The Oldest Unsolved Problem in Math

Am I the only one bothered that he says AND between all the millions, billions, trillions, etc... couldn't help but mention

​@@jacobe280 Yes. You are.

@@jacobe280no you’re not

Fish

@@AMPProfSquid

Right? It feels like if we had found a way to keep the guy alive he would be responsible for the majority of all mathematical discoveries

Number theory concepts*

Possibly the most important mathematician in history

@@ab3040either him or Gauss

@@rogerszmodis6913 Gauss was equal in math and science, so overall he was probably more important, but as far as just math goes I gotta give it to Euler

I saw this exact comment at least 24 hours ago, does that mean i time traveled?? Or did you delete your prev post and reposted

I have an important question
Somebody said that The reason Gödel was able to show that math is incomplete [ that is there are true statements which can never be proven] is because he assumed that math is consistent (Meaning he assumed it's free of contradictions,
So what the hell is happening!!??
If this other guy is right, then Gödel's proof of incompleteness seems completely flawed

@BarryBarrington-zc6lz
As someone's who's 21... sounds _surreal!_ I even feel like congratulating you, lol. 🫱🏻‍🫲🏾

You forgot to end your parentheses. 😉​@@1stlullaby484

​​@@1stlullaby484it's a form of mathematical proof known as proof by contradiction. Gödel showed that if you assume math is consistent and all true statements can be proven, obviously false statements (contradictions) arise.
A simple example is a proof for the non-existence of a largest integer. We assume two things:
1. You can increment any integer to create a larger integer.
2. There exists a largest integer.
If you apply assumption 1 to assumption 2, you end up with an integer that is larger than the supposed "largest integer". Therefore, one of the assumptions is false.

It will mad u

68th like

@@WaddieJoe you mean (n-1)?

@@oliverthomas3134you sound like your on drugs

@@RAGHAV4882a-s-s

"I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."

this guy is the biggest bragger in human history.@@BixbyConsequence

No it’s a joke reference to fermats last theorem lol

​@@BixbyConsequenceThat was Fermat

​@@TheXuism how much do you know about Fermat?
He was anything but a bragger in my Opinion.
He never published any of his genious ideas, his son did it. He became one of the most famous mathematicians, but was an actually a lawyer. So mathematic was only his hobby.
And you call him a bragger?

Euclid god of math

I disagree

Foreal?

Beautiful pun

​@@supremelordoftheuniverse5449why?

The more we learn, the more we realise how little we know

@@mansouralshamri1387 Even though i had the desire to read more books and engage in more subjects (most of them are self taught), it will still not be enough to achieve my goal. i dreamt to become like leonardo davinci but as technology progresses, it is becoming little easier but i question that where is the world going then? To pursue things that we don't know? But it also makes them less wiser, or maybe more? Or is it the phenoemon that sapiens are unaware of? I wish that if finances were not the problem in my whole life, i can figure it by myself

@@stupiocity245 it definitely doesnt make any them less wiser, every form of new knowledge isnt bad, ever. just go ahead, experiment and find little by little how you can introduce change in yourself. as time goes by, no matter the path you went, when you look back you will realize you definitely changed

@@mansouralshamri1387 However, at some point, wisdom must kick in, to make us realize that not all of that knowledge is valuable or useful (except perhaps on trivia night).
Intelligence is knowing a tomato is a fruit.
Wisdom is not putting it in a fruit salad.

Do you know that a woman was given the abortion pill ,gave birth to her child and they cut the spinal cord and put the baby in the bin while he,she was alive

37

@@satriorukito 42. At least, that's what Douglas Adams tells us.

Ghost pepper, Cheeteeeeeeeaeeeaeaeaeaeaeaeaeaeaeaeæéêēêåeeeaeaeaeaeaea

this comment just blew my mind🤯 doing this exact thing while high

Nah it’s alright. Better an attempt at solving it, than not trying at all ❤

Even if you're not a mathematician, you should give it a go if you're interested!
Math problems that stump the masters get solved by a novice perspective all the time, but even if you end up retreading existing ground, you'll end up learning something cool along the way :)

That's so inspiring haha thanks​@CananaMan

Eu(clid x ler)

Imagine the noises the readers would make if Gauss joined in!

@@Xezlec Math : No Way Home

Oiclid and Yooler

Maybe, "I reincarnated into math genius, Euler, and continue my own legacy. Yes, I was Euclid."

dude, i dont know what're you talking about but i agree.

lol

Same

I’m actually early to a Veritasium video

This comment hurts

Same although it’s project about a book

Bro its literally told in the video... Altho slightly differently, but its there...
Cuz 1+...+127 is 127*182/2 and that the euclids representation too

Let's say P is a perfect number.
Any series 1+2+3+4+... +n is n terms long and on average (n + 1)/2, so the sum is n * (n + 1) / 2.
So P = n * (n + 1) / 2.
Another thing we notice, is that all the series are (3, 7, 31, 127) in length. Those are powers of 2, minus 1, so let's say n = 2^m - 1.
Now, you say you divide the perfect number by the last number in the series, that would be n.
So, divide P by n simply gives:
P / n = n * (n + 1) / 2 / n = (n + 1) / 2 = (2^m - 1 + 1) / 2 = 2^m / 2 = 2^(m-1).
In other words, the power of 2 you end up with after dividing by that last number, is m - 1.
Let's look at 6 again. It it the sum of 3 numbers, n = 3, m = 2 (2^2 - 1 = 3).
So P / n is 2^(m - 1) = 2^(2 - 1) = 2^1 = 2.
For 28 n is 7, m is 3, so P / n = 2^2 = 4.
For 496 n is 31, m is 5, so P / n = 2^4 = 16.
For 828 n is 127, m is 7, so P / n = 2^6 = 64.
There is not even really a pattern there. And it doesn't work anymore for the next one: P = 33550336.

The

That actually helps a lot with understanding why RNG is multiplicative in most video games.

omg i was using that in programming, never knew why it was called MT19937 😮 my mind is blown away

@@lpc9929well said

Got any keywords to recommend for searching for information on these PRNGs? If there's something more performant that I can guarantee generates the same sequence regardless of platform that would give me something fun to do for a game engine I'm writing as a hobby.

Clearly you didn't watch the video, it's an even idea.

@@Dranzer_Panzerthat’s a prime quality comment

When my professor asked us to write a program to find perfect number I was like wth is that then he gave us the formula so it was easy but never understood what it actually was until now I found only 2 6 and 28

@@lucashershberger623 wonder away.

@@lucashershberger623 Circumstantial evidence, maybe

I absolutely recommend you Real engineering , Mustard , Vsause , Kirzguat in nuteshell ( Idk perfect name ) , But why , SciencePhileAI , Kosmo ..
there are many more who provide valuable information with the proof and good details and you can learn something new that's worth your time instead of spending time on tiktk..

Penrose, Euler, and Archimedes of Syracuse try and fail to walk into a bar due to the exponential volume of proofs they collectively produce by accident on their journey from the parking lot

I will never not be disappointed that MIT's hockey team isn't the Eulers.

The Age of Unreason series clued me into how awesome Euler is (though he's a secondary character), and I've been stanning ever since.

@@Greyhawksci only like 1% of people would get it. I would bet the vast majority of people read and pronounce Euler phonetically.

There’s the old joke that so many random bits of math are named after the guy, we may as well just start calling numbers Euler letters.

I knew Prime95 was to find Primes in addition to a stress test, but I had no idea of the depth of the GIMPS project. Considering the program is both so simple yet computationally intensive, to be known as one of the most intense stress tests for a computer, really speaks to the sheer computing power we have needed to go this far.

Read this as “as a computer who is also a math enthusiast” at first and had to think for a second lmao

26:17 "Carl Pomerance predicts that between 10 to 2,200 and infinity, there are no more than 10 to the (power of) negative 540 perfect numbers."
I'm not good at math. Can anyone tell me why that number is to the negative power instead of positive power?
As far as I know,
10 ^-1 = 1/10^1 = 1/10 = 0.1
10^-2 = 1/10^2 = 1/100 = 0.01
Therefore, 10^-540 = 1/10^540) = 1/ (1 followed by 540 zeros) = 0. (539 zeros)1
10^-540 is less than 1. However, 51 perfect numbers have already been discovered, so how can the there be no more than 0. (539 zeros)1 perfect numbers in Carl Pomerance's prediction? Is there an error somewhere?

@@simon6071 10^-540 perfect numbers of the form N=pM^2
An odd perfect number must have the form N=pM^2, so there are very close to zero odd perfect numbers expected in the range 10^2200 to infinity.

No doubt, this age will be remembered in history as the beginning of the computer age. It has completely transformed society in a way few technologies have before.

Same, I literally shed a tear.

I remember when a computer beating a human at chess was newsworthy.

Now realize that LLMs dont even come close to representing that increase in the efficiency of labour....

I just had a thought about primes. Has anyone figured 'primes' for fractions? What I mean is, instead of using whole numbers, try using a small fraction, such as 1/1298ths as your potential prime, and figure out if any two larger normal fractions multiplied together can make the smaller one. Or some other scheme using fractions to find fractional 'primes'. I'm thinking some cool new mathematical knowledge could be found, or a cool pattern.

Why is the only irrelevant question in math.

Sisyphus

Most sukkuna quote ever.
They ask me why and if. But i do it when i like to kinda message ( admittedly finnished it few hours ago yet cant recall its quote)

@@ItsJustKaya Why are you writing like this?

When Boolean Algebra was invented in the 1840s it was purely theoretical without any possible practical use.
Today it is the way the circuits in digital computers work.

HELP! I need some conversions. I need all of the following each into Exatons and Kilotons!!
30 Megatons
3 Gigatons
22 Gigatons
48 Gigatons
15 Teratons
4 Petatons
8 Petatons
60 Exatons
400 Exatons

Based genius

Based AF braa

Actions speak louder than words

Nelson Cole is the main Character!

*Drops chalk and walks off stage

The end of your comment reminds me of my Mentor saying one time that part of him hopes someone disproves the Riemann Hypothesis just because of all the papers hes read on "if the Riemann Hypothesis is true then X" and how they'll all have to be withdrawn.
He thinks its true fyi.
I wouldnt call myself an odd prime "truther" but I see no reason infinitely many couldnt exist just the first one being say > 50th Fermat Number would put it out of search range for the forseeable future. Then one about every billion more digits.

1×1=2

Do you know any papers that rely on the existence of odd perfect numbers?

​@@Featherless1keep going...

2x2=4=2+2

I love when people spell immediately correctly

Absolutely😊

@@ThisHandleIsAlreadyTaken839 I love when people realize that not everyone knows how to spell or read, some didn’t go to a fancy uni, check your privilege 😠

@@hanu6158 115 have thumbsed up their message, so this is one person getting their jollies from being petty. But a spell checker is not privilege - all computers, cellphones, etc. have one.

Well, he does add that there are additional arguments that make the original heuristic argument stronger, he just doesn't specify what these arguments are (possibly implossible to explain to laymen in the space of a few minutes?)

A brilliant number theorist, sure, but would you say he's a perfect number theorist?

@@ES-54321 good one

​@@ES-54321 even then.. would he be considered a brilliant perfect number theorist or even a perfect perfect number theorist or maybe a perfect even perfect number theorist?..

@@ES-54321da dum dun tssss

​@@ES-54321 😂😂

omg exactly 37 likes !1!1

@GhostieTheML what it mean sir

@@GhostieTheML37…

@@GhostieTheMLwell it’s at 69 now

I am not smart but I still ended up watching the entire video

Crazy how humans are capable of all this, but still can't stop using plastic for everything lol. We're too intelligent for our own good xd.

​@@Believe5inJesusChristYou may be barking up the wrong tree.
This video is about people setting out to prove or disprove claims with evidence - the exact opposite of religion which asserts a claim and then uses the claim itself as evidence.
"I believe that a god exists, as claimed in the Bible."
"Where's your evidence?"
"Look at this from the Bible..."

@@tincanblower Not only that but also
"Where's your evidence?"
"Look at this book written and rewritten by humans for millennia before the printing press, humans so propense to make mistakes, lie, cheat and push some ideology into the paper if that suits them"
This is why the old testament God, is so different from the new testament God, they were invented and imagined by humans that add very different ideologies, about what is right and wrong.

@@tincanblower It's a bot. There's a lot of them on KRplus that exist just to quote verses.

​@@Argoon1981As Sabine Hossenfelder has said, " The existence of God is not a scientific question. It can neither be proven or disproven by science. It is a philosophical question "

It is used for stress testing overclocks because it is sensitive to mistakes in the calculation caused by overclocking too much.

Damn thats interesting

It says this during the test.

Finding primes was (and still is) its original purpose. It just so turns out that finding primes takes a lot of computation power and it is so well optimized that it can squeeze out every drop from a CPU. And if there is a fault anywhere in the CPU, it will show.

@@fulgerion you probably also read EULA’s 💀

Imagine he just wrote some random ass numbers and it didn't even multiply to the original

😅u

you've been involved with gimps ? 🤨

​@@Filo127you haven't watched the video?

I have a micro super computer, because I both do software development, video editing and play around with AI with huge models and video games. I've just started contributing to the project; since my demands are high, I usually replace parts before it's reasonable to do so. Now I can actually put my CPU and excessive cooling to good use when I'm just watching youtube and not waiting for something to encode or data to parse. I'm already 1.2% into my first assignment.

Do you know what a gimp suit is? If not look it up lol.​@@LeVasTiaN

OG distributed computing projects were the best way to stress test overclocks back in the day. did alot of gimps, fah and seti myself.

I must mention that 3^n -1 is always even so none of those are prime.
But about the test I think you are right.

@@mehrabnikoofaraz233Thanks for correction, I've changed it to different example to avoid confusion.

Ironically, the test is so efficient that someone skilled at arithmetic could perform it using pen and paper in some hours or days, for 15-20 digit numbers. Mersenne's "all time would not suffice" claim was likely based on trial division … the oldest and least efficient primality test.
The test goes like this:
Let n be an odd prime. (NOTE: a prime exponent is necessary anyway, so other than ruling out 3 = 2^2 - 1 this is w.l.o.g.)
Construct a sequence S(i) with:
S(1) := 4
S(k + 1) := S(k)² - 2
p := 2^n - 1 is prime if and only if S(n - 1) is divisible by p.
E.g. n=3 is an odd prime, p=2^3 - 1 = 7, S(3 - 1) = S(2) = 14 = 2 * 7, therefore 7 is a Mersenne prime.
Crucially, because only divisibility matters in the end, it suffices to calculate the remainders of the S(k) modulo p, which prevents the intermediate results from growing very large.

@@TruthNerdsClear and informative. Thank you.

It’s because it’s both: it’s fast-growing but _also_ easy relatively to check.

A book containing the largest known prime and a text file containing the largest known prime are actually equally useless.

It makes a fairly decent random number generator. Flip to a page and stab your finger at a number. Just skip the first and last numbers (the first is more likely to be 1 (I think, I might be thinking of something else), and the last is odd).
It's also kinda like a code pad, but less secure since there's lots of copies of it out there. To be truly secure there should only be 2 copies of a code pad. It's unbreakable though since the data is completely masked by randomness. Assuming the pad is created in a truly random manner.

​@@falconerd343Benford's Law. One Time Pad.

I assumed they were all just scrambling to buy gag gifts for their mathematician loved ones

Imagine how much energy and computation went into making that book.

I was so relieved it was finnally over. BUT IT WASNT

What da faq you doing here ?

Fr Minecraft KRplusr on math 😮

​​@@ruskcoderso what?
Everyone enjoys Veritasium whether they like maths or not

I was looking for this comment..

Hey after 8128 is the next perfect number 41,328?

@@harshrajveermaran5792 No. The next perfect number is with p = 13, so 2¹²(2¹³ - 1) = 33550336

@@harshrajveermaran5792no it's 33,550,336.

Veritasium already did a video on Collatz 🫡

What if there is only one odd perfect number, and it's the only number at which Collatz Conjecture fails? 😳

your feelings are irrational

I was also thinking it's a fallacy to think because someone is working on "something that matters" that they are necessarily accomplishing anything. Given the amount of academic research fraud going on, it's hard to know whether someone got published because they found something interesting, or they are milking the system for more grant money or to get on the tenure track.

​@@Fire_Axus your comment is perfectly odd

Where’s the proof

channels like these are why I love KRplus in general

I agree, Veritasium, Vsauce, SmarterEveryDay and Sabine Hossenfelder are prime examples of channels that make KRplus worth using even if you wouldn't like all the ads and random stuff.

@@MikkoRantalainen "prime" examples

Asianometry

You didn’t really learn anything
You just watched a video for entertainment and will forget everything the moment you click on a different video

Another great thing is that it's fun to try. And that fun is a great motivation to learn the more tedious parts of mathematics. It's like when we used to say "why would I learn the multiplication tables if I have a calculator", and we had a point: what's interesting about something that's already solved?
But every person I've talked about mysteries like this one are suddenly enthralled by the idea of maybe finding the answer, and that motivation to learn is priceless.

I sometimes wonder what else could be invented or discovered if the productivity is redirected to some other endeavours.

Exactly, this whole quest spawned Prime95, which has helped me overclock PCs for years now.

Thanks for sharing this 😊

Toilet flow direction is important.

You sound really smart. Sincerely.

@@Whiterioot Thanks, I try my best.

@@Soken50 congratulations on trying your best to sound really smart, which is what you just agreed with @Whiterioot about. 👍

Yeah Magnus Carlson was just good at Chess at 20 pales to the understatement that 20 year old Euler was just a prodigy

Even though I'm pretty sure there's no better single word that could be applied, I agree.

@@cf-yg4bd I was about to throw one back at you then realized I legitimately can’t think of one either. Well said.

What is special about them? It is my first time seeing their name.

@@PlayerSlotAvailablehe’s a revolutionary in math-you can look him up on your own time, but for example, he’s the one who came up with the modern notation for functions, and also came up with the most beautiful math equation (Euler’s identity).

When did he move from LA?

Can confirm. It's midday here in 🌏

Fr I’m about to sleep soon

It's evening for me

Honestly it feels weird to be awake when a big channel releases a video lmao
Australia's timezone is hilariously inconvenient if you watch US or Euro stuff

For the even perfect numbers, there isn’t a different formula - that is exactly what Euler proved in the 18th century.
In terms of testing, you might have thought the only thing different nowadays is the computation power available, however this is untrue, since this video doesn’t mention any of the techniques used for searching for these perfect numbers (in terms of half an hour this would have added another few minutes of run-time).
This combines the ancient method of factoring (trial division by sieved primes), pre-computer methods (Lucas’ primality test, strengthened in the 1930s by D. H. Lehmer), and modern factoring methods (such as Pollard’s p-1 method or Lenstra’s elliptical curve method of factorisation). The GIMPS project combines all of these (as well as Fermat PRobable Prime testing, owing to greater reliability over the Lucas-Lehmer test); it’s not merely brute force computations.

whgats a GIMPS prime

What a waste of time. Look…
There isn’t an odd one.
This is now officially solved.

@@PaulDeanBumgarner Is the joke that you pretend to be a boomer? Cuz "Bumgarner" surely can't be a real name.

Bro is real

​@@DasAntiNaziBroetchenI've seen both Bumgardner and Baumgartner, I'm sure Bumgarner exists somewhere

It seems likely to be that the heuristic is actually JUST for odd perfect #'s, and the mathematician was briefly confused/incorrect.

26:51

@@FeeblePenguin Not quite. Veratasium is correct here. The basic form of the heuristic does imply there are only finitely many even perfect numbers. There are some variants that partially avoid this but only partially. One way of thinking about it is that the power of 2 themselves are the culprit and allow a pattern to occur that would otherwise be extremely unlikely. But they allow things to line up just right to avoid the heuristic's probabilistic estimates.

Although it would raise the question if infinity exists in the first place.@@joshuazelinsky5213

37!

It's a question so difficult to answer that the attempts to do so have shown people the limits of their technology, which humans have nevertheless persisted in trying to answer for almost the entirety of recorded history: despite there being no obvious use for the answer to this question. So yes, I think it's fair to say it is aesthetic. The fact that we do this, says more about us humans than it does about numbers or the universe. For all we know, the concept of a perfect number has no meaning in nature at all.

Yeah, while I was watching this I started thinking about all the mathematicians he mentioned as badass celebrities/superstars in some kind of drama or thriller.

The story is likely romanticised.

wrg, some tech, math etc s k , write that s k, doesn tmatter, no nerx etc nmw

heh, nerd

​@zenmkultra are you... are you new here? This is the Veritasium youtube channel

its the journey as they say

'The real treasure is the friends you made along the way'

Well, i don't think knowing if there is an odd perfect number would help anywhere

​@@rishikeshwaghyes, especially the friends from 2000 years ago who wrote about perfect numbers

mathematicians should be banned from using computers

After all this years, I have all of them.

a very important observation - good

love me some gimps

I was half expecting the end of this to be one of those "For more information, Google 'Two Girls One Cup'." Sort of jokes.

Ooo ah....your so smart.but are you wise?

😂​@@warrior4christ777

The Euler Totient Function...😮

look up how many things are named after Euler

Sigma Eular 😅

Well if you discover new function i think you earned the right to named it after yourself

he meant sigma guys, chill :)

on the contrary, matlab or wolfram alpha might not exist without Euler discoveries

​@@grissee very true, it's because of these number theory why supercomputer turned out to be super... math is the foundation of everything 🎉

US would be bombimg mars by now.

@@grissee While this is true, it's interesting to imagine what would've happened if the development of the technology could've happen within their lifespan. Impossible, of course, but it's interesting to think about.

I wonder if they would be even more shocked at how much we still can't solve...

bro, that's literally part of the foundation of all of science and mathematics.

@@annoy4nce648 Damn the takeaway from this video though - now I have a burning desire to actually go try something that might be a dud XP

🫂 we brothers should make our own country

These comments are extremely weird.

@@DasAntiNaziBroetchenyou aint lie my boy 😂😂😂

Does it hold true? If so, it could be an indication that there is an infinitely large amount of perfect numbers 🤔 I’m on my way to go look up tau and our known list of perfect numbers…
Edited: it doesn’t hold true, but it’s still neat!

Is it a good stress test?

@@96thelycan Yeah it's one of the best

@@96thelycan Yes. So is linpak. But prime95 is actually contributing to some collective goal.

19:10

Been building computes for 20 years now and back in the day Prime95 was _the_ way to stress test your CPU. I did know it was a math test but this is the first I’ve seen it explained exactly what it was doing.

This Galois dude 😅

I think I earned about them from watching Pulp Fiction...

Nice 🤜🤛

Awesome

Thank you for your service

This sounds like crypto mining lol

What you are seeing is due to what is called modular arithmetic where one does arithmetic just looking at the remainder when you divide by some number m. You've seen a version of this before on a clock. When it is 8 o'clock and you say "In 6 hours it will be 2 o'clock" you are doing modular arithmetic with m=12. (We often just abbreviate this as mod m for short.)
Since every power of 10 leaves a remainder of 1 when divided by 9, the sum of the digits of a number always has the same remainder when divided by 9. So the modular arithmetic of mod 10 corresponds to roughly speaking repeatedly doing this digit sum until you have a single number. So for example, 193 leaves a remainder of 4 when divided by 9, and so does its digit sum which is 13, and so does its digit sum which is 4.
The pattern for even perfect numbers takes a tiny bit more work but involves looking at Euclid's formula for even perfect numbers and thinking carefully about how it behaves mod 9. Unfortunately we cannot prove the same result for odd perfect numbers, although we know that if N is an odd perfect number, then the remainder when N is divided by 9 must be one of 0, 1, 4, or 7.

When Derek's mind is blown, everybody's mind is blown!

💯 agree

We all swim in the water of YT, and as fish say, "What is this 'water'-thing you speak of?"
I watched all of Cosmos when I was a kid. Saw a few Burke's Connections in U.S.A. Just has to sink in that we are living in a golden age of science/math content. "Traditional media" don't care about math! Can't sell the soap, ha,ha!!!!