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    (Original post by cattubato)
    not really this. at least from anecdotal evidence of the ~20 people i know who did it, most people overestimate the effort they need to put into it, and end up getting an A* which they could have got for a fraction of the effort. any more than 14 hours of work and youre being self-indulgent. of course, if youre genuinely interested in it then do as much as you want. but if you just want a letter on your application, then dont worry.
    Haha thats wierd ive heard the complete opposite from all my friends, and I underestimated it as well! I didnt enjoy it at all and didnt even get a good grade. from what I know its not worth it. Barely anyone who did it was asked about it in their inteviews (mainly talking about medicine here) because a lot of the interviewers never heard about it. Im not a very good writer though in the first place so that probably played a role in my opinion of it. Depends on everyones situation I guess.
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    (Original post by cattubato)
    im interested in your intuitive understanding. ive never heard an explanation that was the least bit intuitive. ive read the original proof (tediously going through line by line) and abridged versions by Nagel ect and other proofs using Turing enumerable computability ect, but never really got any deep intuition of WHY it was true. (especially when one considers stuff like completeness of presburger arithmetic). how did you intuitively conceptualize it?
    First Incompleteness Theorem: "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F."

    Second Theorem: For any formal effectively generated system T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.

    In other words (I think), a system of statements can only be verified by a larger system of statements.

    An intuitive explanation of the concept that will probably satisfy your teachers and examiners (but obviously not actual mathematicians) could be: A computer cannot completely simulate the entire Universe; because that would entail simulating itself, which it cannot do. If it tries to simulate itself, it needs to simulate itself simulating itself, thus needs to simulate itself simulating itself simulating itself...

    I am not aware of an intuitive explanation of the proof, however.
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    "Comparing graph drawing algorithms"
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    (Original post by espicton98)
    'was Abraham Lincoln's decision to issue the emancipation proclamation for humanitarian reasons, or as a military tactic to win the Civil War?'
    I absolutely LOVE that title!

    That would be very interesting to examine I'm sure

    Good luck
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    (Original post by ilovegoats)
    I absolutely LOVE that title!

    That would be very interesting to examine I'm sure

    Good luck

    Thankyou! I hope whoever examines it does find it interesting !!!
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    (Original post by Nayzar)
    Haha thats wierd ive heard the complete opposite from all my friends, and I underestimated it as well! I didnt enjoy it at all and didnt even get a good grade. from what I know its not worth it. Barely anyone who did it was asked about it in their inteviews (mainly talking about medicine here) because a lot of the interviewers never heard about it. Im not a very good writer though in the first place so that probably played a role in my opinion of it. Depends on everyones situation I guess.
    yeah fair enough, we all probably had a generous moderator then. i suppose for medicine you know what to expect but if anyones doing a subject they've never done before probably do an epq in it
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    (Original post by Mathemagicien)
    First Incompleteness Theorem: "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F."

    Second Theorem: For any formal effectively generated system T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.

    In other words (I think), a system of statements can only be verified by a larger system of statements.

    An intuitive explanation of the concept that will probably satisfy your teachers and examiners (but obviously not actual mathematicians) could be: A computer cannot completely simulate the entire Universe; because that would entail simulating itself, which it cannot do. If it tries to simulate itself, it needs to simulate itself simulating itself, thus needs to simulate itself simulating itself simulating itself...

    I am not aware of an intuitive explanation of the proof, however.
    haha fair enough then. i did give them a basic proof based on the unproven premise that G is an arithmetic statement (which majority of godels proof proves, if you havent read it yet). but i mainly focused on debunking pseudo-philosophical arguments based on it like "a computer cannot completely simulate the entire Universe".
 
 
 
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