Watching a math related video strictly out of curiosity and having your general math professor Bill Dunham from 25 years ago pop up is a surprise…and finding out he’s now a well respected mathematics historian and not just some guy who endlessly suffered non-math students struggles with train problems is absolutely fantastic. Go Mules!
@ArawnOfAnnwn8 ай бұрын
Mules?
@ArmageddonPhysics8 ай бұрын
I would assume whatever institution his professor whom he recognized in the video taught at had a Mule as their mascot. Either that or this guy really just likes Moscow Mules, which I wouldnt blame him for.@@ArawnOfAnnwn
@LedionZogaj8 ай бұрын
@ArawnOfAnnwn yea mules horses sheep lol....
@sumdumbmick8 ай бұрын
did you have a stroke at some point, or have you always been illiterate?
@deanrinehart8 ай бұрын
(He’s a prof emeritus at Muhlenberg College…mascot is the Mule…Go Mules)
@VintageBlacklist8 ай бұрын
I have a research project due tomorrow and I was really looking for something distracting. My procrastination thanks you.
@jakewolf358 ай бұрын
lol
@S4M33508 ай бұрын
Same
@jin_cotl8 ай бұрын
I’m actually early to a Veritasium video
@liambohl8 ай бұрын
This comment hurts
@BOTthelesser8 ай бұрын
Same although it’s project about a book
@thomasrinschler67838 ай бұрын
13:25 "But Euler wasn't finished yet." I think this sentence appears in most histories of mathematical concepts.
@brettgoldsmith99718 ай бұрын
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
@nananou16878 ай бұрын
Number theory concepts*
@ab30408 ай бұрын
Possibly the most important mathematician in history
@rogerszmodis8 ай бұрын
@@ab3040either him or Gauss
@ab30408 ай бұрын
@@rogerszmodis 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
@haleyroe2647Ай бұрын
I love consistently understanding the first 25% of veritasium maths videos.
@Prakhar-2.17822 күн бұрын
It was same for me, then I started studying math.
@slamn891722 күн бұрын
and then I went to undertand about 26%
@Prakhar-2.17822 күн бұрын
@@slamn8917 😂. But actually I do understand better now, almost completely. Besides the things I have no experience in.
@snaifhassnan634820 күн бұрын
121
@ScaredofPixelsForever19 күн бұрын
I thought I was the only one!
@cupostuff99298 ай бұрын
>walks up to blackboard >multiplies 2 numbers >walks away >round of applause Frank Nelson Cole was unfathomably based
@jacobe2808 ай бұрын
Am I the only one bothered that he says AND between all the millions, billions, trillions, etc... couldn't help but mention
@adriantcullysover46408 ай бұрын
@@jacobe280 Yes. You are.
@herobrine18478 ай бұрын
@@jacobe280no you’re not
@AMPProf8 ай бұрын
Fish
@Bruzzzio8 ай бұрын
@@AMPProfSquid
@jonahmishaga19958 ай бұрын
As a physics undergrad. I’ve come to realize that Euler is a Titan alongside Einstein and Newton. Every single bit of modern physics has Euler to thank for providing the mathematical Tools to construct a vivid picture of the universe and its underlying principles. Absolute legend.
@happmacdonald8 ай бұрын
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
@Greyhawksci8 ай бұрын
I will never not be disappointed that MIT's hockey team isn't the Eulers.
@FCHenchy8 ай бұрын
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.
@rogerszmodis8 ай бұрын
@@Greyhawksci only like 1% of people would get it. I would bet the vast majority of people read and pronounce Euler phonetically.
@NStripleseven8 ай бұрын
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.
@AA-10020 күн бұрын
21:15 As of Oct 2024, largest known prime is now 2^136,279,841 - 1
@Batmans_Pet_Goldfish16 күн бұрын
41,024,320 digits long.
@theromanticist802315 күн бұрын
RAAAHHHHHH
@FireFoxDestroyer10 күн бұрын
2^136,278,842-1 ???
@AA-10010 күн бұрын
@@FireFoxDestroyer the exponent p in 2^p-1 is an even number, that number cant be prime
@FireFoxDestroyer10 күн бұрын
@ how about 2^136,279,843-1
@lifthras11r8 ай бұрын
One big application of Mersenne primes, that came from studying perfect numbers, is a good random number generator. RNGs had been historically very bad, until the introduction of Mersenne Twister in 1997, which uses a property of Mersenne primes to prove a good randomness. The most popular version uses a Mersenne prime 2^19937 - 1 for example, hence the name MT19937. There exist much more performant RNGs than Mersenne Twister now, but Mersenne Twister is still widely used thanks to its initial impact.
@lpc99298 ай бұрын
The
@Inuzika8 ай бұрын
That actually helps a lot with understanding why RNG is multiplicative in most video games.
@till84138 ай бұрын
omg i was using that in programming, never knew why it was called MT19937 😮 my mind is blown away
@kphaxx8 ай бұрын
@@lpc9929well said
@helpiminabox8 ай бұрын
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.
@joshuazelinsky52138 ай бұрын
Video is well done. I'm a mathematician some of whose work has been on this topic (some of the results you put on at 23:51 are mine, and one is due to a joint paper of me with Sean Bibby and Pieter Vyncke). My apologies also for the length of this comment. I do have some quibbles about some of the history details but they are minor. (And it is possible that I'm getting some of the details wrong myself.) Descartes's construction of a spoof perfect number, shows he had a pretty good understanding of how sigma behaves. Descartes's spoof shows he had a pretty good understanding of sigma(n). Also, Descartes likely did prove that an odd perfect number must be of the form he suggested. What Euler did was a bit stronger. Euler showed that if n is an odd perfect number n= p^e m^2 where p is a prime , p does not divide m, and p and e are both 1 (mod 4). Notice that this implies Descartes's result. Regarding the Lenstra-Pomerance-Wagstaff conjecture, while it gives a specific estimate for how large the nth Mersenne prime is, there is some degree of doubt of if it is correct. We're much more confident that the conjecture is correct up to a multiplicative constant near 1. And we are much much confident that there are infinitely many Mersenne primes, even if LPW turns out to be wrong even on the order of growth of Mersenne primes. Regarding Pace's comment to high school students, I want to expand on that slightly. No one should be working on this problem with any hope of solving it any time soon. The problem is genuinely very difficult. The spoofs are in many respects a major obstruction to proving that no odd perfect numbers exist. In particular, many of the things we can prove about odd perfect numbers, also apply to spoofs. So if they were enough to prove that no odd perfect numbers existed, we would have proven that no spoofs exist, which is obvious nonsense. To use an analogy that my spouse suggested a while ago: If we are trying to convince ourselves that Bigfoot doesn't exist, but all we've done is list properties that all mammals have, we can't hope to show Bigfoot isn't real. There are few other big obstructions, one of which has a very similar flavor. But, Pace correctly notes that not that many people are working on the problem, so there may be more low hanging fruit than one would otherwise expect for aspects of the problem. For most really famous open math problems, like say the Riemann Hypothesis, or P ?= NP, lots of people have spent a lot of time thinking about aspects of it. So most mathematicians have a general attitude of not trying to bash their head against problems that a lot of other people have thought about. But in the odd perfect number situation, to some extent, the community may have overcorrected, and thus spent less time on it than they might otherwise. However, this may also be due in part to the odd perfect number problem being famous, but not by itself being very enlightening in terms of what it implies. Hundreds of papers prove theorems of the form "If the Riemann Hypothesis is true then " . And those papers are themselves very broad and varied in what follows after the then. In contrast, I'm aware of only a handful of papers with results of the form "If there are no odd perfect numbers then" and what follows after the then is always something involving divisors of a number in a somewhat straightforward fashion.
@jamesknapp648 ай бұрын
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.
@Featherless18 ай бұрын
1×1=2
@asheep77978 ай бұрын
Do you know any papers that rely on the existence of odd perfect numbers?
@daniels86258 ай бұрын
@@Featherless1keep going...
@justusimperator5378 ай бұрын
2x2=4=2+2
@ytmadpoo8 ай бұрын
I've been involved with GIMPS for about 27 years now and it's great to see us mentioned in the video. It was one of the earliest examples of using distributed computing to work on these enormous tasks, and it's been fun to learn more about the math behind it along the way and talk with all kinds of really smart people around the world in the process.
@Filo1278 ай бұрын
you've been involved with gimps ? 🤨
@LeVasTiaN8 ай бұрын
@@Filo127you haven't watched the video?
@nivyan8 ай бұрын
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.
@SamuelRamirez-js5rb8 ай бұрын
Do you know what a gimp suit is? If not look it up lol.@@LeVasTiaN
@drunkredninja8 ай бұрын
OG distributed computing projects were the best way to stress test overclocks back in the day. did alot of gimps, fah and seti myself.
@alexbranton42614 күн бұрын
The way you break these down and explain each chunk, and then leave just enough time for someone like me to recognize a pattern before being told and have a tiny sliver of the feeling of discovering something important that the greats get - just perfect.
@BronsonMWhite8 ай бұрын
WOAH! Dr. Pace Nielsen was my professor for intro to proofs. I was NOT expecting him to show up in the video. He's a fantastic guy, exceptional professor, and brilliant number theorist.
@ashraf51518 ай бұрын
@ES-54321 good one
@puchacz1998 ай бұрын
@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?..
@theslothwithin8 ай бұрын
@ES-54321da dum dun tssss
@Feytz698 ай бұрын
@ES-54321 😂😂
@Zouzk8 ай бұрын
Sorry for the unrelated question, but did he play Magic the Gathering? I think I see an Estrid the Masked behind him Edit: think there's an Arahbo and Ur-Dragon there as well
@nathanaelhahn8 ай бұрын
4:03 "Euclid was actually thinking along similar lines" Euclid: calculates perfect numbers with actual lines
@idontkownhowiam24248 ай бұрын
Euclid god of math
@supremelordoftheuniverse54498 ай бұрын
I disagree
@pressaltf4forfreevbucks1798 ай бұрын
Foreal?
@isaachester84758 ай бұрын
Beautiful pun
@shay_playz8 ай бұрын
@@supremelordoftheuniverse5449why?
@Irule-og1od13 күн бұрын
The 52nd Mersenne number was found just over a week ago. Made official on Oct 21, 2024.
@logician12348 ай бұрын
There is something so bizarre about Euclid and Euler having a collaboration. If the history of mathematics was a book of fiction, I would call this a fan service 😂
@ObjectsInMotion8 ай бұрын
Eu(clid x ler)
@Xezlec8 ай бұрын
Imagine the noises the readers would make if Gauss joined in!
@logician12348 ай бұрын
@@Xezlec Math : No Way Home
@johnchessant30128 ай бұрын
Oiclid and Yooler
@cefcephatus8 ай бұрын
Maybe, "I reincarnated into math genius, Euler, and continue my own legacy. Yes, I was Euclid."
@concrete4013 ай бұрын
I took a class from Dr. Nielsen in 2009. He was a very engaging, dynamic teacher, to the point that when he wrote an answer on the board, followed by an exclamation point, someone asked, "Is that factorial or excitement?" and he responded, "EXCITEMENT!"
@jeaniebird9993 ай бұрын
Sounds like the best kind of teacher.
@vhawk1951kl2 ай бұрын
I do not mean, seek intend or wish to be or appear to be impertinent, but it is interesting to me that the piece contains a misuse of the word "*perfect*"(which means finished completed or accomplished). why not just call them some short(quick-to-type) word like pig, ant, or god numbers, given that perfect is taken to mean neither more nor less than any-thing-you-please? "When I use a word, Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean - neither more nor less.’ ’The question is,’ said Alice, ‘whether you can make words mean so many different things.’ ’The question is,’ said Humpty Dumpty, ‘which is to be master - that’s all.” Might it be relevant that Charles Lutwidge Dodgson(aka Lewis Carroll) was also a mathematician? In what respect or particular are the "perfect numbers" spoken of in the piece finished completed or accomplished or could be *said* to be finished completed or accomplished? Various people have said that mathematics is strictly a young man's game, might that be true? Please forgive me if I am being impertinent; as there can be the arrogance of youth, so also can there be the impertinence of senescence It may be that any potential to be interested in mathematics can be snuffed out by what is called " education.
@saucenado48442 ай бұрын
@@vhawk1951kl its a noun, no? i dont say "why is the grand canyon called the grand canyon, i dont consider it that grand". Aside from that i do think its perfect as LHS equates to RHS
@vhawk1951kl2 ай бұрын
@@saucenado4844 grand is an adjective meaning big or great depending on the context; you ,might say that the Rio grande is not that great, grand or big
@vhawk1951kl2 ай бұрын
@@saucenado4844""why is the grand canyon called the grand canyon, i don't consider it that grand", is merely you flaunting you complete innocence of any wits and learning
@madjson14298 ай бұрын
When Euler says "it's most difficult", it's gotta be impossible.
@BixbyConsequence8 ай бұрын
"I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."
@TheXuism8 ай бұрын
this guy is the biggest bragger in human history.@@BixbyConsequence
@funtastic12978 ай бұрын
No it’s a joke reference to fermats last theorem lol
@melodyecho41568 ай бұрын
@@BixbyConsequenceThat was Fermat
@MathSMR428 ай бұрын
@@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?
@nrspeed1407Ай бұрын
20:18 The book’s editor deserves a raise for proofreading and making sure all the numbers are correct!
That point at the end, about the value in doing math, felt like the thesis statement every veritasium math problem video. Hats off.
@Fire_Axus8 ай бұрын
your feelings are irrational
@HyenaEmpyema8 ай бұрын
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.
@CCCompiler8 ай бұрын
@@Fire_Axus your comment is perfectly odd
@FuncleChuck8 ай бұрын
Where’s the proof
@Tritone_b58 ай бұрын
As a computer and math enthusiast I'm so disappointed I didn't know what Prime 95 was for, other than a OC stress test tool.
@leksitarmik46368 ай бұрын
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.
@jonasplayedthat22208 ай бұрын
@irradiatedturtle8 ай бұрын
Read this as “as a computer who is also a math enthusiast” at first and had to think for a second lmao
@simon60718 ай бұрын
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?
@Nereus748 ай бұрын
@@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.
@Art_Vandelay_Industries8 ай бұрын
As someone that was never good at math it blows my mind how people could and can think in ways that can actually make sense of math so abstract. And without having computers to do the crunch for them back in the days.
@IdOnThAvEaUsE698 ай бұрын
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.
@tincanblower8 ай бұрын
@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..."
@Argoon19818 ай бұрын
@@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.
@BlueSparxLPs8 ай бұрын
@@tincanblower It's a bot. There's a lot of them on KZbin that exist just to quote verses.
@stompthedragon40108 ай бұрын
@@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 "
@ThatSpaceDude-s8sАй бұрын
The answers is C
@zhaoyuanlow815427 күн бұрын
???
@ThatSpaceDude-s8s27 күн бұрын
@@zhaoyuanlow8154 it’s a joke
@Miquella_was_taken27 күн бұрын
Haven’t picked C in a while - best logic
@youngmasterzhi27 күн бұрын
I thought it was Q
@QuanPookie26 күн бұрын
No it’s A
@martafixarcoolt59938 ай бұрын
I love when people have made up their mind on something, like there is a heuristic argument for that there is no odd perfect numbers, and then faced with a reasonable counter argument, imidiately recognize that their original argument is flawed. Just listening to reason and take that logic in, it is beautiful
@ThisHandleIsAlreadyTaken8398 ай бұрын
I love when people spell immediately correctly
@rishabhchauhan89488 ай бұрын
Absolutely😊
@hanu61588 ай бұрын
@@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 😠
@gavinathling8 ай бұрын
@@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.
@RH-ro3sg8 ай бұрын
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?)
@Ihnst78 ай бұрын
This channel is one of the greatest argument in favour of KZbin as a wonderful medium of learning.
@colepeterson53928 ай бұрын
channels like these are why I love KZbin in general
@MikkoRantalainen8 ай бұрын
I agree, Veritasium, Vsauce, SmarterEveryDay and Sabine Hossenfelder are prime examples of channels that make KZbin worth using even if you wouldn't like all the ads and random stuff.
@farmertree88 ай бұрын
@@MikkoRantalainen "prime" examples
@james64018 ай бұрын
Asianometry
@talosgak12368 ай бұрын
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
@Wunba8 ай бұрын
They lowkey tricked me with the outro at 16:25 I was so disappointed for a second 😂
@SteamyDuck-quack8 ай бұрын
I was so relieved it was finnally over. BUT IT WASNT
@PriggarGaming8 ай бұрын
What da faq you doing here ?
@ruskcoder8 ай бұрын
Fr Minecraft KZbinr on math 😮
@parthhooda37138 ай бұрын
@@ruskcoderso what? Everyone enjoys Veritasium whether they like maths or not
@aamirkhan_8 ай бұрын
I was looking for this comment..
@DrMixelpixel18 күн бұрын
The thing I love about mathematics is that you can represent every geometric problem as algebra and every algebra problem as geometric problem. And most often than not it helps solving the problem using the other representation for it.
@wfaction8 ай бұрын
wow this is crazy. prime95 is widely used for cpu benchmarks during overclocking to check temperatures and crashes. But up until today I didn't know it was calculating mersenne prime numbers. I thought it was just trying to find prime numbers for cpu stress test. great video as always
@zeevtarantov8 ай бұрын
It is used for stress testing overclocks because it is sensitive to mistakes in the calculation caused by overclocking too much.
@isthismyfinalform1698 ай бұрын
Damn thats interesting
@fulgerion8 ай бұрын
It says this during the test.
@ViliamF.8 ай бұрын
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.
@tauzN8 ай бұрын
@@fulgerion you probably also read EULA’s 💀
@brodymcconkey8585Ай бұрын
Ive never been so interested in a video that i have no idea or understanding of anything that was said, yet i want to know more even though i dont even understand the start
@jasoncheng33038 ай бұрын
17:48 Something about this quote just hit me hard, we are in the age of computers that started just a few decades ago and we often ignore how seriously revolutionary computer advancements are, something that could take years can now be done by a child with an iPad.
@DJFracus8 ай бұрын
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.
@dorianguerrazzi50408 ай бұрын
Same, I literally shed a tear.
@rogerszmodis8 ай бұрын
I remember when a computer beating a human at chess was newsworthy.
@elLooto8 ай бұрын
Now realize that LLMs dont even come close to representing that increase in the efficiency of labour....
@FLPhotoCatcher8 ай бұрын
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.
@sil12358 ай бұрын
Very nice video! Just a small thing, the reason why the largest known prime is almost always a Mersenne number is not because it grows so quickly (for example numbers of form 2*3^n-1 would grow quicker...), the real reason is because we have efficient test for numbers of that form so we can test them much faster (the Lucas-Lehmer primality test).
@mehrabnikoofaraz2338 ай бұрын
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.
@sil12358 ай бұрын
@@mehrabnikoofaraz233Thanks for correction, I've changed it to different example to avoid confusion.
@TruthNerds8 ай бұрын
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.
@HeadOnAStick8 ай бұрын
@@TruthNerdsClear and informative. Thank you.
@ragnkja8 ай бұрын
It’s because it’s both: it’s fast-growing but _also_ easy relatively to check.
@theyreMineralsMarie8 ай бұрын
Finding perfect numbers is one of the first algorithm assignments you get in a computer Science degree. I never knew it was such an old idea.
@Dranzer_Panzer8 ай бұрын
Clearly you didn't watch the video, it's an even idea.
@Actrl518 ай бұрын
@@Dranzer_Panzerthat’s a prime quality comment
@xuaalbito83038 ай бұрын
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
One thing that is helpful about solving (or attempting to solve) such problems is that a lot of methodology is developed in the process, and methodology is always useful.
@nachoijp7 ай бұрын
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.
@RUHappyATM7 ай бұрын
I sometimes wonder what else could be invented or discovered if the productivity is redirected to some other endeavours.
@marinmarinhola7 ай бұрын
Exactly, this whole quest spawned Prime95, which has helped me overclock PCs for years now.
@GaussianEntity5 ай бұрын
The methodology is a crucial component in math, sometimes even more than the answer itself.
@halgerson8 ай бұрын
I was watching this on my TV, and I had to pause so I can come to mobile to say this: I love you. There are no traditional media companies who provide anything close to the same content that you do. Thank you, and thank you, and thank you for everything that you do.
@nikhilsharma329078 ай бұрын
💯 agree
@Redmenace968 ай бұрын
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!!!!
@87Avantgarde16 күн бұрын
I am a programmer and have encountered real math during studies and couldn‘t do one proof if my life depended on it. But your math videos are not only lovely but even I can follow them. Outstanding work!
@BoolFalse7 ай бұрын
i'm becoming more respectful to my teachers, when i realize i can now understand and enjoy these kind of videos.. even 15 years later after the school..
@patrickguth37968 ай бұрын
I love your channel so much, because the problems presented are discussed on a very nice level. Not layman's style, not lecture style, right in the middle. Awesome.
@Fire_Axus8 ай бұрын
your feelings are irrational
@Ryan-lk4pu8 ай бұрын
Your "right in the middle" maybe. For an amoeba like me, he lost me after like 3 mins 🤣🤣 I'll just be over here licking the window 😂
@austinhernandez27168 ай бұрын
Math was my best subject in school, I made an A in calculus. But it's hard for me to follow sometimes
@HyenaEmpyema8 ай бұрын
agree 100%. I tried reading about number theory when I was in college 20 years ago, before youtube, and I could only make it a couple pages into the first chapter before these textbooks seemingly go off into outer-space. Derek has done a great job of digesting and explaining. Just what I needed.
@periodictable1188 ай бұрын
The absurdity of that 1000 page book containing that one number is that in paper form it is essentially useless, but the symbolism is so profound that people were scrambling to get a hold of a physical copy, that it sold out within days. I think this has something to do with human nature in that there is some spiritual value in having a physical copy of something, even if it is practically useless and infinitely more useful to just have a text file containing that number.
@PTfan548 ай бұрын
A book containing the largest known prime and a text file containing the largest known prime are actually equally useless.
@falconerd3438 ай бұрын
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.
@BishopStars8 ай бұрын
@@falconerd343Benford's Law. One Time Pad.
@jamesmnguyen8 ай бұрын
Imagine how much energy and computation went into making that book.
@kingkarlito8 ай бұрын
actually there were just not many copies actually printed. he completely made up the part about it being a top seller on amazon.
@SM-qj6jo18 күн бұрын
OMG as I see this video, today I found out, this news it is just 3 days back - Amateur sleuth finds largest known prime number with 41 million digits - 2^136,279,841-1
@Auen17 ай бұрын
Your videos are always so crisp, clean, and educational. I absolutely love how you provide the historical progression of things without a bunch of fluff. There is no doubt you are making a positive impact in minds around the world! THANK YOU!
@satriorukito7 ай бұрын
37
@phildavenport41506 ай бұрын
@@satriorukito 42. At least, that's what Douglas Adams tells us.
@rockykitsune8 ай бұрын
In my intro to abstract math class in college, we had a final project to write a paper that had basically only two requirements: it was about an approved math-related topic and it had a proof that used concepts we were taught. I did mine on perfect numbers and Mersenne primes and gave a proof of the Euclid-Euler Theorem. It was super fun to learn and write about. It is awesome to see Veritasium cover this topic in the amazing quality he does and recognize the stuff that was talked about. I even concluded the paper like the video - it's nice to study stuff just because it's interesting, even if there's no obvious real world uses.
@Soken508 ай бұрын
My favorite bit of "useless" math at the time of its discovery are quaternions, they were discovered/invented a century before we needed it for avionics, orbital dynamics and computer graphics, yet they are integral to our civilisation now, allowing us to compute spatial rotations effortlessly. I hope this leads to a great discovery that enables even more awesome technology in the future.
@marcosmith66138 ай бұрын
Thanks for sharing this 😊
@glennllewellyn73698 ай бұрын
Toilet flow direction is important.
@Whiterioot8 ай бұрын
You sound really smart. Sincerely.
@Soken508 ай бұрын
@@Whiterioot Thanks, I try my best.
@g..h..o..s..t8 ай бұрын
@@Soken50 congratulations on trying your best to sound really smart, which is what you just agreed with @Whiterioot about. 👍
@davidespinosa1910Ай бұрын
*Great* video, thanks ! I was ready to say, "no applications, don't care". But I didn't know the connection with Mersenne primes. Now you got me -- I'm in ! Also: Wikipedia's list of open problems in math in *astonishingly* long !
@joshcryer8 ай бұрын
I absolutely loved Pace Nielsen's candor. And Derek got 'em too with the heuristic argument, fun exchange.
@Rabcup8 ай бұрын
I thought it was weird for this to be uploaded at night for EST but then I remembered he just moved to Australia, so it’s still technically a normal morning upload for him
@TheSuperiorQuickscoper8 ай бұрын
When did he move from LA?
@Lapse-a-lot8 ай бұрын
Can confirm. It's midday here in 🌏
@jin_cotl8 ай бұрын
Fr I’m about to sleep soon
@augisterman36858 ай бұрын
It's evening for me
@THICCTHICCTHICC8 ай бұрын
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
@lifeisfakenews8 ай бұрын
17:37 ish "he gave a talk" "without saying a word" thats a new level of genius
@LuisSierra428 ай бұрын
Based genius
@maddawgzzzz8 ай бұрын
Based AF braa
@djangosouthwest60438 ай бұрын
Actions speak louder than words
@edwinkjobi8 ай бұрын
Nelson Cole is the main Character!
@CrimsonA17 ай бұрын
*Drops chalk and walks off stage
@ScienceNowPodcast23 күн бұрын
Wow, this video is absolutely fascinating and so well put together! 🎉 I really appreciate the clear explanations and the engaging visuals-such a great way to break down complex topics. It's always refreshing to come across content that makes science both informative and fun to watch! Keep up the amazing work, looking forward to seeing more! 🙌
@IamSatria2 ай бұрын
When he say that number theory might not have a real application in real life (but turns out can be use for encryption) I felt that, even as a guy that hate math, i realized that NO math problem is useless/don't have a real life application. And i also started to gain interest in math recently. I started to see math in this way: Solving math problems IS hard and even frustrating, but the moment you get the final result, all of that work will be worth it
@Tryh4rd3rrАй бұрын
Does (e^i(pi)) + 1 = 0 really have a real life application? I didn’t think so.
@CyberFlare-fn9knАй бұрын
@@Tryh4rd3rryes, computer graphics using the polar plane, and complex numbers being solutions to other equations with application
@sirgryphon7212Ай бұрын
@Tryh4rd3rr bruh this is one of the most useful ones
@CyberFlare-fn9knАй бұрын
@@sirgryphon7212 fr
@EricRoettger8 ай бұрын
Terrific video. However, the part about Edouard Lucas could have been much stronger. He did not merely show M_67 was not prime, he was able to show M_127 was prime. This is the largest prime ever found without the aid of a computer. He did so using novel methods that did not rely on trial factorization, but rather exploited properties of the Fibonacci numbers. Using his methods he could test M_n for primality for all n equivalent to 3 modulo 4. These methods were further refined by D. H. Lehmer (who also should have been mentioned) so that all M_n could be tested; giving us the Lucas-Lehmer test for Mersenne primes. It is this test that makes GIMPS possible. For more informations see "Edouard Lucas and Primality Testing" by Hugh. C. Williams.
@tensor1318 ай бұрын
a very important observation - good
@JBG-AjaxzeMedia8 ай бұрын
love me some gimps
@zarki-games8 ай бұрын
I was half expecting the end of this to be one of those "For more information, Google 'Two Girls One Cup'." Sort of jokes.
@warrior4christ7778 ай бұрын
Ooo ah....your so smart.but are you wise?
@WarthogDoctor8 ай бұрын
😂@@warrior4christ777
@markus91478 ай бұрын
Historical math videos have become my favourite type of videos on this chanel. Please continue doing them. It is not necessary to have fancy animations or graphics. Great work
@saatviksharma1532Күн бұрын
Someone said "Math is hell of a drug".
@ZenZooZoo8 ай бұрын
Not me watching thinking I’m gonna try to solve this while eating hot cheetos
this comment just blew my mind🤯 doing this exact thing while high
@jin_cotl8 ай бұрын
Nah it’s alright. Better an attempt at solving it, than not trying at all ❤
@Descenacre8 ай бұрын
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 :)
@joshuagoodsell93308 ай бұрын
That's so inspiring haha thanks@CananaMan
@GroovingPict5 ай бұрын
When even Euler goes "this is a most difficult problem" I think everyone else can basically just pack it in and not even bother trying
@reapicus5572 ай бұрын
No! That's the most golden flag possible for an interesting problem.
@biankacosma2 ай бұрын
*went sunbathing*
@natashalisboa43202 ай бұрын
Yes ! Math is so beautiful@@reapicus557
@DavidThomas6582 ай бұрын
Yeah, when the going gets tough, the tough GIVE UP!
@Kronyx-k3rАй бұрын
that's proof enough for me tbh
@MarkArandjus8 ай бұрын
17:41 I choose to believe he dropped the chalk like it was a mic and just walked out, dapping up a few mathematicians on the way.
@periodictable1188 ай бұрын
Imagine he just wrote some random ass numbers and it didn't even multiply to the original
@cloudyblueskye7 ай бұрын
😅u
@sammamna16 күн бұрын
I FOUND ANOTHER PATTERN BUT I DONT WANT SOMEONE TO STEAL IT
@Hunterlysy16 күн бұрын
Cap
@sammamna15 күн бұрын
@@Hunterlysy I did, it might be a very complex equivalent of something else though
@Hunterlysy15 күн бұрын
@@sammamna ok
@sushilover466 күн бұрын
Bro pls help in the branch of math theory pls
@prestonak2 күн бұрын
@@sushilover46bro 😭
@deepaksinghxo2 ай бұрын
Was doing math problems on perfect numbers, opened youtube saw the thumbnail written 6, 28, 496 recognised they're perfect numbers, couldn't stop myself from clicking on it and here I'm enjoying the video and I've to accept Derek makes videos on topic nobody could even imagine of, hats off to this guy man, incredible
@lookupverazhou859927 күн бұрын
LLM. The AI knows when your vector is projected on it's own vector.
@Pinkcircleguy24 күн бұрын
Personally i clicked because of the funny white pyramid
@LoBoToM817 ай бұрын
This channel is absolutely THE BEST science channel. Not only on YT but in general. I'm a primary school teacher from Poland and the amount of facts and curiosities I get from here and transfer into teaching physics, chemistry and even English is astonishing. Thank you.
@xninja23697 ай бұрын
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..
@chazzbranigaan93546 ай бұрын
Shout out to P(r)oland my favorite country
@johnyoung35115 ай бұрын
Numberphile is a similar channel, but you probably know that 😊
@AntonChernov-c8jАй бұрын
This is the most effective strategy I've ever come across. It's like magic!
@Oriol-oo7jl8 ай бұрын
I admire this guy enough to know that when he says "WHAT BLOWS MY MIND IS" and after saying the thing he does the BOOM gesture... if I stay impassive, it means that i have missed an important chunk somewhere
@vigilantcosmicpenguin87218 ай бұрын
When Derek's mind is blown, everybody's mind is blown!
@grantpitt30408 ай бұрын
So cool to see Professor Nielsen on this! It was such a privilege to sit in that office and work through problem sets for his formal math class last year. Wonderful teacher!
@jorgec988 ай бұрын
I've always found the subject of perfect numbers fascinating. I saw the thumbnail here, recognized what it was about, and actually dropped everything I was doing to watch. That doesn't happen often, so thank you so much for this awesome video
@popcat208528 күн бұрын
We need more education videos on KZbin like this!
@stupiocity2457 ай бұрын
Man, this video made me realise how little we think about the world. I used to think there may be a point where we learn everything from this world, but seeing this, i realise we just think very little of everything, including ourself. I want to introduce change to myself but seeing videos like this, gives me an idea of how to proceed, even though i am not mathemathician, but i hope to become so
@mansouralshamri13877 ай бұрын
The more we learn, the more we realise how little we know
@stupiocity2457 ай бұрын
@@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
@hithere42897 ай бұрын
@@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
@indigowyrdweaver25397 ай бұрын
@@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.
@Fitzer-h7v7 ай бұрын
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
@KevinBrooks_c8 ай бұрын
I really love the direction of this channel was heading towards, which I felt that specially videos from the last 6 months or so, it's not just sharing something amazing or interesting, but really courage who was watching to pursue something, or to realize more possibilities this world offers.
@Xelianow8 ай бұрын
The real benefit of solving those kinds of problems is usually not the solved problem itself, but the insight you gained while solving it and the kinds of techniques and methods developed beeing useful in other areas where you didn't expect them to be useful. Noone knows whether the tool you invented to solve this kind of problem will suddenly crack open other problems as well in (at first glance) unrelated fields of mathmatics. Edit: Thats also the reason why proving something simply by checking all possible cases with a computer isn't very well respected by mathematicians. Sure, you may have the proof that something does/doesn't exist, but it tells you absolutly nothing about *why* it does/doesn't exist. Your understanding of the topic is still the same as befor....
@November88888 ай бұрын
its the journey as they say
@rishikeshwagh8 ай бұрын
'The real treasure is the friends you made along the way'
@Ne_Ne_Vova_UA8 ай бұрын
Well, i don't think knowing if there is an odd perfect number would help anywhere
@Ne_Ne_Vova_UA8 ай бұрын
@@rishikeshwaghyes, especially the friends from 2000 years ago who wrote about perfect numbers
@stxnw8 ай бұрын
mathematicians should be banned from using computers
@louplayz75227 күн бұрын
11:28 the sigma function is very sigma indeed
@Ibrahim-cy3pz22 күн бұрын
Ikr
@AntwanMounir8 ай бұрын
26:47 I LOVE how you were able to respond back to his argument, proves that you actually did your research and put him right back in his place that you're not just some youtuber who tells science stories and doesn't know better.
@SebasCelisOficial8 ай бұрын
That was kind of awesome
@alex1stamford7798 ай бұрын
Wtf do you mean put in his place? Place of what? Being an expert in the field? Dude already admitted it's a heuristic and heuristic come with downsides. It's not a fight where people need to be put in place.
@AntwanMounir8 ай бұрын
@@alex1stamford779 English isn't my first language, I meant it was when he realized he wasn't speaking to some media person who doesn't understand much
@zerokiryuu-ig7wm8 ай бұрын
He's a professor I think. Not just some random youtuber. 😅
@CalvinJKu8 ай бұрын
I actually love how quickly the professor realized he was having a double standard applying the heuristic and laughed about it. You only get that from arguing with smart people.
@samuraichicken92488 ай бұрын
All I can think is how mathematicians throughout history would be absolutely blown away by modern computer technology. I think they would be so proud to know that people picked up and carried their legacy and continued work on this problem. Just imagine what could have happened if Euler got his hands on Matlab or Wolfram alpha
@skyfeelan8 ай бұрын
on the contrary, matlab or wolfram alpha might not exist without Euler discoveries
@mikeinjapan20048 ай бұрын
@@skyfeelan very true, it's because of these number theory why supercomputer turned out to be super... math is the foundation of everything 🎉
@miloradmilutinovic76918 ай бұрын
US would be bombimg mars by now.
@therealax68 ай бұрын
@@skyfeelan 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.
@XIIchiron788 ай бұрын
I wonder if they would be even more shocked at how much we still can't solve...
@AnirudhTammireddy8 ай бұрын
I use prime95 a lot for stability tests and DID NOT know the history behind prime95. I felt chills when it was shown. Thanks!
@96thelycan8 ай бұрын
Is it a good stress test?
@natalyawoop42638 ай бұрын
@@96thelycan Yeah it's one of the best
@AnirudhTammireddy8 ай бұрын
@@96thelycan Yes. So is linpak. But prime95 is actually contributing to some collective goal.
@siddharthdash89468 ай бұрын
19:10
@XeonAlpha8 ай бұрын
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.
@xiflix89569 күн бұрын
bro’s out here talking about some sigma and prime 🤦🏻♂️
@L3MON_SHORT5 күн бұрын
Nah, let him cook
@kshitizmalviya69098 ай бұрын
16:17 Peter Barlow's statement awakened the mathematician in me until this transition
@consentofthegoverned51458 ай бұрын
You have such a knack for presenting information that is way over my head, and I often fail to fully understand it but I'm still fascinated, and consistently placed in awe of the mystery and power of math and numbers. Thank you for your public service Destin!
@smorrow8 ай бұрын
Chemistry KZbin
@dekiverse8 ай бұрын
almost cried at the end. "the only way to know for sure is to try" has always, always made so much sense to me. and i just found another one. I'm so glad to just be alive at times like these.
@grabble76058 ай бұрын
" "the only way to know for sure is to try" has always, always made so much sense to me." ...Why, yes, completely sensible basic truisms do make sense.
@dekiverse8 ай бұрын
@@grabble7605 no haha i meant as in it's true no matter which context i think it from. it's just so simple yet alpt of times i seem to personally ignore it. that's what i was trying to say😅
@barry760829 күн бұрын
Thanks I tried, but for me I need to start running through the various formula to see it working and that takes time and mental agility. I am just a bit past that right now 74 and it's nearly midnight. Take care, still very interesting.
@kumarnilay25988 ай бұрын
26:47 Pace Nilsen shows an incredible sign of intelligence! Not only did he immediately agree with a contradictory statement and not let his own beliefs that "Odd Perfect Numbers don't exist" overpower him, but simultaneously, he also reexamined and concluded that he had a bias. The same theory that heuristically shows Odd Perfect Numbers don't exist also shows that large, even perfect numbers don't exist. This is a true sign of intelligence, not to let your ego get in the way and search for the truth. We all can have biases, but only intelligent people will be able to look past them.
@09NXN068 ай бұрын
Exactly
@yasyasmarangoz35778 ай бұрын
I thought he was joking with that assumption anyway.
@MrTuneslol8 ай бұрын
Unfortunately the scientific community fails to do this _far_ too often. Especially if that bias is either profitable or gets more funding for their projects.
@kumarnilay25988 ай бұрын
@@yasyasmarangoz3577 , haha, might be. But it did feel like he believes that they don't exist, which, probabilistically, might eventually turn out to be true.
@kumarnilay25988 ай бұрын
@@MrTuneslol I think this happens everywhere, but at the same time, many people in the scientific community can look past it, and that is when truly wonderful things are discovered or invented.
@matthewlloyd32554 ай бұрын
It's very rare I can sit through an informational video of more than a few minutes....I watched this all the way through in a single sitting, you're doing something right I guess!
@conceptcrystals4873 ай бұрын
Change your attitude to "I did something right" and you will notice that you find quality content more often.
@Prinzeum2 ай бұрын
Me too. I was thinking of watching the first few minutes and be bored and quit but none of that happened. I think this is one of the most interesting math videos on youtube.
@ZeronimeYT7 ай бұрын
Ancient Greek in their free time be like:
@CFiu87377 ай бұрын
🤣🤣💔
@bash6519Ай бұрын
Been using this video as a sleep aid. It’s excellent thanks
@happmacdonald8 ай бұрын
29:08 - "If you're a high schooler and you just love mathematics and you think 'I want a problem to think about', this one's a great problem to think about. And you can make progress, you can figure out new things. Yeah, don't be scared" Instructions unclear, and now I am caught in the steely grip of the Collatz Conjecture. Gee, thanks Professor Nielsen! 😂
@harshrajveermaran57928 ай бұрын
Hey after 8128 is the next perfect number 41,328?
@Grizzly01-vr4pn8 ай бұрын
@@harshrajveermaran5792 No. The next perfect number is with p = 13, so 2¹²(2¹³ - 1) = 33550336
@minerscale8 ай бұрын
@@harshrajveermaran5792no it's 33,550,336.
@KiLLJoYYouTube8 ай бұрын
Veritasium already did a video on Collatz 🫡
@Felipe-sw8wp7 ай бұрын
What if there is only one odd perfect number, and it's the only number at which Collatz Conjecture fails? 😳
@Tamonduando8 ай бұрын
10:45 I feel that calling Euler a "prodigy" is a bit of an understatement.
@jamesknapp648 ай бұрын
Yeah Magnus Carlson was just good at Chess at 20 pales to the understatement that 20 year old Euler was just a prodigy
@folkrav8 ай бұрын
@cf-yg4bd I was about to throw one back at you then realized I legitimately can’t think of one either. Well said.
@PlayerSlotAvailable8 ай бұрын
What is special about them? It is my first time seeing their name.
@timothyobaob36248 ай бұрын
@@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).
@azice60348 ай бұрын
@@PlayerSlotAvailableHe is the greatest mathematician to ever live. It’s hard to even compare him with other people in other fields. Like I can’t think of anyone having as big of an impact in their field as euler did with mathematics.
@tokenr74148 ай бұрын
As the co-discoverer of the first GIMPS prime (the 35th), I wasn't even aware of this unsolved problem...! -Joel Armengaud
@kitfifty8 ай бұрын
whgats a GIMPS prime
@PaulDeanBumgarner8 ай бұрын
What a waste of time. Look… There isn’t an odd one. This is now officially solved.
@DasAntiNaziBroetchen8 ай бұрын
@@PaulDeanBumgarner Is the joke that you pretend to be a boomer? Cuz "Bumgarner" surely can't be a real name.
@TheCommentor-8 ай бұрын
Bro is real
@N4SCARfaN8 ай бұрын
@@DasAntiNaziBroetchenI've seen both Bumgardner and Baumgartner, I'm sure Bumgarner exists somewhere
@Einstein.Albert.officialАй бұрын
the principle is so simple, but the way to get the answer is very hard! That is very interesting.
@superman397568 ай бұрын
Another maths banger from this channel! I love science but I am a Mathematics and Stats major - please keep this content going!
@AMPProf8 ай бұрын
@KeiFlox8 ай бұрын
I am helpless at math, but always find these complex maths fascinating and just wonderful. Amazing what some minds can do!
@xenorac7 ай бұрын
Same, I watch these hoping something will drop and I will get it. So far, nothing!
@helrem7 ай бұрын
Same Bro!
@MathFromAlphaToOmega8 ай бұрын
Euler also worked on an interesting related problem involving "amicable numbers". Those are integers m and n where the sum of the proper divisors of m is n, and the sum of the proper divisors of n is m (so a perfect number would be where m=n). At the time, only a handful of examples were known, but Euler managed to come up with a recipe for generating many more. With one paper, the number of known pairs went from 3 to 61.
@szymonl43638 ай бұрын
That's like really cool, especially considering that these are also pretty big, like the numbers in the 61st pair are well over 2.5 million!
@alexpotts65208 ай бұрын
Funnily enough, though, in spite of finding some quite large amicable pairs, Euler missed the second smallest pair in existence. It was eventually found by a random nobody about a hundred years later, having been overlooked by dozens of more prolific mathematicians who had searched for amicable pairs.
@patrickmckinley87398 ай бұрын
Unlike the perfect numbers, there are instances of odd amicable pairs. Now, for an open question: Is there an amicable pair where one is even and the other is odd?
@MathFromAlphaToOmega8 ай бұрын
@@patrickmckinley8739 Interesting - I didn't know about that problem. Just to be safe, though, I'm not going to spend too much time trying to find an example that might not exist.
@Michael-kp4bd8 ай бұрын
@@MathFromAlphaToOmega from my basic understanding, that open question would be quite analogous to the Odd Perfect Number question. Likely, the optimal known method for searching for such numbers would ALSO be running a vast network to reach insane levels of compute, for a few decades. Not likely something searchable in an individual’s free time. However, that is an assumption, unless there’s a proof that the problems have a certain equivalence. If there isn’t, then maybe there’s a different approach waiting to be found! And breakthroughs in number theory ARE things that individuals have accomplished, as illustrated by this video.
@crystala.jensen7864Ай бұрын
Michael, you make a trader's job less stressful and more interesting!
@robincharles70578 ай бұрын
16:57 Idc how nerdy this makes me, but for me this feels like the mathematical version of walking away from a house while it explodes and not looking back and I love it. 😍
@slooptrooperunlimitedofthe17728 ай бұрын
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.
@Ceelvain8 ай бұрын
The story is likely romanticised.
@zes38138 ай бұрын
wrg, some tech, math etc s k , write that s k, doesn tmatter, no nerx etc nmw
@zenmkultra8 ай бұрын
heh, nerd
@Sepi-chu_loves_moths8 ай бұрын
@zenmkultra are you... are you new here? This is the Veritasium youtube channel
@bobsburgers88858 ай бұрын
I am constantly amazed by your ability to explain relatively advanced mathematical concepts in such a simple way. I probably should have made this comment after your video on Goedel's incompleteness theorem, but this is a good example too. I actually enjoy your math videos more than your physics ones. Great work as always.
@StoneTheCr0w8 ай бұрын
No one asked
@Darkwarrior4228 ай бұрын
@@StoneTheCr0w and?
@navidahmed18 ай бұрын
I first learned about GIMPS in a science magazine in Bangladesh, I think in around 2012-2013. I set up GIMPS in my dad's laptop (I did not own a laptop then), and then his work computer. Finally I installed it in my laptop in 2019 when I came to the States for higher studies. Currently my dad is retired and the program only runs in my laptop. I have donated computing power to show that more than 50 numbers are not prime, still looking for one. My wife pokes fun at me when around every two to three months the LL test (or now the PRP test) on a potential number nears completion as everytime the number has turned out to be not a prime and I have been sad, and my wife finds this ritual mildly amusing. I do not even shut down my laptop. 😅 it is always on and the program is always running
@jonathanberry11118 ай бұрын
I think I earned about them from watching Pulp Fiction...
@user-Aaron-8 ай бұрын
Nice 🤜🤛
@OnixEdge8 ай бұрын
Awesome
@PFBM868 ай бұрын
Thank you for your service
@randomblueberry50198 ай бұрын
This sounds like crypto mining lol
@blankblank36002 күн бұрын
your stuff is the best. just like a pbs doc. ty.
@MattDoesNothing6 ай бұрын
Normal people would say “There’s no way” Some other people would say “The chance is low, but never zero” And then comes the mathematician: “The chance is never zero, but how low is it?”
The mathematician : "Theres something called a heuristic argument"
@opiumbermerzic89818 ай бұрын
I "worked" on this problem when I was a math student, but miserably failed, thanks for bringing this on youtube. Your channel is a gem man. thanks for your work. If I had to guess there is no odd perfect number but infinite even perfect numbers.
@bradleysampson82308 ай бұрын
Professor Nielsen was the best math teacher I ever had! I was a music major and it was lovely to get away from the practice room to his Abstract Algebra class three times a week.
@matematizandocomluciano5 күн бұрын
Um dos melhores vídeo dos KZbin com certeza!
@AudreyRoberts-jl4yg7 ай бұрын
Your videos are always so crisp, clean, and educational
@mrbfros4548 ай бұрын
Once again your math videos sail way above my comprehension level, but I feel like the more exposure to these concepts you give me the closer I get to actually understanding some of it.
@KJTv..8 ай бұрын
For real, same here.
@micah46288 ай бұрын
same cause before these typa videos id be lost a minute or two in, this one i was perfectly following up until the sigma function stuff
@1stlullaby4848 ай бұрын
@@micah4628 The Sigma function , σ(n) = the sum of all the divisors of n Yes that's it! Since a perfect number is equal to the sum of all of its divisors EXCEPT for the number itself! Therefore, sigma( perfect number) = 2 * the number itself
@micah46288 ай бұрын
@@1stlullaby484 thanks i sorta got that part of it, it was more the part around 14:10 i was confused with but i just rewatched it with that in mind and i got it now, thanks!
@1stlullaby4848 ай бұрын
@@micah4628that's why in case of a prime number say p we get sigma(p) =1+p Because these are the only divisors of p Now you might be thinking what about -1 and -p , but in number theory people are only concerned with positive integers (this doesn't mean that other numbers don't show up, it's just a field focusing on positive ones)
@itsmesaravi7 ай бұрын
Me: > starts watching video > gets engrossed > gets the motivation to find the odd perfect number > forgets what a perfect number is > refuses to elaborate > leaves
@ankitsingh.35 ай бұрын
This is me ! 😀
@butter51445 ай бұрын
😂🤔😡
@OKELLOEMMANUELWECE5 ай бұрын
😂😂
@hasanmuttaqin464Ай бұрын
based
@bardigan1Ай бұрын
Great episode, great guest.
@macsarcule3 ай бұрын
I’m not sure why, but this video was very emotional for me. Humans doing beautiful things with their minds, because they can’t help themselves. But for good and happy reasons.
@OriginalPuro2 ай бұрын
Competent people doing competent things are always interesting. At least if you're average in terms of intelligence.
@MrCOPYPASTEАй бұрын
We really sit on giants shoulders...
@prince_nocturneАй бұрын
The Everest of math. "Why do it?" I dunno. Because it's there.
@guillaumelavoie15448 ай бұрын
Now I want to see a video about old mathematical problems that have been solved and did not change anything. Thank you for the great video!
@sigmaoctantis50838 ай бұрын
The _Four Color Theorem_ might be a candidate for such a video.
@fibanocci3148 ай бұрын
Would love to see that
@judyl.7618 ай бұрын
🤣
@vigilantcosmicpenguin87218 ай бұрын
hang on let me type random stuff into a calculator and it'll count