The Hardest Math Problem | Po-Shen Loh and Lex Fridman
Вставка
- Опубліковано 15 тра 2021
- Lex Fridman Podcast full episode: • Po-Shen Loh: Mathemati...
Please support this podcast by checking out our sponsors:
- The Jordan Harbinger Show: jordanharbinger.com/lex/
- Onnit: lexfridman.com/onnit
- BetterHelp: betterhelp.com/lex to get 10% off
- Eight Sleep: www.eightsleep.com/lex and use code LEX to get special savings
- LMNT: drinkLMNT.com/lex to get free sample pack
GUEST BIO:
Po-Shen Loh is a mathematician at CMU and coach of the USA International Math Olympiad team.
PODCAST INFO:
Podcast website: lexfridman.com/podcast
Apple Podcasts: apple.co/2lwqZIr
Spotify: spoti.fi/2nEwCF8
RSS: lexfridman.com/feed/podcast/
Full episodes playlist: • Lex Fridman Podcast
Clips playlist: • Lex Fridman Podcast Clips
SOCIAL:
- Twitter: / lexfridman
- LinkedIn: / lexfridman
- Facebook: / lexfridman
- Instagram: / lexfridman
- Medium: / lexfridman
- Reddit: / lexfridman
- Support on Patreon: / lexfridman - Наука та технологія
You can tell Po-Shen understands math so well he can visually see what he’s explaining with his hand movements
Its just a type of math person. I'm the same, I flail my hands around while learning the subject, because thats just how my brain works. doesnt make me better than my non hand-wavy peers. this is especially true with mathematics because there is no single way to do it. there is no "abstract mathematics" part of the brain, so different people develop different mental processes to work through math. some are visual, some are more grammatic and formal, almost programming like... both make good mathematicians sometimes.
Representing abstract thought spatially may be a universal thing. ua-cam.com/video/gmc4wEL2aPQ/v-deo.html
@@jaidenmuschett5667 Damn that's a very cool seminar. Thanks for sharing Jaiden!
It’s sort of like he’s thinking faster than he can talk as well. I once worked with a chemist that would always get mixed up with his words because he couldn’t talk fast enough to keep up with his thought.
@@guyavn5504 There is this notion of a spatial and an analitical thinker in mathemathics and STEM in general. Its some form of dimorfism for mathemathicians haha. Spatial types will excell in topology and calculus, analytical thinkers prefer number theory and stuff like that. Its pretty interesting.
I've seen him in other math videos before, and I love how enthusiastic he is. You can tell math is absolutely his life.
I dont know wtf they are talking about but I find it fascinating.
Same feeling .
Lmao
Take a few computer science courses and you will know exactly what they mean. Don’t need to be a genius, just need to be exposed to it
Find his teeth fascinating
@@joedoe2770 Too bad we can't post memes here because this is a great spot for that "It was a joke" meme.
I love these types of conversations. It actually makes having a Comp Sci background and going through all that fucking hell that is conceptual/discrete mathematics.... feel somewhat interesting & fun to use in application
The english auto translated text at 02:05 reads "USE OUR OTHER RED WING PUB PROOF A DOODLE MOOR" i think that sums up how confused we all are on this subject.
having a math teacher like him is a blessing
This guy is inspiring! He loves what he does n even enjoys talking about mathematics 💯✔
I’m a simple man. I enjoy listening to smart people speak. I don’t have a clue what they talk about 🤷♂️
not everyone has the time or passion to learn these things
@@dompit9535 or competency
@@faux4780 or circumstance
@@dompit9535 not if you have internet access
@@faux4780 yeah digital products do make it much easier nowadays, anyone can master high school - university math with effort. I don't know this mathematician btw.
Haha "how the heck did anyone think of that" 😂
It shows you that he has the same problems as us mere mortals when he says that lol.
It's honestly so true though. When you read some proofs you forget that some guy back in the 1700s or 1800s probably worked on the problem for months to get to that proof, and so when you just see it presented in its final form, all the failed attempts it took to get there are hidden and the chain of "insights" as PSL puts it seems ludicrously unintuitive.
This Pod cast is amazing!
Very insightful: breaking a problem into subproblems with inputs and outputs (sockets), for which one knows solutions. Of course, one is as powerful as the number of subproblems he/she has in their inventory.
I've posted something similar but I've called that connections which in your case would be "sockets". So I think what makes any problem hard is the number of sockets in a problem to which I would add that complexity of those sockets would play major role there too.
I'm laughing at myself imagining finding myself in this conversation and they both wait for my input !
Remarkable! The vinacular is on point!
Brilliant way of thinking about difficulty
The two problems I’ve encountered of this idea comes from proving 1) first part of Fundamental Theorem of Calculus (3 insights) and 2) in statistics, the sample mean and the sample variance are independent (4 insights)
This man is extraordinary ! The Math is beautiful!
I'm not smart by any means, but I'm kinda happy that he said that he learn math the way he did because I did that since I was 15yo. I remember because I once asked teacher that annoying questions why and how and she couldn't tell me. She was cool about it and even give me assignment to find out these questions. That's when I learned that fundamental problem with learning something from someone is that if they know something, some equation for example, they will just repeat over and over and over until they forgot why it is the way it is. That the difference between knowing thing and understanding things. I'm not the brightest and I personally doesn't go into detail in things I don't feel I need to, but I do understands what I know enough so when someone ask me about it I'm able to explain them what the problem is and why it is even though it's abstract concept. I will try and find some analogy that I understand and I could apply in real life and you would be surprised how many people are interested after to know more.
I wish our teachers could have good analogies, real life uses or even made up bs stories about how the problem was discovered and how it was solved. And that's what he's doing naturally by himself by doing proofs he's able to understand the nature of the problem.
My point is that what I think he was trying to say was, *what makes math problem hard is the number of connections you have to make in your mind in order to solve the problem.*
Brilliant haha, all maths students need to watch this clip
I only know that plugs go inside socket.
What constitutes an insight in the way that Lex and Po-Shen are using it here? Is it one “Ah ha!” moment? A spontaneous intuition of resolution - not necessarily of a final solution, but to a branch point of junction that gives you something useful to work from? That’s how I’m hearing it… What’s a little confounding to me about it is that ostensibly everything in math is layered with innumerable, embedded insights. It’s that the human mind computes a concrete direction, so the fan of all possible directions collapses into a discrete progression - like that page in a math text book. How many embedded rabbit holes exist within that stream of logic? Anyway, the potential for nonlinear inference strikes me as stupendous. People who compete in the math olympiads have my undying respect.
This man broke it down so beautifully 🙏🏽❤️🔥
Mathematics is simply understanding
Very smart answer
So, the difficulty of a problem is directly proportional to the number of insights that have to be made to solve it?
thank you
I couldnt even do the math in his explanation
there isn’t any math in his explanation
@@nihaarshah7982 Exactly
😂 fr
@@nihaarshah7982 0:55 How is this not math, lol.
@@Jake-bt3fc hes not working with values like you would in math, hes working with ideas
Is he saying that each "line" he sees on the page is an "insight" aka an equation his mind is going to have to make? so for instance, he used the page in his math book as sort of a cheat sheet to know if he was going to have to do a ton of "insights" or just a few. Is this what he was saying?
What they're talking about it is exactly why I scared myself out of engineering and switched to business. It probably wasn't as hard as I thought; I should have stuck with engineering and toughed it out.
Same LOL
I am so confused. Thank you.
Points of view
And how many can you access to see what you are looking at
This is where the saying. Comes
What’s your angle
Brilliant
Rule one of calculus. Make sure you know algebra, geometry and trigonometry first. Those are just the prep steps for the calc, you can do the calc perfectly but if the algebra, geometry and trig are wrong, everything will be wrong.
Good weed brought me here, glad I came, dudes a genius
so its like if 1+1=2 but then 2+2=4 you can divide 4/4 to go back to 1 or you can multiply by 2 to go to 8 and then do -7 =1
Got it 👍🏼
Makes sense.
For math table of vision of art of stairs in many ways
Grant Sanderson and him talking would be fun
Ive watched it 4 times and im more confused than the 1st time
Don't feel too bad. It's a three-insight video.
😂😂😂
Keep watching and look up each part via google
I absolutely love this video. In particular the part where Lex questions Po-Shen’s claim that difficulty can be measured linearly in the proof. Lex objects which demonstrates that he’s a colleague not just a fan. They engage in a negotiation over nothing but P.O.-Shen’s use of linear here. They land on a new compromise: if reviewing proofs is performed in a single text (to eliminate style differences) you could reasonably say that the length of a proof was a linear representation of the difficulty. You guys are nerds, but you knew that!
I wonder if the insight gained from each level of insight completed would help to negate the multi level expotential factor
Of course it does
that Po-Shen calls it a "search space" is really interesting to me. It suggests that doing math is a lot like playing chess, I guess, and that innate ability has something to do with how wide/deep somebody's internal search space is.
"... and yes, everything here is true, but how the heck did anyone think of that?!" - literally everyone throughout their math education
I need to find the English translation for this video.
They speak IQ we cant understand
two plus two is four, minus one that's quick mafs!
Ohhhhh...It`s a Rubik`s Cube wrapped up in a math equation?
I`M OUT!!!
........i couldn't have said it better myself. 👍
So yes...
The exponential possibilities gives me a headache.
He’s saying that the total number of possible ways to solve the problem that you will have to try can be calculated as follows: take the number of possibilities you will have to try for each sub-problem (what he calls a leap or re-framing) and multiply that number by itself n times, where n is the number of sub-problems. So if each sub-problem has 5 possibilities to try, and there are three sub-problems, then the total number of possibilities to try is 5 x 5 x 5 = 125. it’s really on approximation, since each sub-problem is unlikely to have the same number of possible solutions to try.
this guy is cool as hell
I focus on them all idk it was side waysb
The most difficult problems(in general) must be those which arent proveable, and where you can't prove if they are not proveable (the nightmare of mathematicians - love and hate to Gödels). At least those problems could be good generators of new math insights :D
I hate math but this guy makes math seem doable
Haha, exactly guys, I feel ya... hilarious.
He is satoshi!!!
Math really is its own language.
This guy is so likeable!
I don't get it...
I feel marginally smarter
a math prodigy says math textbooks are nonsense. finally
Lex is my gateway to know the genius ones. @Genius-Google
Fits all the stereotypes.. Asian math genius wearing glasses
(Voice of Ogre): "NNEEEERRRRDSS!!"
after listening all i got is headache
Here for the culture
I dont understand it, but i like mc escher
As the British would say, “mafs”
That bloke with glasses is clearly so very intelligent. Bless.
Lex needs a discussion about how the twin towers were a controlled demolition
Lex do a video or podcast or Lucid dreaming!
What?
po-shen potion
If you are on the Left, it is 2+2.
I came I'm here thinking it was gonna be 8×12 or something
I hate when Lex does this, doubting the guest instead of trying to understand where he's right. Luckily in this clip he was absolutely out matched as his guest persisted.
The funny thing is that this explanation itself puts "mathematical problems" into a single form of representation, where what makes for the hardness of mathematical problems is precisely the fact that each of the "steps" he mentions requires a leap out of *any* given form of representation.
What makes mathematical problems hard is the fact that there is no preconceived answer to this question.
Nerds are awesome
It's too bad I didn't have somebody like this in my math class.. Could have cheated off him and passed
I would rather learn how math works by trying it than reading a textbook or watching the teacher
The answer is 4 unless it is Friday when the answer is 4 1/2.
Why am I laughing right now
Because you’re a kharrcuss
@@thatisabsolutelykooooge2211 oi UA-cam newbie
Know your place or show your face
Cowardice isn’t tolerated here
@@Itsahmadworld oh ho ho eerra sico; a kharcuss talking about cowardice LOLOLOLOLOLOLOLOLOL!!!!!!!
@@Itsahmadworld I don’t show my face to people with duck face photos 👍🏿
@@thatisabsolutelykooooge2211 so you don’t show it to your mama?
Boy why you hate yourself so much
Find the happiness within and you wouldn’t have to spout nonsense under some shitty alias on the net big man
But does he know the square root of 16?
Only minds rooted in the fifth dimension could answer such a riddle as that.
Pretty sure that guy's an alien.
Honestly not sure I understood a single thing that was said there?
He is kind live in 4th dimention
Yes. We need more trashing of math textbooks. Those things are fucking trash.
Interviewer: what makes a hard math problem?
The guy: I could quantify it by the numbers of leaps of insights,Ok so this is a very theoritical computer science bit....
Me, a dumb 1st year computer science student: Hol up....
Humans think metaphorically, not literally.
I think I understand the language but have no idea what the heck he is saying..
OMG IT'S THE ALMIGHTY PO-SHEN LOH NOTICE ME!!
P
Omg wtf did i just watch....where the hos at tho?
meh all easy stuff here, i have the solutions but Po-Shen told me not to help him. also, water is wet.
I’ve never felt more of an ape than I do now
What the fuck is a leanier
I dumb
Yea Yea, okay, mmhmm, I see. Yea totally. I agree mmhmm mmhmm
Math isn’t factually precise, formulas in Python or physics all have infinites = incomplete sums. Hence no answers derived from incomplete math are answered. Math is the wrong tool being used incorrectly. We need new ways to think..... ASAP.
Hold up, this man just say taught his self math in college? He tried to back peddal but I think that's what he did.
Skinny in body, fat in brain
@@juliocesarsalazargarcia6872 indeed