Goldbach Conjecture - Numberphile
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- Опубліковано 2 жов 2024
- Professor David Eisenbud on the famed Goldbach Conjecture.
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Numberphile could you do sublime numbers?
we only know of 2 of them
in case you didn't see my twitter comment you can also restate it as every number after a certain point is equidistant from two primes ( technically if you count distance=0 that's from 2 on, for distance>0 that's 4 on.)
+Numberphile The Goldbach's Conjecture and the solution to the Collatz Conjecture are intimately related. I will give you one week to prove it, if you fail in proving it I will prove it myself and post the solution in the comment section.
Again.
The Collatz Conjecture
If a number is even, divide by 2.
If a number is odd, multiply by 3 and add 1.
The Collatz Conjecture states that all numbers converge to 1.
Due to the fact that all even numbers are contained within the power of 2 numberline, we have:
n/2 = 2^s, where s are all positive integers.
n = (2^s)(2)
n = 2^(s + 1)
Due to the fact that in order to make a number even we need to multiply it by 3 and add 1, we equal 3n + 1 to 2^(s + 1); we have:
3n + 1 = 2^(s + 1)
3n = 2^(s + 1) - 1
We equal s to the first strictly positive integer, that is, 1; we have:
3n = 2^((1) + 1) - 1
3n = 2^(1 + 1) - 1
3n = 2^(2) - 1
3n = 4 - 1
3n = 3
n = 3/3
n = 1
All numbers converge to 1.
"Prime numbers are mostly odd numbers." That's an understatement if ever I heard one.
"MOSTLY"
AAAAND, 2
And 2 is an even integer that can’t be written as a sum of 2 primes.
Yeah
yeah, because 2 its a prime number but also an even one dumbass
Late at night, you're on your computer, lights out, hunched over the bright monitor, staring intently at what's on screen. Suddenly, your mom walks in unannounced and stares horrified at what she sees.
"Oh my God! Are you trying to prove Goldbach's Conjecture?"
whiz 85 😂😂
Yo that is pretty horrifying
Haha nice 💯
You look up, realize that you are 47 and probably shouldn't be living in your parent's basement any longer.
are you winning son?
*video starts*
ok I've forgotten English
*panic*
Stargazer hahahahaha lol
Stargazer same
I'm not a native english speaker so it took me some time to understant it's german.
Stargazer Yes!
It looks like some weird cross between Latin and German to me, not that I can speak either!
He speaks about trying to solve Goldbach's conjecture as if it were smoking marijuana or something, haha. "I swear I've never done it!"
This is the same with the Riemann hypothesis, some may think you're crazy for trying, it can even destroy your reputation sometimes.
Somebody solved the mystery, while they were high 🍀 marijuana 🍀
marinujan.
@@pe3akpe3et99 that was a golden comment lol
@@DreckbobBratpfanne That's the problem with modern academia: everyone is too concerned of their reputation as everything is built on the phd system. But in the past people like Einstein and Galois published research that is fundemental to physics and math today, and they were working outside a university environment.
I swear if we didn't have this concern of reputation, the millenium problems would have been solved and we would've had a unified field theory long ago.
Hang on a second, I've got this.
+
"hold my beer"
Srinivasa Ramanujan jokes apart, we need people of that calibre to crack down stuff like this
Asther Phoenix It truly is a shame that Ramanujan died young. With some formal training, he could've rivaled even Euler himself.
So happy to see you are still alive! I thought you died, lol! :D
9:31 This guy definitely works on Goldbach’s Conjecture in his attic.
Yes
Numberphile, the only youtube channel doing 9minutes and 59seconds long videos in 2017
Miche Delarue 9:58
Miche Delarue this is weird. before i click the vid it says 9:59. when im watching it says 9:58
snepNL yeah, the video isn't actually exactly 9:59 or 9:58 minutes, so if you watch it on phone or tablet, most of the time they'll lower it by 1 second, it's hard to explain it really
I posted a video that is exactly 3 minutes and 2 seconds long, and sometimes it rings up as 3 minutes and 3 seconds.
It's not the length...it's the substance.
I loved this video. I hope we can see Professor Eisenbud more often on the channel, I very much enjoy his calm way of talking.
He's like the Bob Ross of math? :) Except usually mistakes in math remain mistakes, and not happy accidents
Yeah, he’s got this really cal in chill avuncular vibe.
One time I got robbed and I said Hey I want my Goldbach
Mike H Once my friend asked me what bread I'd like to eat, I said "I want Riemann and also a beer man."
It does when the German pronunciation of "ch" as in bach is very similar to the English pronunciation of "ck".
except it isn't similar at all
The ship's diesel engine was making a loud squeaking noise so I called in the Euler to fix it.
oh yeah? prove it
Starts video in a foreign language and I think I had a stroke.
😂😂Underrated comment
Looks like Goldbach's Comet contains something like Sloane's Gap.
Understatement of the century: "Prime numbers are mostly odd" is that an open question? Finally found a proof I could tackle!
For some reason these mathematicians seem really pleasant people. This is one of the things I wish I had appreciated when I was young.
2 and 3 are only consecutive prime numbers. We can generate all numbers using two and there as basis.
For rest of prime numbers minimum distance is 2 (twin primes) we can generate all even numbers minimum distance of 2 using twin primes as basis.
David Eisenbud is, hands down, my favorite guest on Numberphile. If I had him as a professor for Differential Equations, I might have actually retained that knowledge.
Me in the first seconds of the video: "Wow I should improve my English, I'm starting not to get some things..."
I prefer Douglass Hofstadter's variation of the Goldbach Conjecture: "every even prime is the sum of two odd numbers". Much easier to prove!
Nordic Exile 1+1=2 lol
David has the most soothing voice on earth.
this conjecture helped me won the Qatar math quiz competition! Will never forget this as this changed my life!!!
Akul Sharma Congrats! How exactly?
Molka Ben It just did
there was a question as to how many conjecture a student knows and how you derive it!
Martin Stu Ignoring the fact that for many centuries the Middle East was the center of the scientific world. (It isn't anymore, but still)
Why are you using Arabic numerals until now butthead?
Working from outer to inner numbers you have the top 4 with bottom 26 equals 30....24 plus 5 29, 6 plus 22 is 28....
Wow 9:58-9:59 mins Brady your a beautiful human being
san kitty "You"re"
*Sees video is 9 minutes and 58 seconds long* "Numberphile being edgy"
+johnny dss
What is the significance of this?
He lost a lot of money by not making the video 2 seconds longer.
johnny dss they don't get paid extra for over 10 minutes anymore now btw
I appreciate his voice and calm talking
Would love to sit in his lectures
I always greatly enjoy Prof. Eisenbud's videos (still remember the Gauss - heptadodecahedron one, and specially, the proof of the Fundamental Theorem of Algebra...
From this conjecture an intesting fact follows. For every n there exist prime p and q for which p-n = n-q....
These conjecture videos are really fascinating. Nice work numberphile.
Wow ths conjecture seems so logical when you see how the number of possible ways to express even number is growing steadily. It is rather interesting no one knows how to actually prove something so obvious.
i emailed and asked for a video about this conjencure a few years ago and i am very happy to see one! hopefully there is material for another video about this crazy and beautiful theory that seems so intuitive and unintuitive at the same time! thank you for the amazing content, i have been a fan for many many years
Uncle Peter and Goldbach's Conjecture
Apparently a Filipino mathematics teacher claimed to have solved this problem
Which is very embarrassing. This only reinforces the stereotype na bobo ang mga Pinoy.
Edit: I mean we have the PISA Studies, but it is what it is.
Man, besides the math, that dude has really nice handwriting skills...
Numberphile is so cool. Which math channel has so much content that something as big as the Goldberg Conjecture gets its video after so many years?
of course the conjecture is false for any even number
I know people who like math are the rare ones, but watching this not being excited and thrilled, they are the ones missing out so much in life.
I keep coming back to this one. Clear, concise, deeply fascinating, and Eisenbud is quite charasmatic.
Emil's Conjecture
for (n) numberphile videos uploaded, at least 334.4 comments containing "first" will be posted during the first x*10 minutes
if there are "n" firsts then how many of them will actually be not first? Let's call that The Kingbach conjecture.
Define x.
between n-1 and n.
And for every Numberphile video posted about a conjecture there will be at least two comments that say "I have proved this conjecture, but the comments are too small to contain it."
Emil Macko Completely unrelated to math, but by any chance, are you the guy who created Five nights at Candy's?
I proved that any odd integer greater than 4 is the sum of a prime number and a positive even number.
Now give me my fields medal !
You can even set the prime number to three!
1 is not a prime, skhuksle :Ü™
yep, and so what?
@@Darker7 Yes it is. One and two are both primes.
@@ezioauditore4944 1 is definitely not a prime...
I like him. He reminds me of a professor I had in college for an intro proof class and then differential equations.
Another banging video, Numberphile. I first encountered the conjecture in one of Ian Stewart's books, and I must say it must be the easiest to understand maths question that still can't be solved. I couldn't wait for you to do a vid on it. Great job.
For easy visualization related to prime distro: GB - EVERY 'number' is the average of two primes.
I've written a wonderful proof of the Goldbach Conjecture, however there is not enough space in the youtube comments section to write it here.
Pierre de Fermat I was looking for this comment xD
And now here it is again. This is getting old.
so is pierre
badman jones - Combat moi.
Pierre de Fermat - Imposteur!
I also love Goldbach conjecture.. Assuming distinct primes are possible, which i guess is the case for even number greater that 8, we can prove that any prime is an average of two other primes. From that Bertrand postulate will follow..Not sure if any prime is average of two other primes is a valid theorem, but interesting that a valid theorem ( Bertrand Postulate) comes out of it.
I have an elegant proof for Goldbach Conjecture but I’m suffering from lack of space in the comment section
FINALLY YOU GUYS DID IT
That miscalculation 3:25
oh boi
Egzolinas Gamer almost thoght i was the only one to ser it
Well, to be fair he did SAY it right... He just followed the wrong line.
Thank you! It was a simple mistake but it gave me such anxiety. lol
I love the shade he threw at Brasy
How does a mathematician even work on a conjecture? Like where do you start?
With an idea at the pub where your mate says "you're full of crap" and so you spend weeks, months or even years to keep your dignity
I've wondered that too for a while. Apparently you need to start off by reading (booking up) all the relevant stuff that has been discovered already and the various methods that have been used/papers that have been published. Then you probably start by working on a smaller problem within one of the already established ideas. I don't think one would just immediately have a groundbreaking idea out of nowhere.
Beer is powerful
JiaMing Lim , In my experience, throw things at the wall, see what sticks, read what other people have tried, try those yourself, read what people have tried for vaguely related problems, try those too. Repeat the above until something seems to not be there when it should, or be there when it shouldn't. That's the first grapple point. Keep working from that foothold until another is found, and just maybe, the climb proper can begin.
Notice a pattern. Check a lot of cases. Seems to be true? Done!
9:41 James Bananaman starts counting the digits of the largest prime in the world.
His german is lit.
I would suspect that the Goldbach Conjecture is a simple consequence of the universal translational/bilateral symmetry specification of an infinitely divisible Euclidean/Cartesian space or line. In such an infinite space or spacetime. the central zero point is entirely arbitrary and the orderability of the entire system moves right along with that arbitrarily selected zero point. And of course, that would compound accorfingly. Goldbach would thus seem to be the prmordial symmetry condition of number theory itself - its "taken-for-granted" universal applicability over space and time.
Thus, to prove Goldbach (in the absolute) would be to prove the most foundational aspect (i,e,, unwritten axiom or assumption) of most all of mathematics and logic - the universality of translation. And that would, of course, seem to require an order of self-referential logic beyond the infinite - to prove the logic of logic itself!
For the prime + twice a prime, instead of writing it a+2b, write it (a+b) + c. If we prove that any even number can be written as a+b and we prove that any prime is an even + a prime, would that be proof that a+2b would be a way to write any number with primes a and b?
Since there is no certain way to find primes I'd say, Goldbach's conjecture is the closest to one. If you take a number significantly larger than the largest known prime, you should always find a prime bigger than the largest prime known.
Goldbach’s conjecture isn’t of any use in finding large primes.
If you take a googolplex it obviously can be written as (googolplex-97) + 97. It’s easy to show 97 is prime but there’s no easy way to show (googolplex-97) is prime.
You missed 5+5...
When Euler says that he can't solve a problem, you better belive the thing is really hard.
7:00 - There could be a unique way: look for the pair of primes with the smallest possible prime, or find the pair of primes with the smallest difference.
I absolutely hate math in school, but things like numberphile and squaring numbers is incredibly interesting
I have learned more maths from Numberphile than school.
I would guess that 2 can't be written as the sum of 2 primes, since 1 isn't a prime, and I suspect 0 isn't a prime either.
While some claim that -2 and -3 etc are also prime numbers, they are in general not considered primes. But if we exclude negative numbers as primes.
Then 2 is an even number that can't be written as the sum of 2 primes.
it’s the only even number that cannot be expressed as the sum of two primes
and negative numbers are not as they have at least a third factor or -1 so they’re generally excluded
Sino nandito dahil kay danny calcaben? Potcha mapapa aral ako ng wala sa oras😭
Here is a conjecture: There exists an even number between 1.00024x10^81 and 1.00025x10^81 that can be written as sum of two primes in exactly one way (besides the obvious permutation). One of those primes is less than 10^57 but greater than 10^50. The other one, of course, is 82 digit long. This is the first even number greater than 12 with this property, and there does ot exist another such example less than 10^100. The first even number that violates Goldbach conjecture lies between 10^(10^51) and 10^(7+10^51).
Where's the proof for the first part?
And this, guys, is the voice you get after a life of shouting on poor students...
So you know him personally?
Hardy once said "It is comparatively easy to make clever guesses; indeed there are theorems, like 'Goldbach's Theorem,' which have never been proved and which any fool could have guessed". Nevertheless, he spend a lot of time trying to prove the conjecture.
I bet James Grime works on this in secret and laughs maniacally whenever he makes progress!
Also the primes are odd all odd They are a pair with 1 more number that are divided by 1 so added the even plus "1+1" will also give even
Jaaa! Deutsch... Endlich verstehe ich etwas...! :D
Dann ist dein Latein aber auch nicht von schlechten Eltern!
Was hab' ich gerade gelacht... :)
Und mein Chinesisch? und mein Japanisch...?
中國話也很好。
俺の英語も大好きですか？
sry... Autismus... :I
dein Japanisch, keine Ahnung, aber dein Chinesisch sieht als es von Google Translator genommen wäre aus ( auf Deutsch du hast gesagt:" Chinesisch er (ist) sehr gut" (Zhongguó yi ta hen háo) )
何ですか。私の日本語はちさいです。
1 can’t be a sum of 2 primes but it can be the difference of 2 primes
You should seriously interview Prof. Eisenbud more often. He's one of the most eloquent mathematicians on your amazing channel.
I'm certain that he's quite busy, being the director of MSRI and all.
Haha fair enough. He is brilliant though.
The joke at the end is all the more funny knowing *full well* that dude and every other nerd that ever looked into primes has worked on the Goldbach Conjecture. XD
I love how taboo it is to try to discover a solution :P
Why be embarrassed about whether you've worked on the conjecture? If like you say lots of people would die to solve it, then you don't even need an excuse. Take a crack at it. What's the worst that can happen?
0:33 the subtle additions drifting away gave away the conjecture (and yes I glossed over the intro)
So if all even integers are expressible as the sum of two primes, then ALL integers are expressible as the sum of 3 primes; just even integer+1
is there any relation between discrete logarithm and integer factorization?
If I can make a working bedwars on Minecraft, can I solve this?
This guess can be expressed in a more beautiful way.
Each number is located in the middle of two prime numbers.
For example 15 is located between 13 and 17.
12 is located between 11 and 13.
Real treat for us germans that someone who is not a native speaker pronoumces the "ch" correctly. Nomally they will pronounce it like "k" but you did nicely.
The first thing u should do when watching a numberphile video is to thumbs up
La conjecture de GOLDBACH est vraie parce que la quantité de possibilités de sommes de nombres premiers égales au nombre pair est toujours au moins égale à la valeur entière du quart de la racine du nombre pair.
A partir du nombre pair 16, cette quantité est toujours au moins égale à 1. Pour tous les nombres pairs inférieurs à 16, il existe toujours au moins une possibilité (en considérant le nombre 1 comme nombre premier comme GOLDBACH).
As a German, i was wondering as I started the video and prof. Eisenbud started speaking German, but just a compliment for prof. Eisenbud: His pronounciation is quite good!
I am FASCINATED by his notation for approximate equality. Is that common and I'm sheltered, or did anyone else find that peculiar?
Videos like these make me realize how minimally I use my brain on a daily basis. A small part of me wants to be a number theorist and really become a mathematician.
Anyone else notice that he puts the numbers of Goldbach’s birthday in a pair of primes?
My God, I love this guy. The voice, the enthusiasm. It gets to me.
When any two odd numbers are added together, they will always make an even number. Since all primes except 2 are odd numbers, it is safe to say that any two prime numbers, except two when added together, will always make an even number.
oh wow german has changed since this has been written
Half the German sentence is actually in Latin - so it's almost not understandable for Germans as well. ;)
"sey"
The picture was of Euler, are you sure it wasn't Dutch?
For this problem, what will one need to show to serve as a solid proof?
The way professor writes the letter q is so cute :D
It may be even qute, the very highest form of cuteness. 😁😁
Goldbach's conjecture works because of the wildcard numbers 2 that go through every pair also the 5 that doubles itself 5.10.15.20.25...prime numbers are not doubled by the number 3 and 7 also perfect squares odd minus ending 5 example 3+3+3... to infinity and 7+7+7... to infinity and the perfect squares
I wanna see Numberphile sit a GCSE maths paper
He's like: "I swear that both of my marriages and my country club membership weren't destroyed because of Goldbach"
Bonjour,
Pour ceux que ça intéresse, je propose une résolution de la conjecture de Goldbach publiée sur UA-cam en 5 épisodes sous le titre générique "Variations Goldbach".
Comme elle s'adresse à tout public, pour ceux qui veulent entrer directement dans le vif du sujet, une formule donnant la proportion minimale de couples de premiers au sein de l'ensemble des couples d'impairs dont la somme vaut un nombre pair se trouve épisode 2 et l'essence de la démonstration épisode 5.
Le commentaire de J ci-dessous est tout à fait exact, mais en fait, il y en a beaucoup plus.
Entre plus ou moins 10.000 et 16.000 le nombre de minimum de couples de premiers monte à environ racine carrée du nombre pair, et ça continue d'augmenter comme je le démontrerai dans l'épisode 6, qui clôturera cette série.
Berendans
Wait, did the prof. say the chance of m being a prime is m divided by the NATURAL logarithm of m squared, but then he gave examples using common logarithm 6:40
By the change of base formula, all logarithms are constant multiples of each other, so they're basically the same thing in the same way that y=2x and y=3x are basically the same function. logb(x) = ln(x)/ln(b) (change of base formula), so the common log is just ln(x)/ln(10). ln(10) turns out to be ~2.3, so multiply the numbers he gave by that amount to get a better answer if you really want to. But the point is, for a crude approximation as is in the video, there is really no difference between log10(x) and ln(x), they are just constant multiples of each other and have exactly the same growth rates.
Thank you Prof. Eisenbud.
What is the oldest unsolved math problem? I'd love to know.
Probably squaring the circle, with the invention of algebra it was done. But if you are using the greek system it is impossible. Possibly also zeno's paradoxes, which were solved with the introduction of calculus. But he created them as a thought experiment of sorts, and as such a solution was not technically required.
Every even integer nn can be expressed as the point of intersection of two lines using linear functions:
f(x)=2p1, f(y)=-0.5x-p2 where x
Incomplete proof
I want to floss him so badly
About time you guys make a video on Goldbach Conjecture. Enjoyed it. Thanks Numphile
I noticed something interesting with goldbachs conjecture if you take the combination of ways to make golbachs conjecture true for every single prime number above 4 youll see that it makes a pattern 1,2,2,1,2,2,1... or seems to could we prove this with induction to be true for goldbachs conjecture and then prove goldbachs conjecture.
You do have a really relaxing voice...! :D