Slashdot Mirror
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.
Isaac Newton came up with Principia and Calculus when he was offered 18 months with paid room and board on a farm. The college kids are solving mundane shit. The only reason it happens is because they don't have to get JOBS. (-1 Flamebait thanks to moderators who worked to put themselves through school)
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!!
Seriosly though, a hot Swedish mathematician? That's so much like my dreams it's scary.
... but in the picture it looks like she's wearing a wedding ring, so dream on ....
I know what ya mean
-kgj
-kgj
in something only 10 slashdotters know anything about;
I couldn't find a google page about her (except the one in Sweedish).
Don't waste your vote! Vote for whoever you want, unless you live in a swing state it won't matter anyways
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
Or what about this?
How small a thought it takes to fill a whole life
....are always the ones to solve the major problems
Proof?
If a 45 year old college professor solved it, would this be news?
Kinda like the pessimist saying that he always gets stuck in the long lines. He just doesn't note the times he's in the short line.
Actually not at all like that, but you get the point.
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.
>Is this the same Hilbert of "Hilbert Space" fame?
Yep. But he's likely much more famous for the 23 problems he presented in 1900. Proof of closure on C and R with the vector stuff implied by Hilbert is probably pretty cool, I just wish I understood it... I've only gotten as far as Riemann integration, and only on elementary functions.
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.
If it were the latter, I bet she could write out a formula showing the declining rate of erection possibiility.
I'm impressed by the sweedish girls at Stockholm University.
:)
:)
One
Two
Three
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.
I wouldn't really agree with that..
But it does seem true that math is "the young man's game".
(To quote the great mathematician GH Hardy)
Some of history's great mathematicians never lived to see their 30th birthday. Galois, and Abel for instance.
There are counterexamples, of course, the chemist Joel Hildebrand published his last research paper at over 100 years of age.
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.
I proved when I was 13 that the angle of the dangle is directly related to the heat of the meat. Google for it.
I just read that as
"Swedish Student Party Solves 16th Hilbert Problem"
And
Why didn't they just ask me the answer - I knew it was 42 the whole time. As a general rule the answer is always 42.
Stay tuned for new sig...
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?
Dangit! I have that song in my head...
"Mentos, The Freshmaker!"
If you ignore the other uses of a tool, does that make the tool less useful, or you less useful?
That is true. Also of note is the angle is inversely proportional to the mass of the ass.
I really hate Dan Patrick.
I doubt there's a single hetero- or homosexual female on this earth that will sleep with someone because they solved a math problem.
you underestimate the loneliness of the slashdot crowd
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.
"Ain't I a stinka..." - Bugs
shes hot? man, us geeks must really have low standards. wait. i dont have standards that low. maybe im not a geek! woot! no...im probably just more out of touch with reality than most other geeks.
Geeks who don't have a girlfriend don't have high standards. Geeks who have a harem of girlfriends whose surnames are JPG have high standards, as evident by their harem.
Beware: In C++, your friends can see your privates!
What? They didn't solve any unsolved problems. They just made a lot of money.
Even if she is a lesbian, I doubt there's a single hetero- or homosexual female on this earth that will sleep with someone because they solved a math problem.
You don't think Erdos is dreamy, then I take it?
Oh, I dunno... Real nerds know that nothing is the world is sexier than a woman who is smarter than they are. First, we want to crib off their trig homework, then make wild, passionate love to them until she reluctantly asks if we can stop -- because Battlestar Galactica is coming on.
Thanks, Ernie Cline.
No, seriously... Pictures, anyone?
GMFTatsujin
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.
You gotta love a nerdy chick who shows some hip (I see skin, I see skin!)
"Ain't I a stinka..." - Bugs
Or the volume, in this case. ;-)
Karma: It's all a bunch of tree-huggin' hippy crap!
Beaver hit bus with tree
There is a disproportionately high number of kernel hackers in Scandinavia. This is what happens to our environment when open source is released into it. I'm contacting the Norwegian Green Party about having Linux banned, immidiately.
Irene KHAAAAAAN!
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.
Years ago on my way to an MS Physics degree, I tried my hand at many imponderables and love to see a success.
Of additional interest is this story of a Swedish mathematics student is being reported in a paper from Norway (I love Opera browser BTW) and at the bottom of the page are other headines:
Drunken moose alert in southern Norway
Beaver hit bus with tree
Free Norwegian music overload
Researchers zero in on new Viking ship
aftenposten.no is on my favs list for sure !
TG
Our mathematicians are busy dribbling^H^H^H^H^H^H^Hanalizing around the girl^H^H^H^Hproblem
sign(c14n(envelop(this)), x509)
you sir, are mistaken.
unless my 16-colour display is hiding something from me, this girl is not only smart as a dolphin, but pretty, too.
kind of wants to make me work harder at math, even for the day...
GENERATION 26: The first time you see this, copy it into your sig on any forum and add 1 to the generation.
I believe it'll remain imaginary for you...
This is also true for physicics, eg Einstien was 26 when he published the special theory of relativity, and Hawking was 28 when he published his work on the big bang and 32 when he published his work on black holes and Hawking radiation. Probably other similar cerebal fields probably have similar patterns.
Only on Slashdot does the expression "shove a greased Yoda doll up your ass" get an Informative moderation.
Karma: It's all a bunch of tree-huggin' hippy crap!
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 Sweden right. So, not much point moving to Norway. Yes they're close, but does that mean you'll switch?
What's so sexy about a woman who can't figure out how to use Tivo?
As copyright owner of this comment, I authorize everyone to defeat any technological measure which limits access to it.
Forget estimation, I'll give an exact answer.
This is America, damnit. Speak Spanish!
I'm bi and female and I'd definitly sleep with her because she partially solved that problem.
I'd probably want her to explain it to me first too. Geek fetishes do exist. And they probably hang out on /.
That is not generally true. Most problems that get solved are by hundreds of hours of hard work and dedication. Age is not a determining factor in a person's ability to dream and have the talent, work ethic, and determination to follow through with those dreams.
Definitely, at times, some problems are solved by accident or as a side result to another, even unrelated, problem. Those are just as meaningful as the ones solved over a lifetime a work.
"Dada ended art."
actually bulldada ended art.
it was a mercy killing.
A blog about stuff.
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.
that not all swede chicks are blond and cute
Could be fake [wedding ring] to avoid being hit on by the /. geeks.
....
Oh, please. Let's review: young woman, beautiful, smart. That makes her a Slashdotter's dream. I think such a woman knows that Slashdotters won't dare hit on a woman of their dreams
-kgj
-kgj
It's not such a problem in mathematics (AFAIK), where definitions tend to be a bit more rigorous, but a tremendous number of philosophical problems can be boiled down to incomplete or incorrect definitions.
May we never see th
To hell with estimating, I'd rather have a firm grasp on the number.
There's a reason I said estimate: it's more "hands on", and to ensure accuracy, I'd have to repeat the process many times.
Many, many times. All in the interest of science, of course. Hubba, hubba.
Opinions on the Twiddler2 hand-held keyboard?
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
I wonder whether Ms Oxenhielm solved this first because no one else has heard of Hilberts challenges?
"So I was writing my algebraic theorem om my promotor's computer, and it went beep beep beep..."
Just what major unsolved problems did Steve Jobs, Bill Gates, and Steve Wozniak solve?
>
>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!
It does not, however, prove that I'd get her name right. Sorry, Elin. But I'd still hit it. *G*
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've had friends visiting Sweden and all they had to say was: "man, these are weird people!" Compared to us italians they look much more apt to adveturous flirts and easy relationships, yet almost all of them get independent form their families very early but don't enter a 'single' phase; they just marry very early or make unofficial yet stable couples. This is totally opposite to italian customs: we mostly five off our parents for as much as we can, engaging in the most lascivious affaires and mosly dribbling all kind of responsibility until some father/brother decides enough is enough and we are driven to the altar at gunpoint...
Mi domando chi à il mandante di tutte le cazzate che faccio - Altan
I once met this girl that was a med student, and was ridiculously gorgeous. Although actually I guess managing to get nude pictures of her to put on my website doesn't really count as hitting on her, huh.
Doesn't count as hitting on her. But if there were any justice, those pix would send your karma rating sky-high.
Ok, well there was this other girl a few weeks ago that I asked out to coffee and then couldn't talk to...
The Slashdot Effect, dammit.
Maybe skip the coffee, try alcohol instead?
-kgj
-kgj
Just one good example of the way men cannot think of smart women without their dick interferring your resolution. Maybe it could be for equality if she were 42 year old and looked like one middle-aged woman. All in all, she is damn cute and 99.9 per cent of /.tters are the opposite of her.
Moderating 101
I was once told by my college neighbours that some girls wear wedding rings as a way to politely turn down unwanted advances. It doesn't hurt to ask :)
Yes. Broad generalizations never work well.
You can find a list of all 23 problems here. Some of them have already been solved.
The abstract of the paper, linked elsewhere:
Let k be an integer such that k is larger than or equal to zero, and let H be the Hilbert number. In this paper, we use the method of describing functions to prove that in the Lienard equation, the upper bound for H(2k+1) is k. By applying this method to any planar polynomial vector field, it is possible to completely solve the second part of Hilbert's 16th problem.
Maybe apocryphal, but one of my math profs told about a final exam. Six unsolved problems. Got something like three answers and a couple of partials from the class.
The profs quip: "Amazing what graduate students can do under pressure".
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:
http://www.aftenposten.no/english/local/article.jh tml?articleID=676663
When I read this headline, I had visions of a couple of geeks sitting in a dorm room with a big coffee pot, some crates of beer, some pizza's sitting around listening to ABBA - talking (as geeks do) when one of them pipes up and says: "You know, when you say that, this makes me think of that maths problem in class yesterday." another pipes up: "You know, I just think we solved it."
Anyway bit of a let down when it was part*l*y, rather than party!
|>>?
Student party solves 16th Hilbert Problem? Jeez, when I was a student, we did drugs and group sex at parties, not math! Being a student just isn't what it used to be.
Are you sure you'd want someone from a country where they can't tell the difference between a blackboard and a web page?
There's also a feature film based on his life, called A Beautiful Mind - quite a good show too.
A student party in Sweden looks more like this :
Party #1
Party #2
Party #3
I know not what course others may take; but as for me, give me liberty or give me death!
What's so sexy about a woman who can't figure out how to use Tivo?
Other than the fact that she couldn't read the manual with her head stuffed in her pillow?
Like what I said? You might like my music
good thing there is no nobel prize in mathematics, dumb-ass
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.
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.
Seriously, Norwegians don't understand Danes either? :-) I've always regarded Norwegian as being sort of halfway in-between Swedish and Danish...
Sorry guys, but you've GOT to get out of the house more often!! LOL
I concede that she's not a total dog and does have some curves, but she's not even close to hot on my scale.
Hey, but I'd do her just at the remote chance that it would raise my own IQ by a few nodges.
Here's my own equation:
moreIQ = doMeNow(hornygeek + curvy smart chick);
From what I remember from my college studies (seem to have flushed most of it out by now), any book where the title started with "Introduction to..." or "Elementary" was a warning you'd better sit down and brace yourself before opening the cover.
Those books were, as you say, nightmares.
You're an idiot.
Any woman who plays that little game (and there are many) is only ever going to be approached by the overconfident, disrespectful assmunches of the world, the very kind that doesn't respect the "fact" that she's taken, and yet will manage to bitch about it when she's dumped for some new novelty of the week. Such a woman is not worth my time or attention.
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.
Yes, Elin might have solved Hilbert Q16 for "fun", or to keep her gradstudent job. But now that we have her solution (partial though it is), how can we use it? Hilbert "spaces" are important to the 20th century topology insights that quantum mechanics uses, therefore to our worldview, as well as technology. What can we do with the topology in a proof of Q16?
--
make install -not war
What computer problems did they accenentaly solve? Jobs and Gates started companies, and Woz built a computer that did what it was supposed to do.
autopr0n is like, down and stuff.
did you see the pic? She's friggn' hot. I doubt she has any trouble finding willing sexual partners...
autopr0n is like, down and stuff.
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.
(Yes, that's a joke, I'm not Elin) :)
Really? I never would have guessed!
autopr0n is like, down and stuff.
I can assure you she has no more than a B
Whoa, deja vu: #7574336 #7574399
Yes, and his comment only makes sense by if there is also a nobel prize in mathematics, dumbass
this thread is making me feel old, sad and dumb :(
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.
Maybe its also because they are the ones whose thinking has also not been conditioned(not to the full extent anyway) and hence they dont follow the well beaten path and make the mistakes made already.
Wanted : A Signature.
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 somewhat agree but Euler seems to fall under quite the contrary (published great works up until his death)
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.
Danish is not a language, it's a speech impediment. Denmark is not a country, it's just a place God forgot. The only good Dane
The liver is evil and must be punished.
No, Einstein was 26 when he copied the special theory of relativity from Jules Henri Poincare, who himself was 50 when he presented the principle of relativity in 1904.
-- Qu'est-ce que la propriété intellectuelle? It is thought control.
Her homepage has a hig res version of her picture. ;)
Sindri Traustason.
Damm why don't I ever get invites to parties like that, you know with girls that solve hilbert problems, seriously that sounds like my kind of party fun, booze chic's and maths what more could a maths geek ask for.
in my life God comes first.... but Linux is pretty high after that
Francis Smit
What an amazing coincidence. I've just been waiting for a solution to the second half of Hilbert's 16th problem to be able start construction of the first transatlantic tunnel, featureing all transparent aluminum construction to allow seeing into other cars.
Who is John Cabal?
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
Why did you feel the need to post as Anonymous Coward?
...deep linking.
Go here, follow the right path, and you would know it was true before you read the story.
+&x
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.
I think it's "the angle of the dangle is directly proportional to the heat of the meat." Or so beavis would have us believe...
I agree they did some impressive things, but to the best of my knowledge, none of them have ever solved any unsolved problems such as the student in the article.
But I could be wrong.
So just what unsolved problems did they solve?
To be fair, she *is* a math geek, and there have been times when the subject of a story here has posted a comment his/her self... Didn't want people to get the impression she was trolling Slashdot after a hard day of math problems :)
Whah, flamebait :-)
These days, nobody recognizes "funny" anymore...
"We can confirm that Debian does *not* ship the version with the trojan horse. Our version predates it." [CA-2002-28]
Well i find her to be not-so-baad. And before yelling here about ("i'd hit her" or "i'd do her"), i would first talk to her, and estimate her intellgence and interests.
i'm sure she might be extremely interesting and smart.
Just wanted to tell something good, in case if she, herself, gots there and finds all this mud about doing and hitting
I'm sure i wouldn't find it to be very pleasant. Also we should note that girls are subject to cry whenever possible, and reading most of these coment's might be cause of that.
Well, I canot remember if I said it that strongly, but in either case I didn't mean that in the absolute. PhD students don't tend to work on hard problems because it's not the smart thing to do, you'd be rightly discouraged. Your own anecdote even corroborates that. Had he choosen a different problem he'd be out of there already, on to bigger and better things.
I'm not saying that's necessarily a good thing, someone has to tackle the difficult stuff otherwise we'll never make any progress. I'm just pointing out that even though many belive that PhD students are the ones doing this, that's not really true. They're few and far between, and that's not surprising, since doing that leads to a failed PhD more often than not, and that's a shame on good people when it happens. It's the people at the very beginning (i.e. before they start their PhD work), or at the very end (i.e. after their retirement, if you can talk of such in academia) that have time to spend on the long odds investigations. Didn't Einstein spend the last 15 years of his life chasing after a unification of his earlier theories? He never came even close, but at that point that didn't matter.
Stefan Axelsson
Now be honest: You were hoping on getting that goatse.cx link again, didin't you?
But if they are imaginary, they can be approached in any direction as long as they are analytic.
Mathematician, n.:
Someone who believes imaginary things appear right before your i's.
The Norwegian newspaper Aftenposten has a story called Landmark 'proof' under heavy fire.