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    In case anyone is interested, there's a discussion of IMO 2009 Q6 (which seems to have been a particularly difficult IMO question) going on at Terry Tao's blog. The idea is for people to form a collaborative solution. Tao has already found a solution and so is acting as moderator. Gowers is one of the people searching for a solution.

    Even if you can't follow what's going on (and I can't, at least not with the amount of time I'm prepared to put in), it's interesting to see how people go about it, and also (on a very simplistic level), interesting to see how even Fields medalists can't knock these questions out without effort.
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    Yes, I always found it reassuring to hear stories from my lecturers about how they found a particular topic difficult. It shows that being successful in maths (proving theorems, etc.) is usually achieved with hard work rather than spontaneous insights. Another good website in a similar vein in Timothy Gowers' blog (search on google). He recently posted his thoughts on the new A Level "Use of Mathematics", which is causing a bit of fuss at the moment.
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    Oh, god; this reminds me of a talk we had from Siklos about how he once set a STEP question so hard it took him three months to do. Interesting that a few IMO participants got it out; it kinda shows the necessity of collaboration in mathematics. Sometimes the simplest things can be overlooked, and different people have different ideas, some of which work better in a given situation than others.

    (As an irrelevant comment, I think he's better known as "Timothy Gowers". )
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    Long very long, but it's good to see how mathematicians interact and revise other's work.
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    I got the solution, I'm a genius.




    Only joking.

    I will write it down and think about it later, maybe playing Mario Kart 64.

    P.S. Pretty pointless posting a problem that is already solved.
    P.P.S. I don't know why Tao and Gowers and other bloggers want communism i.e. big collaboration.
    P.P.P.S. Seriously, if it needs topology to prove it then I'm not going to bother.
    P.P.P.P.S. Can't be bothered I think I'm more of a theory person then solving
    hard problems person. Although, it does look like a easy proof by induction.
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    No offence to Mr Tao but if he has to try hard to solve Int Maths Olympiad problems which a few contestants solved all by themselves within the stipulated time, then Mr Tao really is hyped up by the anglophone media.
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    (Original post by maths-enthusiast)
    No offence to Mr Tao but if he has to try hard to solve Int Maths Olympiad problems which a few contestants solved all by themselves within the stipulated time, then Mr Tao really is hyped up by the anglophone media.
    Prof. Tao.

    In December I found a GCSE question that took me 20 minutes to solve. Does that mean I can't do GCSE maths? No, just that I'm not looking for the right things any more; other people might just happen to spot the right method before me, particularly GCSE students who've been trained to spot only the right method and not to look for a method themselves. Same with the IMO.
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    (Original post by maths-enthusiast)
    No offence to Mr Tao but if he has to try hard to solve Int Maths Olympiad problems which a few contestants solved all by themselves within the stipulated time, then Mr Tao really is hyped up by the anglophone media.
    Yeah, I'm pretty sure they gave him the field medal because of the anglophone media.

    Racism:rolleyes:

    (Original post by DFranklin)
    interesting to see how even Fields medalists can't knock these questions out without effort.
    I guess two reasons for this. Firstly, you don't focus on how to do trivial stuff at a hard level so for example you will see a GCSE question but don't know how to do it because your an algebraic topologist. Secondly, I heard that once you get into PhD level maths instead of solving problems you need to think about problems for months which is abit different then solving a problem that takes an hour.

    (Original post by generalebriety)
    In December I found a GCSE question that took me 20 minutes to solve.
    Was it a old higher tier paper? As I have been looking at the new papers and most of question don't even require maths. Well, thats the impression I got with some GCSE questions. However, I haven't really seen any higher tier papers as at college it mostly people doing foundation tier.

    If you can remeber the question can you post it.
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    (Original post by generalebriety)
    Oh, god; this reminds me of a talk we had from Siklos about how he once set a STEP question so hard it took him three months to do.
    Did you ever find out which question it was? (I'm betting it was a probability/stats one)!

    Interesting that a few IMO participants got it out; it kinda shows the necessity of collaboration in mathematics.
    IMO solutions can usually be written in only a few lines - it's just finding those few lines can be a complete nightmare. So if you hit the right approach, you'll get it out fairly easily (compare with, say, FLT, where the best approach known still takes many hundreds of pages of work).
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    (Original post by DFranklin)
    So if you hit the right approach, you'll get it out fairly easily (compare with, say, FLT, where the best approach known still takes many hundreds of pages of work).
    Sorry, but what is FLT?
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    (Original post by Simplicity)
    Sorry, but what is FLT?
    Fermat's Last Theorem.
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    (Original post by DFranklin)
    Fermat's Last Theorem.
    Well, its certainly larger than a margin. I thought the proof is like 200 pages?
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    (Original post by DFranklin)
    Did you ever find out which question it was? (I'm betting it was a probability/stats one)!
    I'm afraid I don't remember - perhaps someone else who attended the same open day will remember which it was. I remember it was to do with deriving an inequality.

    (Original post by DFranklin)
    IMO solutions can usually be written in only a few lines - it's just finding those few lines can be a complete nightmare. So if you hit the right approach, you'll get it out fairly easily (compare with, say, FLT, where the best approach known still takes many hundreds of pages of work).
    I'm not sure I count FLT as collaborative work, though. Even so, Wiles wouldn't have been able to do it without a lot of work from previous mathematicians, and Taniyama and Shimura and whoever else couldn't do it even though they got quite "close"...

    (Original post by Simplicity)
    Was it a old higher tier paper?
    Nope. And I don't quite remember the question, but it was a statisticky one to do with proportions, and I was just massively overcomplicating it.
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    (Original post by generalebriety)
    I'm not sure I count FLT as collaborative work, though. Even so, Wiles wouldn't have been able to do it without a lot of work from previous mathematicians, and Taniyama and Shimura and whoever else couldn't do it even though they got quite "close"...
    Yeah. If it wasn't clear, all I was meaning is that for an IMO question, you can get somewhere purely by "luck" - you just randomly chose a good strategy. But proving FLT by "luck" would be akin to winning the national lottery 52 weeks running.

    Nope. And I don't quite remember the question, but it was a statisticky one to do with proportions, and I was just massively overcomplicating it.
    There's a danger in being "too good" for a problem. Littlewood talks about this in Mathematician's Miscellany - how he would sometimes solve problems in "horrible" ways, because he could look at it for 15 seconds, see "oh well, I can do it by doing XYZ" and plough on through, whereas most of his contemporaries wouldn't have a clue how to do "XYZ" and so were forced to find a nicer approach.
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    (Original post by Simplicity)
    Well, its certainly larger than a margin. I thought the proof is like 200 pages?
    But a mathematician with no background in the topic would have to study several hundred pages of maths simply to be able to follow the actual proof.
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    (Original post by Simplicity)
    Well, its certainly larger than a margin. I thought the proof is like 200 pages?
    It's about 105 pages long, with 3 pages of references. (link to proof — 56k warning!)
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    I read something pretty destressing. It said something about the three big proofs in the past twenty years have came from people that have focused seven years on a single problem.
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    (Original post by Simplicity)
    I read something pretty destressing. It said something about the three big proofs in the past twenty years have came from people that have focused seven years on a single problem.
    don't worry, you're young enough to have plenty of time to solve the Riemann Hypothesis.
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    (Original post by DFranklin)
    Fermat's Last Theorem.

    I remember reading somewhere that Fermat claimed before he died that he found "a beautiful proof" to it which presumibly didn't take many years and high tech computing power to do, although they never found his proof so some people think he made a mistake. Would be amazing if there was an elegant proof though.
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    (Original post by Tallon)
    I remember reading somewhere that Fermat claimed before he died that he found "a beautiful proof" to it which presumibly didn't take many years and high tech computing power to do, although they never found his proof so some people think he made a mistake. Would be amazing if there was an elegant proof though.
    Actually, pretty much everyone in the field thinks he made a mistake. The claim of a proof appears once in the famous 'marginal note'. But later on, he published results for specific small values of n. Which would be very odd if he had a general proof.
 
 
 
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