## Swedish Student Partly Solves 16th Hilbert Problem 471

Posted
by
timothy

from the my-calculator-is-broken dept.

from the my-calculator-is-broken dept.

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."*
## Where I went to school (Score:5, Funny)

## Wow he's good (Score:5, Funny)

## Re:Wow he's good (Score:5, Informative)

## I wonder how many people (Score:5, Funny)

onlybecause of this post here.I know I did.

## Re:Wow he's good (Score:2)

She's swedish as well.

## I remember (Score:3, Funny)

Just somethingto think of.

## Re:I remember (Score:5, Funny)

## Re:I remember (Score:2)

## Re:I remember (Score:2)

## Re:I remember (Score:5, Interesting)

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>

## Huffman coding is not minimaly redundant (Score:3, Insightful)

## Re:I remember (Score:5, Informative)

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.

## This one is true, AND... (Score:3, Interesting)

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:

In under one minute, I slapped on the blackboard a geometric and algebraic version## Re:I remember (Score:5, Funny)

"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.

## Re:I remember (Score:4, Informative)

As far as we know, this legend is based upon a true incident.## I'd hit it! (Score:5, Funny)

Seriosly though, a hot Swedish mathematician? That's so much like my dreams it's scary.

## Looks Like She's Married (Score:2)

Seriosly though, a hot Swedish mathematician? That's so much like my dreams it's scary.I know what ya mean

-kgj

## Re:Looks Like She's Married (Score:2)

Anyone over there care to confirm (either way...)?

## Re:Looks Like She's Married (Score:2)

## Re:Looks Like She's Married (Score:2)

not only that... but it's like she's showing off the ring too!!

## Re:Looks Like She's Married (Score:4, Funny)

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?

## Re:Looks Like She's Married (Score:2)

## Re:I'd hit it! (Score:3, Funny)

Seriously.

Hot *and* smart.

Happy Thanksgiving indeed.

## Re:I'd hit it! (Score:2, Funny)

Personally, I prefer smaller asses and hard tits.There's a name for those: they're called "boys".

## Re:I'd hit it! (Score:3, Funny)

## Re:I'd hit it! (Score:2)

## Re:I'd hit it! (Score:2, Offtopic)

I think that about sums it up.

## Re:I'd hit it! (Score:3, Informative)

## Re:I'd hit it! (Score:4, Funny)

## Re:I'd hit it! (Score:3, Funny)

## Re:I'd hit it! (Score:3, Insightful)

Maybe its time

## Re:I'd hit it! (Score:2, Funny)

## Re:I'd hit it! (Score:3, Informative)

## Link for the lazy to her website (Score:3, Informative)

## was it just me... (Score:2, Funny)

Seemed to be an interesting image!!

## Slashdot announces breakthough (Score:2, Funny)

## Re:Slashdot announces breakthough (Score:3, Funny)

Just because you aren't a Math or Physics major doesn't mean we aren't in here.

## Useful Links / Karma Whoring: (Score:4, Informative)

The abstract for her paper is here [sciencedirect.com].

## Re:Useful Links / Karma Whoring: (Score:2)

Looking at it's size proved it, almost a half megabyte!

Here is the big version:

without height/width tags [math.su.se]

Almost 500 KB per visit should give that server some cute traffic.

## Have you noticed (Score:5, Funny)

And you thought

## Re:Have you noticed (Score:3, Funny)

Drunken moose alert in southern NorwayI always thought Norwegian Moose got more tired when they drink. Must be coffee drinks.

## I'm convinced (Score:5, Funny)

## Re:I'm convinced (Score:2)

## Re:I'm convinced (Score:2, Funny)

What I heard on a hitchhiking trip (in Denmark):

Norwegian to a Swede: "Norway has everything Sweden has except for one thing."

Swede: "Uh ok,.but what's this thing?"

Norwegian: "Good neighbors."

Moral: Norwegians and Danes don't seem to get along with Swedes.

## Re:Have you noticed (Score:2)

Flying moose lands on car's roof [aftenposten.no]

Driving along..smooth...KABOOM!...770 pound moose landing on your car.

## Stoned beaver (Score:2)

Beaver hit bus with tree [aftenposten.no]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 [gronne.no] about having Linux banned,

immidiately.## Re:Have you noticed (Score:5, Funny)

## Mathematicians cheering in the aisles (Score:5, Funny)

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?

## hmmmmm (Score:5, Funny)

looks like a chalkboard to me...

oh well.

## Swedish Student Party? (Score:3, Funny)

## Hot sweedish chicks (Score:5, Funny)

One [math.su.se]

Two [math.su.se]

Three [math.su.se]

Four [math.su.se]

Enjoy

## Re:Hot sweedish chicks (Score:2)

## You bastard. (Score:5, Funny)

## aaargh!! (Score:2, Insightful)

90 posts already down the drain...

## Translation? (Score:5, Funny)

Norwegian Aftenposten has an English version of the reports."Uh..can anybody translate the english version into moron for me?

## problem description (Score:5, Informative)

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?

## Re:problem description: not today (Score:2, Funny)

## Re:problem description (Score:3, Informative)

But in brief, it appears to be a problem about the "topology of real algebraic curves"

"Topology" is all about the shape of things. e.g a donut and coffee cup are the same from a topological viewpoint because you can transform one to the other without tearing the donut or coffee cup. There is probably lots of good introductions on the web.

As to "real algebraic curves

## Damn... (Score:2, Funny)

I just read that as

"Swedish Student

PartySolves 16th Hilbert Problem"And

## not really (Score:5, Insightful)

"Oxenhielm's solution pertains to a(bold by me).special versionof the second part of problem 16"In other word's, problem no 16 is still unsolved besides special cases.

Special versionsof 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.## EQ vs Math (Score:3, Funny)

## SwedishHot at SlashDot (Score:5, Funny)

oneSlashdotter 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.

## Context (Score:5, Informative)

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 [wolfram.com].

Then, a link to a text of Hilbert's original lecture in Paris in 1900 [clarku.edu].

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 problemTo 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 [math.su.se] 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

## Re:Context (Score:5, Insightful)

The author tries to determine the number of limit cycles for the Lienard equation. This would not solve the full 16th problem, but it would deal with an interesting special case, and it would likely take powerful new techniques to solve even this case. She tries to do so as follows:

She notes that numerical calculations show that the solution is well approximated by a simple trig function. (The figures are evidence in support of this assertion.) She then bounds the number of limit cycles, under this approximation, in a straightforward and elementary way. I have not carefully checked this bound, but I see no reason to doubt it (or to believe there's anything novel about it, for that matter). However, there is no attempt whatsoever at a rigorous justification of the approximation, or even a rigorous formulation of it. Therefore this simply does not constitute a full proof, although the article refers to it as a proof. Hilbert's 16th problem is already well understood in simple cases, and any attempt to reduce the more complex cases to simple cases must justify all approximations.

Incidentally, if this were an important theoretical paper on Hilbert's 16th problem, the journal "Nonlinear analysis" would be a strange place for it (it's more interdisciplinary, and is not a mainstream outlet for theoretical mathematics). That's no reason it couldn't be true, but it's some cause for initial suspicion as well as explanation for why the article was accepted. Probably the editors and referees were applied scientists unfamiliar with the problem, who were perfectly happy to accept an approximation justified by some numerical data.

## (Attempted) explanation of Hilbert's 16th (Score:5, Informative)

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.

## Elin's phone number... (Score:3, Funny)

## Re:It's funny that college kids.... (Score:4, Insightful)

## Re:It's funny that college kids.... (Score:3, Insightful)

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

## Re:It's funny that college kids.... (Score:2, Funny)

In this case the theory that it's to get chicks can probably be ruled out, as:

## Re:It's funny that college kids.... (Score:5, Funny)

It's a chick who solved itMath chicks always get me hot. And she is one hot math chick.

I'd

loveto estimate the area under her curves.## Re:It's funny that college kids.... (Score:2, Funny)

## Re:It's funny that college kids.... (Score:5, Funny)

## Re:It's funny that college kids.... (Score:5, Funny)

## Re:It's funny that college kids.... (Score:3, Funny)

> 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.

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!## Re:It's funny that college kids.... (Score:5, Funny)

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)

## Re:It's funny that college kids.... (Score:3, Funny)

...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.

## Re:It's funny that college kids.... (Score:2, Funny)

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

## Re:It's funny that college kids.... (Score:2)

Thanks, Ernie Cline.

No, seriously... Pictures, anyone?

GMFTatsujin

## Re:It's funny that college kids.... (Score:2)

....are always the ones to solve the major problemsProof?

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.

## Re:It's funny that college kids.... (Score:3, Informative)

....are always the ones to solve the major problemsProof?

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 balle

## Re:It's funny that college kids.... (Score:2)

## Re:It's funny that college kids.... (Score:4, Interesting)

Nash himself said he felt his best years were behind him at age 30That's very typical. As people get older, they get less creative. As people get married, they become unimaginative dolts. [abc.net.au]

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?

## Maybe math, then.. (Score:2)

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 [wolfram.com], and Abel [wolfram.com] for instance.

There are counterexamples, of course, the chemist Joel Hildebrand [berkeley.edu] published his last research paper at over 100 years of age.

## Re:Maybe math, then.. (Score:3, Funny)

## Re:Maybe math, then.. (Score:3, Interesting)

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 [st-and.ac.uk].

## Re:Maybe math, then.. (Score:2, Interesting)

Not to mention C. F. Gauss [st-and.ac.uk] (1777-1855)

## Re:It's funny that college kids.... (Score:5, Interesting)

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)

## Re:It's funny that college kids.... (Score:3, Insightful)

## Re:It's funny that college kids.... (Score:3, Interesting)

Well, you're actually technically wrong on both counts. First according to the dept's webpage she's

nota 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 posit

## Re:It's funny that college kids.... (Score:3, Insightful)

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 achiev

## Re:It's funny that college kids.... (Score:5, Informative)

However, Andrew Wiles, who solved Fermat's last theorem [st-and.ac.uk], spent seven years in his attic to do so.

I guess broad generalizations don't work so well, eh?

## Re:It's funny that college kids.... (Score:5, Funny)

## Time's up, put your pencils down. (Score:4, Funny)

The set of 23 problems was put forward by Prussian mathematician David Hilbert in 1900 as"challenges for the 20th century. Three remain unsolved, numbers 6,8 and 16.Looks like the 20th century

FAILED IT!!!!Awww crap, did I say that out loud?!!! I'm gonna get a karma burn for that!## Re:hot? cute? (Score:2, Funny)

## LOL! (Score:3, Insightful)

## Re:argh... evidence that... (Score:3, Funny)

## Re:Heh (Score:5, Insightful)

## Re:SECKS (Score:2)

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.

## Re:SECKS (Score:5, Funny)

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.

## Thanks for ruining a rare geek fantasy (Score:3, Funny)

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