I really enjoyed this conversation with Grant. Here's the outline: 0:00 - Introduction 1:56 - What kind of math would aliens have? 3:48 - Euler's identity and the least favorite piece of notation 10:31 - Is math discovered or invented? 14:30 - Difference between physics and math 17:24 - Why is reality compressible into simple equations? 21:44 - Are we living in a simulation? 26:27 - Infinity and abstractions 35:48 - Most beautiful idea in mathematics 41:32 - Favorite video to create 45:04 - Video creation process 50:04 - Euler identity 51:47 - Mortality and meaning 55:16 - How do you know when a video is done? 56:18 - What is the best way to learn math for beginners? 59:17 - Happy moment
Dear Lex, I would love it if you would consider inviting both Grant Sanderson and Randall Munroe and moderate a discussion between them :) Bet I am not the only one feeling that way!
#I have four questions about neutrons and low-power bosons The first question is whether all the short-lived particles will be converted into weak Guo bosons Or only the neutron decomposes into a weak force The second question is about primary particles Is neutrino composed of fluctuations in quantum vacuum as well? The third question, how does the neutrino form during nuclear fusion in the sun? Does nuclear fusion lead to the loss of part of the energy? the fourth question Is this neutrino the lost energy during the nuclear fusion process? We hope that you send the four questions to physicists Please post the answers in science websites in a web browser
Yes but he seems to go heavy on pulling back the veil of mathematics only targeted to what mathematics represents in a physics and engineering mindset.
lol when you write proofs and theorem all day it rubs off on you. i do that too xD To many hours trying to memorize it instead of understanding its beauty like grant does
Feynman would disagree. You can see a pretty flower, and enjoy it at this level without thinking about electrons jumping onto and from energy states as they are hit by photons, emitting a specific wavelength you percieve as color. Even if you somehow end up thinking about electrons, you are then not thinking about how evolution shaped this specific flower to attract its pollinator, how the local geology made it possible for this flower to grow, how this was all started because something somewhere exploded and matter got pulled together by gravity forming a planet with active geology... The point is, the depth of your understanding of something is not important, you cannot think about it all at once, and at any time, you are left trapped experiencing complexity and beauty at a given level. And there is more beauty and elegance to be found at each level of understanding.
Gromov has this lovely quote to the effect of 'anything worth proving in mathematics just shouldn't be true.' I think that it is important to keep in mind that we never truly understand something in mathematics, we only find alternate ways of looking at it.
@@ryPish well of course if you try to apply it in general terms you'll find that it's not always true. It's true mostly for more abstract concepts that the more you understand it the less beautiful it is because an abstract concept doesn't have the same direct visual stimulation as looking at a flower, so that's just a bad analogy.
Sort of the reason I love writing personally. I dont always understand what I write and that is okay, I am only human. I mean that in a sense that when writing, we have to display information in a easily accessible but with a bias, either a narrative one or a thematic one. But once you accept that, the more you write and imperfect it may be, the more beautiful it is. As counterintuitive as that sounds, I think there is a balance of understanding and aesthetics personally. Idk, maybe I am looking into it. The take is also just beautiful. I suck at math, but glad to know mathematics can normalize beauty because I sure as hell cant understand it.
I remember in my first semester of high school, I had decided that I wanted to study mathematics. I was horrible at it, I didn't know anything, and I got the worst grades (C's and D's). I gave up a couple of times, but now I'm getting top grades in topics like complex analysis, real analysis, and partial differential equations. I had lost motivation at times, but people like Grant Sanderson really inspired me to see WHY I am studying mathematics. It's a really beautiful subject, and Grant just radiates zeal for it - it's great to see.
Man, I remember I was really good at maths in elementary school, probably the best in the school, and then middle school hit and I couldn't even solve systems of two linear equations with 2 unknowns. It was at around that time that my older brother taught me a lot of stuff I was behind at at school, and simultaneously found maths on TH-cam, and among the many awesome TH-camrs I found one of them was 3B1B. That really got me into maths and was how and why I started to love it. Now, after passing my final exams (with a clean 100/100 on maths), I am on my way to study physics, but I will greatly use mathematics to my advantage!
Grant Sanderson is an understated genius. 3Blue1Brown is the type of channel that can ACTUALLY change the world - One mind at a time. He makes understanding the world around us interesting, while also making higher Maths accessible. Such a refreshing change from the usual distractions.
I really believe Grant is the smartest person I've heard speak. Not just because he understands a whole lot, but because he is able to communicate it. I see him as Feynman's successor in that regard. What a champion!
Definitely an amazing communicator, but comparing him with someone that made profound contributions to advancing the actual field of mathematics is a bit of a stretch. Until he atleast comes up with something like a Feynman diagram, we can hold off on such a comparison. He definitely makes Neil Degrass Tyson look quite silly though!
Seriously, Lex, you’ve been doing an outstanding job at bringing in amazing guests and having interesting conversations! 3B1B is one of my favorite channels, for sure. Thank you!
Mr Sanderson has a clarity with abstractions which makes you feel like he can wield them like swords respectfully sharpened beyond peacetime demonstration. You simply can't help giving him a lot of respect out of pure self-preservation.
I’m just confused about how his idea of physical information limits in bits per unit area isn’t contradictory to his idea of infinity by simply adding a letter to a word to arbitrarily extend it. He said we have physical limits to information as an argument against simulations but then argues for abstract infinity?
@@alleyway I agree it's a hole in this story, but I'm not sure it's a contradiction. 'Abstraction', if we chose to think of it as another degree of freedom (as oppose to generalization - this is arguably different) , will only have a physical meaning if we can map those freedom degrees to physical dimensions, otherwise we must work with projections which extend in time (serialization says the programmer in me). If time is infinite, then abstract infinity is a thing but at the same time the number of bits per unit will be limited because of physical constrains which limits the speed by which pieces of information can interact.
@@KristoferPettersson So infinity is a thing if we never stop counting and time is itself infinite. Or I guess if we never stop moving away from a fixed point in space and space is itself infinite. I think many people use "infinity" but really mean to add "for all intents and purposes". I think that would make a big difference.
for someone who has been struggling with maths since I was a kid. I force myself to learn calculus In univesity. The only way I could understand It Is by understanding the concept by their roots. The only place where I found the same way of understanding math is on 3blue1brown YT channel. I am not saying I have the skills, but I learn the concepts the same way 3blue1brown explains It, and I wasn't teached that way. I am sure formal math education can learn a LOT from his youtube channel.
The best thing about Lex is that he never pretends that he completely understands, and he never pretends that his questions are naive. He prepares beforehand and is so honest about what he knows and what he wants to know during these interviews. Like "Are you ok with the existence of infinity" is a great question. He asks the questions that stem students, like me lol, don't really get to ask or don't know how to ask.
No, I'm sorry that's not a great question. Actually his questions often reveal fundamental ignorance about the subject matter, which makes me wonder what makes these great guests want to go on his podcast
Grant Sanderson's eloquence is simply amazing. Concepts , Ideas and Visualisation seem to get converted into almost musical articulation with effortless ease in his brain. The cascade of words, phrases and sentences that gush forth from his mouth as he conveys his Mathematical understanding in English language simply enthralls me! I have never seen him fumble for a single word, ever !!!! Thank you Grant . Keep going.
This was (at least for me) hands down, the best interview I`ve experienced. 2 people with minds set in two different fields yet still relevant to each other. Many of the things Grant says really is mind opening. Grant making great claims about questions about infinity and Lex showing great responses "some push backs too" to those. You both are great and I loved listening to this.
I’m absolutely head over heels that I found this channel in 2020! It’s everything I wanted from rogan with no filler and less entertainment based guests. I love rogan too. But we needed this! Lex proves not all heroes wear capes!
I'm blown away: I just googled "Grant Sanderson" and he is the guy behind 3Blue1Brown! One of the most cogent and explanatory TH-cam channels I've come across!
I can't explain.....It gives me immense pleasure to see two of you talking deep things, discussing things that I have interest in too. Two blessed souls.
Wow, wow, wow, My wish has been granted!! I was eagerly waiting for this one!! There is nothing more beautiful than to sit back and have two of your favourite creators talk on thw topics dear to you heart-STEM. This has to be the best one hour on TH-cam for a while now. Thanks for inviting Grant for such a stimulating and enlightening conversation!
Grant's description of the process of understanding is gold. Starting from definitions is like providing students a list of places to visit with no map to put them on. Providing visuals (or other concretizing examples) early on provides a structure that later knowledge can adhere to
Wow! While I could not grasp some of the more technical mathematical concepts discussed, I still enjoyed how clearly Grant can think and express himself. It's clear how his deep learning playlist is so beautifully explained
Thank you Lex for putting these interviews together, putting yourself out there, and having damn good conversations with risky questions. Really appreciate you, friend. Cheers
51:48 “Would your life be four times as meaningful if you died at 25?” This has got to be one of the most quick-witted and profound responses to a serious, complex question I’ve ever heard, and I don’t know why, but it had me laughing my ass off.
Wow, Grant's mind is sharp as it can get. Amazing to see him articulating complex responses while talking around the subject. Listening to the podcast is great. Watching it is another level. Thanks Lex!
This is such a beautiful conversation. The brutal honesty of Grant's "I don't know, man!", the 'aha'-moments, the way the both of you can compress years of discussions I've had with friends in to one-liners and then build upon them further... This just keeps giving! Thanks so much for this
~32:10 "I don't think of myself as particularly good at math" -- not sure if humblebrag or serious... :P Joking aside, it's amazing and inspiring to see Grant's humility and honesty here.
This guys channel has taught me more about math in minutes than any traditional teacher has taught me in hours, and it was entertaining. Teachers should be showing his videos in class.
Always watching his videos with his voice and manim, and also his pandemic videos about maths, and then this feels so different now, having him speak to someone else and seeing how much enthusiasm he has for all these things!
Wow, Grant's comment at 35:11 is amazing. I too get bogged down and confused and bored when the theory is presented first... but his methods of showing examples first and then tying it together with theory is amazing. Now I know why his videos are so good at explaining things so much better than the average lecturer...
I have watched many of your videos, and just discovered these with Grant... I decided I'm going to jump back into math for data analysis and revisited 3blue1brown recently. Thankfully, the YT algorithm gods gave me these video suggestions of yours. Lex, I really can't tell you how grateful I am to have found your podcast. When I'm too exhausted to work late or study, I can cook/clean/etc. and still listen to such high quality, intelligent and entertaining conversations knowing that my mental reserves are spent in a productive and stimulating way. I appreciate you and your work very much.
Lex, I've listened to so many of your more recent interviews, and just today learned that you've interviewed Grant Sanderson multiple times. I had to check it out! The man is a legend in my mind, and I sooo enjoyed hearing more of his thoughts, beyond just what shows up in his videos. This was great. Thank you!
From Lex's facial expression, I'm pretty sure he is trying really hard to catch up with Grant's thoughts and come up with meaningful questions that can move the conversation forward at the same time. This is probably one of the most challenging podcast for him. It requires a lot more than common sense, or general knowledge of math, this requires deep and critical thinking of fundamentals in math. But Lex is already doing a great job, I can't fathom a better host.
How is it that you seem to always get the most interesting people week after week. I am a huge fan of 3Blue1Brown, and he's even better in person. Great video! And great discussion.
I love the discussion about whether we all live in a simulation. Grant raises an interesting point by highlighting the immense computational power needed to simulate the entire universe. However, I would like to contribute an additional thought: if our reality were indeed a simulation, it might not encompass an entire universe, but rather a singular mind-more precisely, your mind (whoever currently is reading this youtube comment).
The speaker's knowledge of the limits of information per unit area/volume is fascinating. He's not punting. One of your best guests for his understanding, imo.
Thanks for sharing this video. As someone who has taught others math, chemistry, and physics, I can confirm that teaching others imprint the info very strongly with you. Having to try to relate "the book" with all is absolutes to someone who doesn't necessarily retain all of the prerequisite facts means that you have to do so much more that just repeat the info. If forces you to see things from different angles, make different analogies, adjust to different phrasings, and so much more. You often gain new insights from doing this, even if neither of you understand the problem completely. On a side-note, if you could ask Grant to include a link to some related problems on Khan or where ever that people can take on with the things he address in his videos, that would bring a huge improvement to the understanding of those who engage it. Without working with the tools you don't retain it well, and then the value of the video is severely diminished.
Thank you, Grant, you've turned on so many lights I didn't know were off. Keep up the good work! And you too, Lex, you're doing something important with these interviews.
Grant has one of my favorite TH-cam channels and I’m not being hyperbolic why I say that I understand very little. But I watch again and again with hope. Best Regards Lex and thank you for everything Gilbert Strang to Grant to the one you released yesterday about self-replicating robots. I taught English for many years at PEA and only faintly remember math.
What e^ipi captures is that the only analytic map which wraps a cartesian axis around the unit circle must have exponential growth in the radial direction. This captures a deep connection between rotation and dilation, and allows us to unify the concept of torque and linear force in the plane, into a single concept of vector. This procedure is very beautiful, and the extension of the notion of repeated multiplication is essential to the generalized operator calculus -> leading toward greater enlightenment -> I think that the notation is excellent and beloved because its mystery draws our intuitions to the important and more subtle properties of the idea of 'number'
Grant and lex conversation about abstraction from visualisation to the concept of infinity and the very essence of science is the highlight of this video. So succinct and apt to use the abstraction as processed by an AI to human concepts. Love your work Lex and Grant. Keep up the good work.
I just got into the Lex Fridman podcast a couple months ago, and today I thought, 'Oh man, Lex HAS to interview Grant!'... Imagine my surprise when I found that the conversation already exists! Now to enjoy some Lex + Grant goodness.
At each Lex upload i stop everything i do to watch these amazing talks, these talks almost put you into a philosophical state of mind. Absolutely amazing.
Thank you very much for this Interview. 3Blue1Brown is my one of my 2 favorite Math series on TH-cam. Additionally it is the best mathematic show. Extremely helpful. You are doing great work Lex. Lex and JRE are hands down the best podcast on TH-cam.
This was one of your best interviews yet on this channel. You really have a gift for asking thoughtful questions that guide your guests toward insightful discussions. Keep up the great work.
20:40 Sir, that was one beautiful question , from what i interpreted from what you were trying to ask was that whether it is possible for the realm of mathematics to not explain physical phenomenon we might stumble upon in future or highly compiled systems that we ignore presently . edit - given that the prior context before asking the question was that constrains we humans have opposed in mathematics due to notation might lead to chaining our imagination , basically proposing the idea that our bias towards hardships may lead us to overlook complex mathematical models
happy talking to each other? Lex Friedman barely asks sensible question on himself. He has them written on paper. I dont think the guy can interview math or programming people successully because of lack of background. The interviewees are nice enough to turn around the question avoiding confronting ignorance on Lex side.
Excellent discourse from two great thinkers. Blue-Brown is brilliant, even though some videos are still hard to understand, showing that math is inherently difficult. Thanks to both for an extremely stimulating discourse.
20:12 I can't really imagine how our universe would even hold itself together and have consistency if there weren't some orderly underlying principles which dictate how it behaves. Its along the same lines of thinking when people ask the question: well if the perfect conditions for humans are so rare, why do we see them on Earth? They don't understand that they have the cause and effect switch. Cause: the conditions existed; Effect: we are here to ask the question. In other universes where this cause was not met doesn't allow the nonexistant beings there to ask the question.
@@gmork5051 well, at least the anthropic principle can be used in a somewhat useful non-normie way(meaning not confusing cause and effect) by observing SOME conditions earth has that are observed to be rare. that being said, your point makes sense
31:17 love the discussion on accepting that you can't concretely understand very abstract concepts in a way that you can anchor your understanding simply. Kind of makes me think that is why these concepts are intrinsically abstract. :)
35:20 incidentally, this is also the way to go about learning new languages - being exposed to examples, and then be presented with the grammar of it afterwards (and not before).
Amazing guest and content - I will suggest it again : get Jim Simmons on the podcast to talk math ! (billionaire mathematician founder of Renaissance Capital)
Thats the inevitable endpoint of mastery in any field, you start "touching the divine" and thinking about philosophical implications. All science ends in theology :)
This interview coupled with "Grant's Opus" in the background (a musical piece by Grant himself) gives a very different experience. It feels like I'm watching something legendary (In fact, I am!).
I don't remember how I found Lex Fridman's channel, but I'm always amazed by it. Who the heck is this guy? How does he get such amazing people to interview?
I really enjoyed this conversation with Grant. Here's the outline:
0:00 - Introduction
1:56 - What kind of math would aliens have?
3:48 - Euler's identity and the least favorite piece of notation
10:31 - Is math discovered or invented?
14:30 - Difference between physics and math
17:24 - Why is reality compressible into simple equations?
21:44 - Are we living in a simulation?
26:27 - Infinity and abstractions
35:48 - Most beautiful idea in mathematics
41:32 - Favorite video to create
45:04 - Video creation process
50:04 - Euler identity
51:47 - Mortality and meaning
55:16 - How do you know when a video is done?
56:18 - What is the best way to learn math for beginners?
59:17 - Happy moment
curious to know if Grant is left handed or if the video is flipped
Dear Lex, I would love it if you would consider inviting both Grant Sanderson and Randall Munroe and moderate a discussion between them :) Bet I am not the only one feeling that way!
are you using deepfake to do the ads? ;) a practical use of your field. also you have plenty of stable images and audio to be able to render it
It is because he lists these time stamps that I listen to the ads.
#I have four questions about neutrons and low-power bosons
The first question is whether all the short-lived particles will be converted into weak Guo bosons
Or only the neutron decomposes into a weak force
The second question is about primary particles
Is neutrino composed of fluctuations in quantum vacuum as well?
The third question, how does the neutrino form during nuclear fusion in the sun?
Does nuclear fusion lead to the loss of part of the energy?
the fourth question
Is this neutrino the lost energy during the nuclear fusion process?
We hope that you send the four questions to physicists
Please post the answers in science websites in a web browser
3B1B is really doing so much for math
Jacob Lee jesus lee christ 😂😂😂😂
Yes but he seems to go heavy on pulling back the veil of mathematics only targeted to what mathematics represents in a physics and engineering mindset.
@@melonduofromage6058 For some reason many of 3Blue1Brown's intuitive explanations don't seem to work well for me. I'm not sure why.
didnt get it ;(
He's awesome!
You know Grant is a mathematician when he says, "such that".
lol when you write proofs and theorem all day it rubs off on you. i do that too xD
To many hours trying to memorize it instead of understanding its beauty like grant does
So true😂
lol
@@DavidsGameplayMC gvvvvggģgchvkkhjjljh
Ever since I started doing math in college I start saying things like "if and only if" and "such that" all the time
“Once you understand something it doesn’t have the same beauty” - 3B1B
Somehow such relatable human feeling.
Atrifex I know right! It’s remarkable how much we aliens can relate to these “humans”.
Feynman would disagree. You can see a pretty flower, and enjoy it at this level without thinking about electrons jumping onto and from energy states as they are hit by photons, emitting a specific wavelength you percieve as color. Even if you somehow end up thinking about electrons, you are then not thinking about how evolution shaped this specific flower to attract its pollinator, how the local geology made it possible for this flower to grow, how this was all started because something somewhere exploded and matter got pulled together by gravity forming a planet with active geology...
The point is, the depth of your understanding of something is not important, you cannot think about it all at once,
and at any time, you are left trapped experiencing complexity and beauty at a given level.
And there is more beauty and elegance to be found at each level of understanding.
Gromov has this lovely quote to the effect of 'anything worth proving in mathematics just shouldn't be true.' I think that it is important to keep in mind that we never truly understand something in mathematics, we only find alternate ways of looking at it.
@@ryPish well of course if you try to apply it in general terms you'll find that it's not always true. It's true mostly for more abstract concepts that the more you understand it the less beautiful it is because an abstract concept doesn't have the same direct visual stimulation as looking at a flower, so that's just a bad analogy.
Sort of the reason I love writing personally.
I dont always understand what I write and that is okay, I am only human. I mean that in a sense that when writing, we have to display information in a easily accessible but with a bias, either a narrative one or a thematic one.
But once you accept that, the more you write and imperfect it may be, the more beautiful it is.
As counterintuitive as that sounds, I think there is a balance of understanding and aesthetics personally.
Idk, maybe I am looking into it. The take is also just beautiful. I suck at math, but glad to know mathematics can normalize beauty because I sure as hell cant understand it.
Dude you're killing it with these guests!
@@slightlygruff Yes Please!
exactly my thought!
Jim gates was excellent!
sure I am glad I belong to this generation
Yep, hes basically going down my list of idols.
I remember in my first semester of high school, I had decided that I wanted to study mathematics. I was horrible at it, I didn't know anything, and I got the worst grades (C's and D's). I gave up a couple of times, but now I'm getting top grades in topics like complex analysis, real analysis, and partial differential equations. I had lost motivation at times, but people like Grant Sanderson really inspired me to see WHY I am studying mathematics. It's a really beautiful subject, and Grant just radiates zeal for it - it's great to see.
It would be interesting to know what your motivating factor was, given that you were horrible at it, at the beginning...
@@coscinaippogrifoOne finds it in time.
Man, I remember I was really good at maths in elementary school, probably the best in the school, and then middle school hit and I couldn't even solve systems of two linear equations with 2 unknowns. It was at around that time that my older brother taught me a lot of stuff I was behind at at school, and simultaneously found maths on TH-cam, and among the many awesome TH-camrs I found one of them was 3B1B. That really got me into maths and was how and why I started to love it. Now, after passing my final exams (with a clean 100/100 on maths), I am on my way to study physics, but I will greatly use mathematics to my advantage!
3blue is a modern day hero i tell ya. and hes my hero for sure
he is my intellectual elder
Actually he save my math exams lol
Yep. If I were a billionaire, Grant would be too.
Grant Sanderson is an understated genius. 3Blue1Brown is the type of channel that can ACTUALLY change the world - One mind at a time. He makes understanding the world around us interesting, while also making higher Maths accessible. Such a refreshing change from the usual distractions.
I really believe Grant is the smartest person I've heard speak. Not just because he understands a whole lot, but because he is able to communicate it. I see him as Feynman's successor in that regard. What a champion!
Definitely an amazing communicator, but comparing him with someone that made profound contributions to advancing the actual field of mathematics is a bit of a stretch. Until he atleast comes up with something like a Feynman diagram, we can hold off on such a comparison.
He definitely makes Neil Degrass Tyson look quite silly though!
Seriously, Lex, you’ve been doing an outstanding job at bringing in amazing guests and having interesting conversations!
3B1B is one of my favorite channels, for sure.
Thank you!
Who is this Lex guy? I swear he's some genius super villain dude.
Mr Sanderson has a clarity with abstractions which makes you feel like he can wield them like swords respectfully sharpened beyond peacetime demonstration. You simply can't help giving him a lot of respect out of pure self-preservation.
I’m just confused about how his idea of physical information limits in bits per unit area isn’t contradictory to his idea of infinity by simply adding a letter to a word to arbitrarily extend it. He said we have physical limits to information as an argument against simulations but then argues for abstract infinity?
@@alleyway I agree it's a hole in this story, but I'm not sure it's a contradiction. 'Abstraction', if we chose to think of it as another degree of freedom (as oppose to generalization - this is arguably different) , will only have a physical meaning if we can map those freedom degrees to physical dimensions, otherwise we must work with projections which extend in time (serialization says the programmer in me). If time is infinite, then abstract infinity is a thing but at the same time the number of bits per unit will be limited because of physical constrains which limits the speed by which pieces of information can interact.
@@KristoferPettersson So infinity is a thing if we never stop counting and time is itself infinite. Or I guess if we never stop moving away from a fixed point in space and space is itself infinite. I think many people use "infinity" but really mean to add "for all intents and purposes". I think that would make a big difference.
@@io3213 Is time infinite? :) I wouldn't be so sure.
@@KristoferPettersson IF there is such a thing as absolute time, then it must be infinite. If it's not infinite, it's not absolute. Right ? :)
3Blue1Brown has changed the world of education itself, introducing easy to visualise understanding of complex concepts. Love from India🇮🇳💗
for someone who has been struggling with maths since I was a kid. I force myself to learn calculus In univesity. The only way I could understand It Is by understanding the concept by their roots. The only place where I found the same way of understanding math is on 3blue1brown YT channel. I am not saying I have the skills, but I learn the concepts the same way 3blue1brown explains It, and I wasn't teached that way. I am sure formal math education can learn a LOT from his youtube channel.
The best thing about Lex is that he never pretends that he completely understands, and he never pretends that his questions are naive. He prepares beforehand and is so honest about what he knows and what he wants to know during these interviews. Like "Are you ok with the existence of infinity" is a great question. He asks the questions that stem students, like me lol, don't really get to ask or don't know how to ask.
No, I'm sorry that's not a great question. Actually his questions often reveal fundamental ignorance about the subject matter, which makes me wonder what makes these great guests want to go on his podcast
Grant Sanderson's eloquence is simply amazing. Concepts , Ideas and Visualisation seem to get converted into almost musical articulation with effortless ease in his brain. The cascade of words, phrases and sentences that gush forth from his mouth as he conveys his Mathematical understanding in English language simply enthralls me! I have never seen him fumble for a single word, ever !!!!
Thank you Grant . Keep going.
This was (at least for me) hands down, the best interview I`ve experienced.
2 people with minds set in two different fields yet still relevant to each other.
Many of the things Grant says really is mind opening.
Grant making great claims about questions about infinity and Lex showing great responses "some push backs too" to those.
You both are great and I loved listening to this.
I’m absolutely head over heels that I found this channel in 2020! It’s everything I wanted from rogan with no filler and less entertainment based guests. I love rogan too. But we needed this! Lex proves not all heroes wear capes!
I'm blown away: I just googled "Grant Sanderson" and he is the guy behind 3Blue1Brown! One of the most cogent and explanatory TH-cam channels I've come across!
I can't explain.....It gives me immense pleasure to see two of you talking deep things, discussing things that I have interest in too. Two blessed souls.
Wow, wow, wow, My wish has been granted!! I was eagerly waiting for this one!! There is nothing more beautiful than to sit back and have two of your favourite creators talk on thw topics dear to you heart-STEM. This has to be the best one hour on TH-cam for a while now. Thanks for inviting Grant for such a stimulating and enlightening conversation!
Did you say your wish has been Grant-ed?
@@noomade 😁😁
Grant's description of the process of understanding is gold. Starting from definitions is like providing students a list of places to visit with no map to put them on. Providing visuals (or other concretizing examples) early on provides a structure that later knowledge can adhere to
Grant is one of the greatest educators of our time and the most underappreciated of them by the world
1:01:14 Such a great ending note on how Grant Sanderson helped showcase the creative side of mathematics.
This guy is my favorite guest on this podcast so far.
Wow! While I could not grasp some of the more technical mathematical concepts discussed, I still enjoyed how clearly Grant can think and express himself. It's clear how his deep learning playlist is so beautifully explained
Thank you Lex for putting these interviews together, putting yourself out there, and having damn good conversations with risky questions. Really appreciate you, friend. Cheers
I can't describe the joy I get from Grant's arguments. He sees the essance of everything he talks about, as if he programmed the universe
I am from Bangladesh and each time I watch Mr. Grant explaining something, I experience pure joy.
Thank you for making the world a better place.
Love 3blue1brown have this guy back on! Need more podcasts getting “into the weeds” with math in a conversational manner. Awesome job!
51:48 “Would your life be four times as meaningful if you died at 25?” This has got to be one of the most quick-witted and profound responses to a serious, complex question I’ve ever heard, and I don’t know why, but it had me laughing my ass off.
You might be laughing because you're high af
Wow, Grant's mind is sharp as it can get. Amazing to see him articulating complex responses while talking around the subject.
Listening to the podcast is great. Watching it is another level.
Thanks Lex!
Thank you so much for having Grant on the podcast. Fascinating young man!
Grant's visualisation of mathematical concepts becomes the heart and soul of insights!
These are just unbelievably amazing interviews. You are so right when you say "never too philosophical."
This is such a beautiful conversation. The brutal honesty of Grant's "I don't know, man!", the 'aha'-moments, the way the both of you can compress years of discussions I've had with friends in to one-liners and then build upon them further... This just keeps giving! Thanks so much for this
So weird looking at Grant's face having never seen it - like meeting a vendor that you've only ever talked to on the phone! Great chat!
~32:10 "I don't think of myself as particularly good at math" -- not sure if humblebrag or serious... :P Joking aside, it's amazing and inspiring to see Grant's humility and honesty here.
Being able to participate in a conversation with two such amazing and super enthusiastic individuals would surely be a defining point in my life
Grant Sanderson, One of the people I'll always be grateful until the last day I breathe!
I could listen to them talk all day!
I love Grant's demeanor. He is opposite of the Catholic Italian nuns I had, not that there's anything wrong with that, when I was in Catholic school.
That was the most beautiful way to end a discussion. Bravo!
This guys channel has taught me more about math in minutes than any traditional teacher has taught me in hours, and it was entertaining. Teachers should be showing his videos in class.
This guys videos on neural networks and blockchains are the best on youtube. Grant should start his own teaching platform.
Always watching his videos with his voice and manim, and also his pandemic videos about maths, and then this feels so different now, having him speak to someone else and seeing how much enthusiasm he has for all these things!
Wow, Grant's comment at 35:11 is amazing. I too get bogged down and confused and bored when the theory is presented first... but his methods of showing examples first and then tying it together with theory is amazing. Now I know why his videos are so good at explaining things so much better than the average lecturer...
I have watched many of your videos, and just discovered these with Grant... I decided I'm going to jump back into math for data analysis and revisited 3blue1brown recently. Thankfully, the YT algorithm gods gave me these video suggestions of yours. Lex, I really can't tell you how grateful I am to have found your podcast. When I'm too exhausted to work late or study, I can cook/clean/etc. and still listen to such high quality, intelligent and entertaining conversations knowing that my mental reserves are spent in a productive and stimulating way. I appreciate you and your work very much.
Lex, I've listened to so many of your more recent interviews, and just today learned that you've interviewed Grant Sanderson multiple times. I had to check it out! The man is a legend in my mind, and I sooo enjoyed hearing more of his thoughts, beyond just what shows up in his videos. This was great. Thank you!
From Lex's facial expression, I'm pretty sure he is trying really hard to catch up with Grant's thoughts and come up with meaningful questions that can move the conversation forward at the same time. This is probably one of the most challenging podcast for him. It requires a lot more than common sense, or general knowledge of math, this requires deep and critical thinking of fundamentals in math. But Lex is already doing a great job, I can't fathom a better host.
I think Grant may be in danger of his brain collapsing into a black hole.
Right??? I keep alerting the authorities but they keep calling me a moron
Pranav Limaye 911, what's your emergency?
3B1B is the most authentic and conceptual math educational channel in all of TH-cam.
How is it that you seem to always get the most interesting people week after week. I am a huge fan of 3Blue1Brown, and he's even better in person. Great video! And great discussion.
I loved his Essence of Linear Algebra series
One of the top 5 guests you've ever had.
Already showed an architectural view of physics and math. Front end and back end. Brilliant.
I love the discussion about whether we all live in a simulation. Grant raises an interesting point by highlighting the immense computational power needed to simulate the entire universe. However, I would like to contribute an additional thought: if our reality were indeed a simulation, it might not encompass an entire universe, but rather a singular mind-more precisely, your mind (whoever currently is reading this youtube comment).
The speaker's knowledge of the limits of information per unit area/volume is fascinating. He's not punting. One of your best guests for his understanding, imo.
27:00 definition of abstraction… brilliant❤
Thanks for sharing this video. As someone who has taught others math, chemistry, and physics, I can confirm that teaching others imprint the info very strongly with you. Having to try to relate "the book" with all is absolutes to someone who doesn't necessarily retain all of the prerequisite facts means that you have to do so much more that just repeat the info. If forces you to see things from different angles, make different analogies, adjust to different phrasings, and so much more. You often gain new insights from doing this, even if neither of you understand the problem completely.
On a side-note, if you could ask Grant to include a link to some related problems on Khan or where ever that people can take on with the things he address in his videos, that would bring a huge improvement to the understanding of those who engage it. Without working with the tools you don't retain it well, and then the value of the video is severely diminished.
Thank you, Grant, you've turned on so many lights I didn't know were off. Keep up the good work! And you too,
Lex, you're doing something important with these interviews.
Grant is an exceptional teacher. He is the one that truly taught me calculus!
Grant has one of my favorite TH-cam channels and I’m not being hyperbolic why I say that I understand very little. But I watch again and again with hope. Best Regards Lex and thank you for everything Gilbert Strang to Grant to the one you released yesterday about self-replicating robots. I taught English for many years at PEA and only faintly remember math.
What e^ipi captures is that the only analytic map which wraps a cartesian axis around the unit circle must have exponential growth in the radial direction. This captures a deep connection between rotation and dilation, and allows us to unify the concept of torque and linear force in the plane, into a single concept of vector. This procedure is very beautiful, and the extension of the notion of repeated multiplication is essential to the generalized operator calculus -> leading toward greater enlightenment -> I think that the notation is excellent and beloved because its mystery draws our intuitions to the important and more subtle properties of the idea of 'number'
you basically said what he did, except about liking the notation
Thank you so much, Lex, for gifting such a beautiful podcast with such a superb personality. God bless you.
Grant and lex conversation about abstraction from visualisation to the concept of infinity and the very essence of science is the highlight of this video. So succinct and apt to use the abstraction as processed by an AI to human concepts. Love your work Lex and Grant. Keep up the good work.
my only regret is that I can only give this one like. thank you 3B1B, and Lex!
The video presentation style and time breakup given along with every video are simply awesome ! Great content.
Regards from University of Padeborn.
3b1b brings math education to a whole new level
This channel is officially my favourite. Keep it up Lex!
I just got into the Lex Fridman podcast a couple months ago, and today I thought, 'Oh man, Lex HAS to interview Grant!'... Imagine my surprise when I found that the conversation already exists! Now to enjoy some Lex + Grant goodness.
At each Lex upload i stop everything i do to watch these amazing talks, these talks almost put you into a philosophical state of mind. Absolutely amazing.
It was nice to see Lex being more relaxed and talkative.
Thank you very much for this Interview. 3Blue1Brown is my one of my 2 favorite Math series on TH-cam. Additionally it is the best mathematic show. Extremely helpful. You are doing great work Lex. Lex and JRE are hands down the best podcast on TH-cam.
Oh, I think now I have some intuition about what infinity is. I could listen to these two infinitely!
Good job, Lex, as always!
The specificity of your guest is wonderful to hear. Your guest is quite a brilliant speaker! He reminds me of no other than Ed Witten!
This was one of your best interviews yet on this channel. You really have a gift for asking thoughtful questions that guide your guests toward insightful discussions. Keep up the great work.
"You don't really know anyone other than the past versions of yourself"
20:40 Sir, that was one beautiful question , from what i interpreted from what you were trying to ask was that whether it is possible for the realm of mathematics to not explain physical phenomenon we might stumble upon in future or highly compiled systems that we ignore presently .
edit - given that the prior context before asking the question was that constrains we humans have opposed in mathematics due to notation might lead to chaining our imagination , basically proposing the idea that our bias towards hardships may lead us to overlook complex mathematical models
Programming indeed inspired me to understand, learn, and see the beauty of math in a way that no other medium has done.
This is a superb interview! It's interesting from the start to the finish.
I like the way those 2 guys talk. Sounds so rational and peaceful
Watching how genuinely happy they get taking to each other is amazing!
happy talking to each other? Lex Friedman barely asks sensible question on himself. He has them written on paper. I dont think the guy can interview math or programming people successully because of lack of background. The interviewees are nice enough to turn around the question avoiding confronting ignorance on Lex side.
"Thank you for revealing the art of mathematics"
Perfect description of his videos.
Wonderful.
Excellent discourse from two great thinkers. Blue-Brown is brilliant, even though some videos are still hard to understand, showing that math is inherently difficult. Thanks to both for an extremely stimulating discourse.
20:12 I can't really imagine how our universe would even hold itself together and have consistency if there weren't some orderly underlying principles which dictate how it behaves. Its along the same lines of thinking when people ask the question: well if the perfect conditions for humans are so rare, why do we see them on Earth? They don't understand that they have the cause and effect switch. Cause: the conditions existed; Effect: we are here to ask the question. In other universes where this cause was not met doesn't allow the nonexistant beings there to ask the question.
As far as we know there is only one universe.
@@snippletrap I agree. I meant possible types of universes that could have existed with different laws.
@@gmork5051 well, at least the anthropic principle can be used in a somewhat useful non-normie way(meaning not confusing cause and effect) by observing SOME conditions earth has that are observed to be rare. that being said, your point makes sense
"because you only really ever know versions of yourself" good lord that's a hot quote
31:17 love the discussion on accepting that you can't concretely understand very abstract concepts in a way that you can anchor your understanding simply. Kind of makes me think that is why these concepts are intrinsically abstract. :)
35:20 incidentally, this is also the way to go about learning new languages - being exposed to examples, and then be presented with the grammar of it afterwards (and not before).
51:30 This makes me desire to live for all eternity. Infinity of existence is a prompt to live good because nothing truly dies.
Seriously one of the absolute best videos ever made, I wish I could broadcast it to everyone! At least it's here, to be found, whatever that "means".
Love how Grand explains concepts
this guy is sooo bloody intellegent man..at such a young age
Amazing guest and content - I will suggest it again : get Jim Simmons on the podcast to talk math ! (billionaire mathematician founder of Renaissance Capital)
Great podcast, I love how Lex puts deeper thoughts into the subject than just more superficial technical views
me too I did like enjoy the questions as much as the answers
Thats the inevitable endpoint of mastery in any field, you start "touching the divine" and thinking about philosophical implications.
All science ends in theology :)
It is kinda annoying actually. Lex tried so hard to get grant to say some spiritual bullshit.
My two favorite science/math TH-camrs joined in conversation. Brilliant!
This interview coupled with "Grant's Opus" in the background (a musical piece by Grant himself) gives a very different experience. It feels like I'm watching something legendary (In fact, I am!).
I don't remember how I found Lex Fridman's channel, but I'm always amazed by it. Who the heck is this guy? How does he get such amazing people to interview?
His channel is 3blue1brown.
3b1b is the best teacher I've even had ❤❤
This gets interesting every minute of it, love it !!
Math is much more fun when discussed.
Grant Sanderson is a Light
51:10 "So you passed the dating stage..." I cracked up! This is such a sweet and nerdy idea, being romatic with certain math functions.