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An Overly Sophisticated Proof of a Disproportionately Simple Fact 

Joseph Newton
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Proof that the cube root of 2 is irrational.
This proof has been around for a while, but I originally saw it here:
mathoverflow.n...
The best thing about this proof is that it doesn’t even work for the square root of 2.

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26 сен 2024

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Комментарии : 61   
@Adomas_B
@Adomas_B Год назад
This is like using a chainsaw to slice an onion
@HenriFaust
@HenriFaust Год назад
Ironically, the chainsaw was invented for use in surgeries to deliver babies.
@cosmicvoidtree
@cosmicvoidtree Год назад
More like an industrial buzzsaw to cut an apple
@AloisMahdal
@AloisMahdal Год назад
More like a nuclear plant to crack a nut
@Xnoob545
@Xnoob545 3 месяца назад
Lithuanian spotted
@beautyofmath6821
@beautyofmath6821 2 года назад
lmaoo, nice use of Fermats last theorem, but to make it better, include the entire proof of fermats last theorem.
@brianfunt2619
@brianfunt2619 Год назад
"for completeness"
@1224chrisng
@1224chrisng Год назад
well, the proof is marvelous, but too small to contain in a youtube video
@AgentFire0
@AgentFire0 Год назад
@@brianfunt2619 well, that's just unnecessary denormalization, mind you!
@IntegralMoon
@IntegralMoon 2 года назад
LOL I actually laughed at the last line XD I was completely expecting a standard ""therefore a³ is even" ... Great job :P
@γιώργοςγιόφτσος
I love that you dont even use just the n=3 case which has been known for like 200 years, but you go for the full theorem
@djridoo
@djridoo Год назад
I didn't know it was known, where can we find a proof of it please ?
@ericzhu6620
@ericzhu6620 Год назад
@@djridoo the n=3 case was proven by Euler, while the n=4 case was proven by Fermat himself
@tylerbird9301
@tylerbird9301 Год назад
@@ericzhu6620 i thought that n
@bane2201
@bane2201 Год назад
@@tylerbird9301 Fermat gave a (full) proof that the equation x^4 - y^4 = z^2 can never be true (for integers). If you take the special cases where z = k^2 for some k, that implies x^4 = y^4 + k^4 is never true, so he effectively proved FLT for the case n=4. (I don't know if Fermat made _that_ connection himself, though.)
@mikakuna102
@mikakuna102 3 месяца назад
​@@tylerbird9301 ok i know it was 9 months ago but fun fact: it was prooven that flt holds true for primes that smaller than 200, or some of them could be even bigger i dont remember exactly
@Ganerrr
@Ganerrr Год назад
clearly the most important corollary of FLT
@bajes328
@bajes328 Год назад
This is the mathematical equivalent of seeing a rat and instinctively and immediately deploying a thermonuclear device to ensure you are safe from the rat.
@LucasWills
@LucasWills Год назад
Oh my god this is genius This is truly what Fermat was envisioning when he wrote FLT
@RWBHere
@RWBHere 5 месяцев назад
Ahh! But, when he wrote it, did Fermat know that it would be his last theorem? 😉
@taimunozhan
@taimunozhan Год назад
[Sees the title] Huh? Interesting... [Sees that the video is less than half a minute long] What? How? [Watches the video] Oh, that's how
@thorin1045
@thorin1045 Год назад
ah yes, the fun that anything already proved is valid to use, no matter how ridiculous to use it.
@collinmarando6515
@collinmarando6515 2 года назад
Watching this for the first time at 4am was the right call
@purplenanite
@purplenanite Год назад
I suppose you could extend this to say that the nth root of 2 is irrational, n>2
@laz272727
@laz272727 2 месяца назад
nth root of m where n > m
@mikaelarschibald
@mikaelarschibald Год назад
best plottwist in youtube history :'D german mathematicians have this colloquial of saying "mit kanonen auf spatzen schießen" - roughly meaning: using canons to shoot down a sparrow. that's probably the funniest example I've seen so far of someone using a Kanone to schießen a Spatzen ;D
@GarryDumblowski
@GarryDumblowski Год назад
I feel like you could argue this isn't actually a valid proof if anything required to prove the FLT assumes the cube root of 2 is irrational.
@InsecureCreator
@InsecureCreator Год назад
so wait Fermat still applies when you're adding the same variables together? I always saw it expressed as two different ones so this is very neat to know :)
@bjornfeuerbacher5514
@bjornfeuerbacher5514 Год назад
That two variables have different names doesn't change the fact that they can have the same value. And if you have that special case that two variables have the same value, obviously you can then also use the same letter for both variables.
@xXJ4FARGAMERXx
@xXJ4FARGAMERXx 3 месяца назад
​@@bjornfeuerbacher5514 Maybe they were used to the a ≠ b ≠ c condition in other number problems
@visheshsomani9731
@visheshsomani9731 2 месяца назад
The fact that he called this overly soficticated
@bhargavinerusu
@bhargavinerusu Месяц назад
This is the most complicated proof as we need to go through the entire FLT to complete the proof. 🙂
@ulisesruiz3732
@ulisesruiz3732 Год назад
How can I laugh so hard at a 30 sec proof? Lmao
@yocats9974
@yocats9974 2 месяца назад
I am so sad that I have no idea what Fermat's last theorem is but I still found it funny because of the comparisons of the comments and how I completely lost track of the process in a single step. Edit: After watching like 2 minutes of a Numberphile video, I now know what Fermat's last theorem is. I did not expect it to be so simple.
@Akto
@Akto 2 дня назад
This is that domino that gets bigger meme, but the final domino is smaller than the first one. Fermat doesnt write his proof → Mathematician struggle for centuries → Andrew Wiles proved it → 2^(1/3) is irrational
@zapazap
@zapazap Год назад
This made me chuckle!
@DlBuli
@DlBuli Месяц назад
Not sure if this is correct. FMT says this isn't true for whole numbers. But it says nothing about fractional numbers. So you could find fractional a and b for which this applies
@parzh
@parzh 3 месяца назад
Still more elegant than a 26-minutes long video about √2 being irrational
@gudmundurjonsson4357
@gudmundurjonsson4357 2 года назад
i love it
@esaciel6805
@esaciel6805 2 месяца назад
Which occasionally works for every other root power greater than 3 😃
@simoneferrari6568
@simoneferrari6568 3 месяца назад
The definition of overkill
@josippetkovic389
@josippetkovic389 Год назад
2.78K subs ATM?! If this proves something Joseph Newton knows it lol
@TheLoneWolfling
@TheLoneWolfling Год назад
I did not see that one coming.
@theimmux3034
@theimmux3034 3 месяца назад
me using an integral to calculate the area of a triangle
@Alan-zf2tt
@Alan-zf2tt 9 месяцев назад
lol - polite applause
@keveneven1410
@keveneven1410 3 месяца назад
Someone show this to Terrence Howard
@recordkeepingandinformatio8206
@recordkeepingandinformatio8206 2 месяца назад
The funniest thing is that you can't prove sqrt(2) is irrational with this
@tolep
@tolep Год назад
How about root of a fourth degree?
@ScienceD9000
@ScienceD9000 Год назад
Exactly the same logic for any root greater than 2
@freddier47
@freddier47 Год назад
@@ScienceD9000 Pretty sure you can even generalise the proof for the nth root of 2 given that n is greater than 2
@thorinsee5129
@thorinsee5129 Год назад
Jo what?
@ryanmcadams1209
@ryanmcadams1209 Год назад
this is hilarious
@DontMockMySmock
@DontMockMySmock Год назад
lmao
@artoursad
@artoursad Год назад
LMAO
@islandfireballkill
@islandfireballkill Год назад
Is this circular? Does the proof of fermats last theorem require knowing about irrationality of cube roots of non cubic numbers anywhere?
@hits_different
@hits_different 2 месяца назад
Asking the real questions here. This made me realise that working with FLT must be a nightmare
@danielrhouck
@danielrhouck Год назад
For years this has been my favorite proof of this fact; Iʼm glad someone made a video about it.
@callumvlex7059
@callumvlex7059 2 года назад
I havn't laughed like that in a long time.
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