Feynman on Fermat's Last Theorem
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Feynman on Fermat's Last Theorem
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Re: Feynman on Fermat's Last Theorem
#2I wonder how many false conjectures could pass muster using this sort of probabilistic argument.
Re: Feynman on Fermat's Last Theorem
#3Using way simpler math, the probability that an even number is prime is zero. One cannot conclude from that that there are no even primes (in fact, many mathematicians think the smallest prime is even (https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.h... ))
Mathematicians do use this kind of back of the envelope calculations to get a feeling for whether a statement may be true, but they can never prove something.
Re: Feynman on Fermat's Last Theorem
#4The last quote on the page should be familiar to HN readers as a different version of "fail fast, fail often".
Re: Feynman on Fermat's Last Theorem
#5finding that the probability is extremely small doesn't really get you any closer to proving it. for such a hard to prove theorem, it makes sense the probability is small. that's why it was interesting in the first place.
I find it hard to believe Feynman concluded from this that the theorem is probably correct. it only takes 1 case among an infinity to make the theorem false.
Re: Feynman on Fermat's Last Theorem
#6The last quote on the page should be familiar to HN readers as a different version of "fail fast, fail often".
yes, they both summarize the scientific method in a clickbaity way
Re: Feynman on Fermat's Last Theorem
#7I wonder how many false conjectures could pass muster using this sort of probabilistic argument.
I guess every false conjecture can be made to pass it. The trick is to make the set of items searched in large enough.
For example, to show that no elephants exist, start with the (infinite) set of all possible chromosome sets. The proportion of them that produces an elephant is zero. QED.
Examples from mathematics:
The number 42 does not exist (logic: pick an integer. The probability that it equals 42 is zero. QED)
There are no even primes.
There are no primes.
There are no integers.
There are no rational numbers.
All numbers are transcendental.
Continuous functions do not exist.
There are no regular polygons.
Re: Feynman on Fermat's Last Theorem
#8The last quote on the page should be familiar to HN readers as a different version of "fail fast, fail often".
In other words, prefer breadth-first searches to depth-first searches.
Re: Feynman on Fermat's Last Theorem
#9I wonder how many false conjectures could pass muster using this sort of probabilistic argument.
I guess every false conjecture can be made to pass it. The trick is to make the set of items searched in large enough. For example, to show that no elephants exist, start with the (infinite) set of all possible chromosome sets. The proportion of them that produces an elephant is zero. QED. Examples from mathematics: The number 42 does not exist (logic: pick an integer. The probability that it equals 42 is zero. QED)…
Several of these don't work, as it's assumed you tackle smaller values in another way, before your -> infinity method kicks in, so most of these would be easily knocked off.
Re: Feynman on Fermat's Last Theorem
#10Using way simpler math, the probability that an even number is prime is zero. One cannot conclude from that that there are no even primes (in fact, many mathematicians think the smallest prime is even ( https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.h... )) Mathematicians do use this kind of back of the envelope calculations to get a feeling for whether a statement may be true, but they can never prove so…
Your link doesn't work for me…