Feynman on Fermat's Last Theorem (2016)
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Feynman on Fermat's Last Theorem (2016)
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Re: Feynman on Fermat's Last Theorem (2016)
#2_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 = 10^2 - 6^2 = (1+3+5+7+9+11+13+15+17+19) - (1+3+5+7+9+11) = 64
5^3 = 15^2 - 10^2 = (21+23+25+27+29) = 125
It's not that hard people. Stop believing everything you're told about how "hard" something is.
HINT: The number of odd numbers in the series exactly matches the starting square base number
Re: Feynman on Fermat's Last Theorem (2016)
#3> Feynman concluded: “for my money Fermat’s theorem is true”.
> "the main job of theoretical physics is to prove yourself wrong as soon as possible."
Great example of the main difference between mathematicians and theoretical physicists .
This reminds me of another magician, Enrico Fermi, who was also an extremely good mathematician but didn't pursue rigor or precision for the sake of it: 20% was good enough precision for him for most cases.
Re: Feynman on Fermat's Last Theorem (2016)
#4_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…
> It's not that hard people. Stop believing everything you're told about how "hard" something is.
There are still many problems in physics and mathematics which are considered "hard" (e.g., dark energy, Riemann hypothesis, etc). Can we crack them by simply adopting your positive mindset?
Re: Feynman on Fermat's Last Theorem (2016)
#5This 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?
Re: Feynman on Fermat's Last Theorem (2016)
#6> Feynman concluded: “for my money Fermat’s theorem is true”. > "the main job of theoretical physics is to prove yourself wrong as soon as possible." Great example of the main difference between mathematicians and theoretical physicists . This reminds me of another magician, Enrico Fermi, who was also an extremely good mathematician but didn't pursue rigor or precision for the sake of it: 20% was good enough precisio…
I feel like it is a very "physics" motivated approach to at least "investigating" this theorem. Calculating probabilities is a line of thinking Feynman would be familiar with (quantum mechanics). Physics is often responsible for mathematical development, while they are different, they complement each other. It's nice to see different perspectives, and how ideas are connected.
Re: Feynman on Fermat's Last Theorem (2016)
#7_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…
Sounds interesting, but not sure what you mean by:
> you'll discover that there will always be a gap if you try and combine two odd number series together
Can you elaborate?
Re: Feynman on Fermat's Last Theorem (2016)
#8_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?
Re: Feynman on Fermat's Last Theorem (2016)
#9This 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?
This isn't a proof.
Re: Feynman on Fermat's Last Theorem (2016)
#10_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…
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.