone these ones !
The textbook at Uni was only an inch thick and was titled "Elementary Differential Equations"
Better titled "your worst nightmare"
Let us award genius when it is due... she deserves it.
TG
Except engagement rings in Sweden don't look like American engagement rings.
In Sweden, the telltale sign of an engagement ring is an _absence_ of any stone. It's a nondescript gold ring. It looks pretty much like The One Ring but without the elvish runes. On the inside of the ring, though, date and names are engraved.
I'd say this particular ring is either a family heirloom, or that she's extremely Americanized. My guess at odds for the two options would be about 90/10.
Nash himself said he felt his best years were behind him at age 30
That's very typical. As people get older, they get less creative. As people get married, they become unimaginative dolts.
Of course, I'm happily married, and I'd like to think that I still have *some* creative spark, but then, I *am* here, at 6:33 PM on Turkey-Day eve, reading slashdot...
Maybe they're right, after all?
I have no problem with your religion until you decide it's reason to deprive others of the truth.
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.
Huffman coding is not minimaly redundant, because you always need at least one bit per symbol. If more then 50% of a signal is one symbol, it's wasteful. There's an encoding out there that lets you use less then a bit, but I forget.
autopr0n is like, down and stuff.
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.
...I'm changing clothes on a train going from New York to Stockholm at 80 mph that leaves at 8pm local time.
I would sure like to see a _train_ from New York to Stockholm. Even better would be seing someone trying to put clothes on it.
There are 010 kinds of people. Those who understand octal, those who don't, and 06 other kinds of morons.
More experienced mathematicians will use all of the tricks and techniques that they have picked up over the years. The potential for new and creative thought is, in my opinion, greater before you pick up all of those tricks and techniques. I have witnessed undergraduate students come up with proofs that would never occur to more experienced mathematicians, simply becuase the experienced mathematician would apply the standard technique almost without thinking.
Well, almost (depending on who you define 'it', granted). PhD students also have time, but if you were to go to your supervisor and exclaim you want to work on 'famous' problems you'd be discouraged, and rightly so. The thing with being a PhD student is that you're supposed to do work that will lead to publications, and spending time on something that's been researched for a hundred years isn't likely to.
For an undergrad though, the situation is different. If you were to say to the same supervisor that you'd like to work on a famous problems they'd be all for it. They wouldn't think you'd make any progress on the solution but it'd be a great learning experience, and since your survival is guaranteed by other means, it's quite OK to fail.
Compare Turing if you will, who as an undergrad proved the law of large numbers (if memory serves). That had already been proven twenty years earlier, but Turing didn't know about that result. Hence his professors were quite impressed with his results, and as a result admitted him for higher studies. As a modern day PhD student that would have been a failure, even though it's a great success as an undergrad.
Stefan Axelsson
I am married to a mathematician. After receiving his PhD he went to work within academe
However, some 12 months ago he quit academe for private business
So
However, be that as it may, I also think it is a little bit over-simplistic to disparage anyone for coming up with a brilliant idea while just lazing around not gainfully employed. I read somewhere that Goedel came up with some of his best ideas while at a sex romp in the Austrian alps. That doesn't make those ideas any worse, now does it?!
The liver is evil and must be punished.
is on her website. We are really a big bunch of nerds on Slashdot. We talk about how hot and sexy Elin is, but nobody actually calls her up :)
Well, you're actually technically wrong on both counts. First according to the dept's webpage she's not a PhD student, she's a teaching assistant (amanuens). And thus her job is actually to teach, not to do research.
No doubt she was given the amanuensis position in anticipation of becoming a PhD student, but since Sweden changed their PhD acceptance criteria, departments have become wary of accepting students (there aren't as many positions available these days). (My own department for example had 120 applicants for four positions this year, you basically had to have published papers to even get in as a PhD student). Hence departments like to pull stunts such as these, i.e. hiring someone beforehand as e.g. a TA (or similar) to see if they can do the work before comitting to taking them on. I'd say she passed... :-)
As to why students (as in undergrads) have come up with breakthroughs as of late my own theory is that they are the ones that can actually work on these problems, having nothing to lose. As a PhD student that's not a smart thing to do, see my other post on this topic.
Stefan Axelsson
Thanks for the insight. I wasn't aware of the Swedish PhD position scarcity. Here in the US, the TA jobs are usually filled with PhD students, and if there is any left those are filled with Master's stundets. I have yet to see a TA that is not a student at the same time.
I agree with you on the other count as well, unexperienced students walk off the beaten path (thankfully).
I would, however, disagree with you on PhD students not taking up hard problems. It is true that it is unsafe (ie. might never achieve closure, where closure is actually the diploma), but I would say that is the T.R.U.E.(tm) PhD. Out of my quite large group of PhD students (15-20) I only know one who really went into an unsafe territory (Math PhD), and not coincidentally he is the one still a student after 5 years (having suffered multiple setbacks), while all others have finished. However there is really no way of distinguishing one PhD from another based on this criteria (since there is only few who can even understand the thesises). I guess if you want the paper for the paper's sake, go for it, but if you have a calling, that will take time.
Code poet, espresso fiend, starter upper.