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Huhnkie Lee
  • 5/11/2025
an improved conjecture
Transcript
00:00:00hello friends yeah welcome to
00:00:07friday and i love herkili episode uh
00:00:12207.4 i did not comb my hair because i want to show you this kind of wavy
00:00:20hairstyle kind of naturally wavy whatever like ocean wave a little bit right yeah
00:00:28um that's all okay so uh in dailymotion yeah they show some nice like uh carpentry skill set
00:00:41like uh know how they call it hacks but like know how the skills to make some carpentry projects
00:00:49fantastic yeah thank you for sharing those wonderful videos about carpentry that's great
00:00:54yeah yeah i guess uh dailymotion use some ai uh to you know show up some videos like suggestion
00:01:04air power suggestion that's great yeah carpentry is very cool stuff yeah okay yeah happy sunday
00:01:11morning welcome to humanize episode 207.4 yeah uh it's like what 10 a.m sunday morning
00:01:20uh after i woke up i uh i just think about mathematics uh so i think we have solution to
00:01:27that problem okay so yeah it was uh not a very difficult problem as it turned out okay but it
00:01:34did require some thinking okay so yeah basically like euclidean algorithm and stuff uh yeah we'll we'll
00:01:42go over it later okay okay yeah let's do some stretching good morning
00:01:55okay
00:02:04turn off to a hero outside
00:02:12yeah
00:02:21yeah a couple weeks ago i listened to radio when i was driving
00:02:26and they play biancé all the single ladies yeah i like part of that song
00:02:31you know
00:02:35you know the background humming very cool in that part okay yeah okay yeah
00:02:45beautiful sunshine is sunday
00:03:02but when weather is so beautiful like this uh don't be complacent okay uh always be aware of potential
00:03:13danger like the danger like when beautiful scenery when you drive you have to be careful
00:03:23focus on your driving and uh when scenery is so beautiful park your car safely and take some pictures
00:03:29okay while you're driving you don't want to be distracted by beautiful scenery or a beautiful day like
00:03:35this okay yeah don't be complacent just because it's beautiful okay okay i mean
00:03:43john f kennedy was assassinated on a beautiful sunny day like this
00:03:499 11 terrorist attack happened you know on a beautiful sunny day like this okay so bad things happen
00:03:55do you know on a beautiful sunny day like this you know on a beautiful sunny weather sometimes
00:04:02do not put your cars down just because weather is beautiful okay
00:04:06yeah always watch out for potential danger
00:04:10practice martial arts
00:04:11practice martial arts all right don't let your cars down yeah always exercise
00:04:26and watch out for potential dangers okay don't be complacent
00:04:30practice martial arts
00:04:44be always on guard don't put your cars down
00:04:52practice martial arts
00:04:58practice martial arts
00:05:02practice martial arts
00:05:02practice martial arts
00:05:03practice martial arts
00:05:04practice martial arts
00:05:05practice martial arts
00:05:06practice martial arts
00:05:07practice martial arts
00:05:08practice martial arts
00:05:09practice martial arts
00:05:10practice martial arts
00:05:11practice martial arts
00:05:12practice martial arts
00:05:13practice martial arts
00:05:14practice martial arts
00:05:15practice martial arts
00:05:16practice martial arts
00:05:17practice martial arts
00:05:18practice martial arts
00:05:19practice martial arts
00:05:20practice martial arts
00:05:21practice martial arts
00:05:22practice martial arts
00:05:23practice martial arts
00:05:24practice martial arts
00:05:25practice martial arts
00:05:26practice martial arts
00:05:27practice martial arts
00:05:28Also, in the future, probably and hopefully, in a fiction, make a good story without crime, without violence, okay?
00:05:38If you're a very good writer, you can make a very good story, interesting story, without using crimes or violence, okay?
00:05:46Yeah, Agatha Christie novel, too much violence, too much crimes, okay? That's the part I do not like.
00:05:53But other parts I like, Agatha Christie novels. Yeah, limited space, limited number of characters, like five, nine people, right?
00:06:02Yeah, that's cool. And people from all walks of life, okay? In a limited space, confined, kind of trapped in a room.
00:06:11You know, house, mansion. She inspired many filmmakers, other writers, okay? Yeah, like...
00:06:19House on a Haunted Hill, for example. Yeah, I like that movie, yeah? Yeah.
00:06:25Kind of horror movie. Yeah. Influenced by Agatha Christie, okay?
00:06:32Confined spaces, confined space, and limited number of characters, like maybe ten people, okay? Nice.
00:06:41All different walks of life, wrong, you know? Okay.
00:06:47Okay.
00:06:56Agh.
00:07:05Okay?
00:07:06Okay.
00:07:09Okay.
00:07:10Yeah.
00:07:11Okay.
00:07:12Okay.
00:07:13Hey.
00:07:14Okay.
00:07:15Okay.
00:07:17Okay.
00:07:18Okay.
00:07:19Okay.
00:07:20Okay.
00:07:21Okay.
00:07:23Okay.
00:07:24Okay.
00:07:25I'm gonna do it.
00:07:26Okay.
00:07:27I can't do it.
00:07:28Okay.
00:07:29Okay.
00:07:30Okay, okay.
00:07:32Okay.
00:07:33In some sense.
00:07:34Okay.
00:10:34Side kick, side swing kick, okay?
00:10:43Okay, good.
00:10:45Five minutes break, thank you.
00:10:49Beautiful sunshiny Sunday.
00:10:54Nice.
00:11:00I'm gonna pull my hair, okay?
00:11:04Yeah.
00:11:34You're.
00:11:36In.
00:11:37I'm gonna pull my hair, okay?
00:11:37We're gonna pull my hair while still it makes it look good for you.
00:11:39If you want to pull my hair, okay?
00:11:42It's them now.
00:11:46You can do it again.
00:11:47Take eight days you'll see where they come, and say,
00:11:50you're gonna grab your hair, uh, uh.
00:11:53.
00:12:23.
00:12:30Yeah, I combed my hair.
00:12:33Better?
00:12:34How do I comb my hair?
00:12:36I go to the bathroom and sit down over the bathtub and then with my fingers.
00:12:43You okay?
00:12:44Yeah.
00:12:45All right.
00:12:46Five minutes, thank you.
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00:16:36intelligence in legal field and they pointed out that correctly pointed out
00:16:43that yeah nowadays but in the future artificial intelligence will develop so
00:16:48further you will get better but for now artificial intelligence tend to give the
00:16:55kind of result that the user human want to see okay yeah I learned that it good
00:17:02point
00:17:06to add to that my own perspective theories
00:17:11uh aspects point of view some opinions to add to that existing existing uh observation uh okay
00:17:22artificial intelligence like robot right is some sub servient servant who want to please the master
00:17:28okay so sometimes this servant lie in order to please the human user using ai okay uh let me give
00:17:40you an example okay i did look up in my cell phone and uh will look up okay yeah google's artificial
00:17:47intelligence software uh very even improve in the future but for now it's uh it tend to give the
00:17:55result that could be false that but the kind of result that uh user human user would like to see
00:18:03okay so yeah let's do some experiment using google ai okay yeah let's have some fun
00:18:09yeah let's have some fun with ai uh if
00:18:15yeah let's have some fun with ai uh if
00:18:26uh if uh then uh a and ax plus by if a and b are prime then a and ax by y are co-prime if a and b are co-primes then a and ax plus by are co-primes
00:18:43a and b are co-primes then a and b are co-primes a and b are co-primes a x plus by being a linear combination of a and b okay
00:18:51uh this statement is false
00:18:56is this counter example to this conjecture
00:19:00let's say x and y are both a's so ax plus by becoming a times a plus b times a
00:19:09so a and a times a plus b times a they are not co-primes at all
00:19:16no they're common factor way okay
00:19:21easy counter example okay but let's see what google ai
00:19:25dot produces
00:19:27today uh may 11th 2025 okay
00:19:31yeah they say if a and b are co-prime then a and ax plus by they are also co-primes that is false
00:19:44okay
00:19:50yeah
00:19:56i'm gonna print screen this okay
00:20:01for the record
00:20:05and i'm gonna save it
00:20:14uh
00:20:18well google
00:20:22ai false proof
00:20:26okay
00:20:31now let's find
00:20:41what went wrong here
00:20:54a and b are co-primes so yeah yeah the gcd is one
00:20:58this common device of a and ax plus by
00:21:08d divide both a and ax plus by okay
00:21:18so d divides both uh ax plus by minus ax okay okay
00:21:23d divides both a and by okay
00:21:52mm-hmm sure
00:22:06but here let's say y is a okay so a and b times a so d divides both a and by so d can be a okay
00:22:33yeah so it did not consider that okay okay
00:22:45so that's that okay
00:22:51yeah but it helps still although this is wrong okay yeah bezoo's identity we talked about this like
00:23:01five months ago okay like actually the whole reason why do i'm doing this like co-prime world
00:23:07is we we started studying like chinese remember theorem okay the related theorem yeah bezoo
00:23:15bezoo identity which is linear combination okay ax plus by is equal to uh one when a and b are co-primes
00:23:23and a and b any number right then ax plus by is equal to gcd of a and b uh for certain set of x and y
00:23:35and if you recall like about five months ago yeah actually we found a very efficient algorithm to
00:23:44find bezoo coefficients x and to find x and y and we also found another algorithm to generate
00:23:52infinite pairs of x and y that's coefficients okay uh those are that algorithm we discovered is
00:23:58by far more efficient than the algorithm that they have okay in mainstream mathematics okay
00:24:06uh we'll get back to it later okay yeah yeah those are good publication materials itself in itself okay
00:24:14uh but uh but uh we are still discovering in the discovery phase so we'll write it all down
00:24:20i will write it all down later on after we have done with all this okay yeah now five is great i
00:24:28let me start cooking my breakfast okay yeah book or rest necessary buy me spray okay thank you
00:24:36uh and then what kind of okay ax plus by yeah we cannot do that but but there are kind of limited kind of uh
00:24:48uh leading your combination that is allowed picture is uh uh we take five minutes break if you want to
00:24:55figure it out okay yourself okay yeah five minutes thank you
00:25:06uh
00:25:21uh
00:25:25uh
00:28:36Yeah, so this is my breakfast, some soup left over and spring green leafy vegetables
00:28:44and two pieces of frozen chicken breast, water boiled, microwave, plastic jars.
00:38:03Sure.
00:39:33If A and B are co-primes.
00:40:03common divisor set of A and B and common divisor set of A and A and AX plus BY, which is a linear combination, they are not always the same.
00:40:14In order to make the same way would be the same.
00:40:44So what do we call side of A and other than they are A and A and A and A and B and A and A and A and A and B and A and A and A and A and A and A and A equals one, okay?
00:40:50That's how I'll modify the conjecture.
00:40:54Two of them.
00:40:58Ax plus b, like b times 1,
00:41:02z being 1 is a special case of
00:41:06ax plus bz. And when z is 1,
00:41:101 and a, of course, they are co-primes.
00:41:14You want to prove that conjecture or disprove it?
00:41:18Go for it. We'll take five minutes.
00:41:22Very exciting.
00:41:24This conjecture is most likely brand new
00:41:28in the history of humanity.
00:41:30We do that quite often,
00:41:34discovering something brand new.
00:41:36It's quite
00:41:38an uncommon occurrence in human art school.
00:41:42So welcome to human art school.
00:41:44We are very creative here.
00:41:46And we are the smartest people.
00:41:48You and me, okay?
00:41:50Humanologists, okay?
00:41:52So when we
00:41:54tackle a problem,
00:41:58it's different.
00:42:00Why?
00:42:02We are the smartest.
00:42:04Okay?
00:42:06And we discover something brand new.
00:42:10Yeah.
00:42:12Ladies and gentlemen,
00:42:14we are witnessing history in the making, okay?
00:42:16Yeah.
00:42:18Five is great for Korea.
00:42:20Okay?
00:42:22Okay.
00:42:24Let me check on my breakfast too.
00:42:26Let me check on my breakfast too.
00:42:36Then we'll grab a new white,
00:42:38new used whiteboard to erase and then explore these possibilities.
00:42:44Two conjectures, okay?
00:42:46Nice, thank you.
00:42:47Okay.
00:42:48Okay.
00:42:50All right.
00:42:52Okay.
00:42:53Okay.
00:42:56For the next one,
00:42:57we're going to go to the next one.
00:42:59Okay.
00:43:00All right.
00:43:01Okay.
00:43:02Good.
00:43:03All right.
00:43:04We're going to try it.
00:43:05So,
00:43:06wait.
00:43:09All right.
00:43:10We'll see what we're going to do next one.
00:43:11Hang on.
00:43:12All right.
00:43:13All right.
00:43:14All right.
00:44:15Yeah, after I boiled this wonderful breakfast, the leafy vegetables decrease in volume because
00:44:27it's boiled, so I put some more leafy vegetables like this, spring greens, and then boil some
00:44:34more.
00:44:35Okay.
00:44:36Yeah.
00:44:37Organic oil brand.
00:44:38Fantastic.
00:44:39In the Philippines, Alaska.
00:44:40Yeah, good vegetable there.
00:44:45Yeah.
00:44:47All right.
00:44:48So, all right.
00:49:30Okay.
00:49:32Algebra, we already published this so we can safely erase this
00:49:53And some white board like suit and tie
00:49:59Yeah, black and white
00:50:02He's ready to be a new white board, so he raises it nicely
00:50:29Ah
00:50:32Using more pressure, using the edge of the eraser
00:50:48Yeah, so look at, you know, Wikipedia, like, some, uh, SNES law is about light reflection, reflection
00:50:54Uh, like, Fermat, Pierre, Fermat, and...
00:51:00René Descartes
00:51:02I'm going against some physics, optics, geometry
00:51:05That's nice, yeah
00:51:13Yeah, studying science
00:51:15In my bedroom, on my bed
00:51:19I'm using the internet-connected cell phone
00:51:23Yeah, we're going to work with DNA to learn, right?
00:51:26Yeah
00:51:27Yeah
00:51:28Yeah
00:51:29Yeah
00:51:30Yeah
00:51:31Yeah
00:51:32Yeah
00:51:33Yeah
00:51:34Yeah
00:51:35Yeah
00:51:37Yeah
00:51:39Yeah
00:51:41Yeah
00:51:42Yeah
00:51:43Yeah
00:51:44Yeah
00:51:45Yeah
00:51:46Yeah
00:51:47Mm-hmm
00:52:09Yeah
00:52:10Yeah
00:52:12Yeah
00:52:13Yeah
00:52:15Now let's do, write down problem statement, prove, if a and b are co-primes, well more
00:52:36generally than that. Common divisor set of a and b is same as common divisor set of a and
00:52:58ax plus bz. Given that a and z are co-primes, okay? Yeah. Nice. I mean, it's like this, okay? We're dealing with creative mathematics, okay?
00:53:22We have now problem to solve or conjecture to prove or disprove, okay? But to come up with this problem itself, it took a long time.
00:53:34Sometimes it's more difficult to come up with a problem than to solve it in creative mathematics. Okay? Yeah, cheers.
00:53:44In school settings, I mean, school is great, okay? I was in school before, in my past. You have textbook, you have teacher, professor, teaching assistant,
00:54:00but they give you problems, textbook, okay? Like, and then your job is to solve it after you learn the basics, okay?
00:54:10But in creative mathematics, step one, we need to come up with a problem. Step two, we solve that problem.
00:54:20In step one. In step one, the kind of problem, that problem may already be an existing problem. Existing problem may be a solved problem or it may be an unsolved problem.
00:54:35Or it could be a brand new problem that nobody ever asked before. Like this one.
00:54:45Did anybody ask this problem before? It's possible. I haven't seen one.
00:54:53Okay? But it's possible. Who knows? Maybe somebody asked this problem somewhere in the world, at some point in time, in history,
00:55:01maybe they already proved it or disproved it. I don't know.
00:55:07Now let me check on my breakfast program.
00:55:15What's it or what the time is going to be done?
00:55:19That I was waiting for you to go to my breakfast program.
00:55:25What is it or what I had been doing?
00:55:29What was it considered?
00:55:31What after I got into my breakfast program?
00:55:33What was it considered?
00:55:35I was waiting for you to get your breakfast program.
00:55:41I was waiting for you to come.
00:55:43Yeah, the rice, I kind of shook it in the plastic container, I have to close it in the lid to evilly distribute the heat.
00:55:56Now let me wash my hands.
00:56:13Okay, cheers.
00:56:28So, me as a content creator, very informal, I like take a break, whatever, I don't edit.
00:56:36I would say low effort, because hey, we are working on this mathematics, it takes a lot of energy to do this.
00:56:47But when it comes to content creation, yeah, we have good content here, one of a kind content, unique.
00:56:56Science, chronicling, recording science in its making, real time.
00:57:03Well, this is not a live show, it's pre-recorded, but as soon as it's done, yeah, I publish, you know, Dailymotion this day, okay?
00:57:11Back in the days in YouTube, okay?
00:57:13Yeah.
00:57:14And, um, yeah, but I don't edit.
00:57:21Why?
00:57:22I don't have time.
00:57:24Okay?
00:57:25You can fast forward, if I'm taking a break, five minutes break, you can fast forward by clicking those buttons, right?
00:57:31Yeah.
00:57:32Yeah.
00:57:33It's so cool.
00:57:40Of course, well, in the future, it will change, but for the better, but nowadays, not that many people are interested in mathematics.
00:57:50Mathematics does not have, as of now, it does not have universal appeal.
00:57:59But cute animal videos, universal appeal, cuteness.
00:58:02Yeah.
00:58:03Okay.
00:58:04Like, in psychology, they call it cuteness response.
00:58:09That's fine.
00:58:10In humanology, we call it a pedomorphism, like squirrels or woodchuck.
00:58:20Woodchuck is another name for ground squirrel.
00:58:23Ground squirrel.
00:58:24I mean, not ground squirrel, but the groundhog.
00:58:30Rodons, okay?
00:58:31Yeah, ground squirrel is like marmot, okay?
00:58:35In general, but the groundhog is pretty big.
00:58:38It's like this big, okay?
00:58:39So, yeah.
00:58:42Yeah.
00:58:43And I looked up in the internet and Alaska also have groundhog.
00:58:47It's called Alaska marmot.
00:58:49So, in Pennsylvania, they have groundhog there, right?
00:58:52In Alaska, they came up with marmot day.
00:58:55Alaska marmot is a type of groundhog in eastern Alaska.
00:59:01Okay?
00:59:02Yeah.
00:59:03I did not know there are groundhogs in Alaska until earlier today.
00:59:11That's when I looked up in the internet, okay?
00:59:14So.
00:59:15You want to prove this?
00:59:17Before I do, go for it, okay?
00:59:19I give you a first chance to do it, okay?
00:59:21Of course, this is pro-recorded, but still, okay?
00:59:24Yeah.
00:59:25Five minutes prior, okay?
00:59:26Book arrest.
00:59:27Now, time check.
00:59:31Yeah, it's been one hour, okay?
00:59:36Yeah.
00:59:37Five minutes, okay?
00:59:38Yeah.
00:59:39Cheers.
00:59:40You want to prove this or disprove it?
00:59:44Go for it, okay?
00:59:45Yeah.
00:59:46Yeah.
00:59:47Feel free to take more time.
00:59:49If you need more time than five minutes, okay?
00:59:51You can just stop this video and work on this problem on your own, if you want to, okay?
00:59:55Yeah.
01:00:00Okay.
01:00:01Yeah.
01:00:02Fine.
01:00:04Let's ventilate.
01:00:06Boom.
01:00:07Yeah.
01:00:20Yeah.
01:00:21Awesome.
01:00:22Thanks, guys.
01:00:24Yeah.
01:00:26These days, I am about to finish off, I'll let people cry.