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Is anyone still trying to come up with Fermat's original "truly marvelous proof"? Or have math folk talked themselves out of its possible existence?
Is anyone still trying to come up with Fermat's original "truly marvelous proof"? Or have math folk talked themselves out of its possible existence?
_DON'T DOWN VOTE JUST BECAUSE YOU CAN'T DO MATH_ The proof Fermat hinted to was about the difference between squares. All whole numbers taken to a power greater than two (n^3) can be represented as the difference between two whole squares (x^2 - y^2). These differences can then be shown as the sum of consecutive odd numbers: 2^3 = 3^2 - 1^2 = (1+3+5) - (1) = 8, 3^3 = 6^2 - 3^2 = (1+3+5+7+9+11) - (1+3+5) = 27, 4^3 = 1…
Off topic: why doesn't HN support LaTeX?
This proof (or "plausibility argument") bugs me so much. Just because something thins out and becomes rare doesn't mean it doesn't exist. As n gets bigger, the probability of n being a perfect square gets smaller and smaller. In the limit, the probability is zero. Does this mean square numbers don't exist?
It doesn't lead you directly proof - but often just knowing what the answer 'should be' can be a real guiding light.
Earlier quoted context omitted.
I don't think the "you can do anything" mindset works in real life. It helps self-help book authors sell their stuff, but it's not a good strategy to live by. (Incidentally, this reminds me of Key & Peele's "You can fly" sketch). What does work though is this: advanced formal education in a topic. Once you have that you can start thinking on how to solve some simple open problems. And if you are lucky and turn out to…
Oh man, that reminds me of an experience I had in college. I was working with the aerospace department on their fusion reactor (I was just writing software to help them process data from it, not involved in the science itself). My boss kept getting calls from crackpots who'd go on and on and on about their bogus theories, and how they were being shut out of the mainstream by small minded fools, etc etc. It was pretty…
Earlier quoted context omitted.
Do you really believe that: (a) This constitutes a proof; (b) This is the "proof" that Fermat had; (c) Mathematicians missed this for over 350 year? I'm not quite sure exactly what you are claiming.
It's completely arrogant to assume that because it hasn't been solved by "better" people that I couldn't solve it.
Seriously, can you walk us through the steps of why x^5+y^5=z^5 has no (non-trivial) solutions?
And to be fair, there are cases where, say, undergrads have proven significant results that had been outstanding for a long time. Proving that prime recognition is in P is one such case. but in that case they published a complete, clear paper. In this case I can't really see what you're saying you've done, or why it's true, which is why a walk-through of the case n=5 would be so helpful.
Thanks.
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For anyone interested, this is what the comment used to say ...
The series of odd numbers must be consecutive and they simply are not when you add two different series together for all powers greater than two. It's okay. You'll get it.
1) a whole number, n, taken
to a power greater than two
2) can be represented as a
consecutive series of odd
numbers
3) where there will always be
a gap in the series between
consecutive base numbers,
for all p and p+1
4) therefore there will be
a gap for all p and p+n,
n>=1 combinationsEarlier quoted context omitted.
What other mindset do you see working better?
I don't think the "you can do anything" mindset works in real life. It helps self-help book authors sell their stuff, but it's not a good strategy to live by. (Incidentally, this reminds me of Key & Peele's "You can fly" sketch). What does work though is this: advanced formal education in a topic. Once you have that you can start thinking on how to solve some simple open problems. And if you are lucky and turn out to…
Earlier quoted context omitted.
I know, but it's being exhibited as an example of how back-of-the-envelope type of approximations by physicists can be just as good as rigid mathematical thinking. And I don't find this to be a convincing example of how loose physicist arguments can work. Schwartz distributions, infintesimals; okay, fine, those turned out to be a weird trick that can be formalised. But sometimes their tricks are just plain wrong and…
That’s not what’s happening. Consider, many useful primality tests are statistical in nature. It’s pure math, and exact answer is possible but it’s still useful to get a quick check to see if something is a waste of time. Really, if a full solution takes 20 years you don’t want to actually spend 20 years without having a very good idea it’s going to work.
Earlier quoted context omitted.
I don't think the "you can do anything" mindset works in real life. It helps self-help book authors sell their stuff, but it's not a good strategy to live by. (Incidentally, this reminds me of Key & Peele's "You can fly" sketch). What does work though is this: advanced formal education in a topic. Once you have that you can start thinking on how to solve some simple open problems. And if you are lucky and turn out to…
So what your saying is... We should ignore letters from patent clerks?
If you're asserting something that's likely to encounter resistance, it's worth being clear and careful.