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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."
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.
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.
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.
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.
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.
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.
I've taken a look at her article (downloaded it via an institutional subscription). It's eight pages long, with a lot of figures, and is short and easy to read. It's also categorically not an important theoretical contribution to Hilbert's 16th problem.
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.
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
Correct. Listen guys! Just because a chick shows a bit of midriff doesn't mean she's hot. Admittedly the young lady 'isn't bad' - but I feel I should point out that 'HOT' and 'HOTTER THAN ANYTHING I'LL EVER GET WITHIN A COUNTRY MILE OF' are two different things.
/. lowered the tone and opened a new catergory - BRAINS AND HOT OR BRAINS AND NOT
Maybe its time
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.
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.