The Hope Diamond (with 3blue1brown) - Numberphile Podcast

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Numberphile2

Numberphile2

Күн бұрын

SUBSCRIBE TO THIS PODCAST ON ITUNES AND ELSEWHERE...
Here's how: www.bradyharanblog.com/blog/th...
Grant Sanderson makes incredibly popular math videos - but his views on math education may surprise you.
3blue1brown on KZfaq - / @3blue1brown
Grant's 'Hope Diamond' Eye - / 793632149656272896 )
The actual Hope Diamond - en.wikipedia.org/wiki/Hope_Di...
With thanks to...
MSRI - www.msri.org
Meyer Sound - meyersound.com/
Podcast by Brady Haran - www.bradyharanblog.com

Пікірлер: 261
@numberphile2
@numberphile2 5 жыл бұрын
We've popped it here, but it's a legit podcast... Podcast webpage: www.numberphile.com/podcast/ iTunes: itunes.apple.com/gb/podcast/the-numberphile-podcast/id1441474794 Overcast: overcast.fm/itunes1441474794/the-numberphile-podcast RSS: www.numberphile.com/podcast?format=rss
@GijsvanDam
@GijsvanDam 5 жыл бұрын
It's not on Stitcher, though. Any plans of releasing it there? The podcast is great content and a great addition to the Numberphile universe.
@drewdurant3835
@drewdurant3835 4 жыл бұрын
Numberphile2 OMG!! I had no idea you guys had a podcast!!! I am so excited and just downloaded several to get through my work day!! I am one of those special people that smile about a clever solution to a quadratic equation.
@naota3k
@naota3k 5 жыл бұрын
GRONT SONDERSON
@eltyo340
@eltyo340 5 жыл бұрын
sant granderson?
@unfetteredparacosmian
@unfetteredparacosmian 5 жыл бұрын
*pronounces "Grant Sanderson" in French accent*
@HauntaskhanHYPNOSIS
@HauntaskhanHYPNOSIS 5 жыл бұрын
Grunt Sundersun
@andymcl92
@andymcl92 5 жыл бұрын
Subtitles (I presume): "So do you want me to call you Grant Sanderson or Grant Sanderson, or Grant Sanderson, or Grant Sanderson?" "Well my British relatives call me Grant Sanderson but my American ones called me Grant Sanderson, obviously." "So not Grant Sanderson then? Okay, well I'll try and call you Grant Sanderson but I might forget and call you Grant Sanderson!"
@romanski5811
@romanski5811 5 жыл бұрын
Darude Sandstorm
@isaactfa
@isaactfa 5 жыл бұрын
The greatest cross-over event in history.
@drewgauthier1521
@drewgauthier1521 5 жыл бұрын
Isaac The Fallen Apple this is the most ambitious crossover in ~~gaming~~ maths history
@joryjones6808
@joryjones6808 5 жыл бұрын
Isaac The Fallen Apple is probably a better crossover than endgame.
@nicogutholz9399
@nicogutholz9399 5 жыл бұрын
Numberphile and 3Blue1Brown? One hour long? Awesome.
@aspden8809
@aspden8809 5 жыл бұрын
Was thinking that exact same thing. Cannot wait to relax and listen to this.
@XanderGouws
@XanderGouws 5 жыл бұрын
"When you're forced to articulate things, it clarifies thoughts" Love that quote
@drewman428
@drewman428 5 жыл бұрын
I'm a math curious software engineer and have always found it fascinating how much I learn from teaching or explaining to others. Sometimes it takes that articulation to work out a problem you are trying to solve. en.wikipedia.org/wiki/Rubber_duck_debugging
@gawys28
@gawys28 2 жыл бұрын
Same
@ayudan24688
@ayudan24688 2 жыл бұрын
@@drewman428 just about to comment the same, im in structural engineering
@Michelinman420
@Michelinman420 5 жыл бұрын
Grant is a happy go lucky version of Grey
@purplechimkin3404
@purplechimkin3404 5 жыл бұрын
He's the complete opposite version in every possible way is what I gained from the podcast 😅
@jacobschmidt
@jacobschmidt 5 жыл бұрын
@@purplechimkin3404 but their voices
@NoriMori1992
@NoriMori1992 5 жыл бұрын
Yes!
@SK-my5is
@SK-my5is 5 жыл бұрын
If Grant wrote a textbook, I'd certainly buy it immediately...
@larryd9577
@larryd9577 3 жыл бұрын
Watch his videos and take notes?
@dasaggropop1244
@dasaggropop1244 5 жыл бұрын
yay, the two guys who did more for my education than school.
@dulli41
@dulli41 5 жыл бұрын
i love this comment=)
@SathvickSatish
@SathvickSatish 4 жыл бұрын
Max Aggropop how did numberphile help you? I mean they do some cool math videos, but not related to school at all
@masterjack8544
@masterjack8544 4 жыл бұрын
We all must be agreed that khan academy has learned us more but these two guys have talked more about the art aspect of mathematics
@torin1006
@torin1006 5 жыл бұрын
*TOP 10 GREATEST CROSSOVERS*
@VorpalGun
@VorpalGun 5 жыл бұрын
That animation in this video is almost hypnotic
@chadrknight
@chadrknight 5 жыл бұрын
3 blue to every 1 brown 🤙
@erichjunghans9002
@erichjunghans9002 4 жыл бұрын
@@chadrknight is* hypnotic
@StreuB1
@StreuB1 5 жыл бұрын
My private calculus tutor, Jesse, told me about 3blue1brown about a year ago at this point. I am still thankful to this day that Jesse saw the burning interest in maths I had, beyond my horrific struggles, and wanted to encourage it further by influencing me to watch Grants work. It was life changing for me. While I am still struggling at calculus; it will likely take me 4 years to get through the calculus sequence + DiffEq when it takes most people 2-2.5 years. Grants videos, and some others, helped me to see what's beyond the knowing and see the understanding which is what made me double down and not quit.....I'm over 40 BTW and sticking with this has been the biggest soul search in my life so far. People like this, who make this content, really help more than they will likely ever realize. Thank you Grant and Brady
@wildreams
@wildreams 5 жыл бұрын
Thanks for sharing, your passion is infectious.
@joshp3446
@joshp3446 4 жыл бұрын
Calculus and Diff EQ are genuinely difficult classes, especially in terms of applications. I know how to do calculus and Diff EQ, but I couldn't set up a problem to save my life, I'm 25 and a struggling college student
@steliostoulis1875
@steliostoulis1875 5 жыл бұрын
A surprise to be sure but a welcome one.
@AaronHollander314
@AaronHollander314 5 жыл бұрын
“You're much more influenced by the people you spend your time with than you are by pre-established passions.” ~ Grant Sandrson I tell my kids, want to see your future, look at your friends.
@beanbag_VEVO
@beanbag_VEVO 5 жыл бұрын
34:44 thought this was a hello internet episode for a second, sounded like cgpgrey there
@devinmurray4984
@devinmurray4984 5 жыл бұрын
I think the first 3b1b video I saw was "What does it feel like to invent mathematics." I was in my 3rd or 4th year in a mathematics PhD program at the time and was just starting to write my first results that lead to my dissertation. I've really adored Grants videos and have been watching them since. I make sure to tell my students to watch at least one of his videos every semester. As for your predilection for mathematics not being up for research, eh, I doubt it. Research is not particularly more than understanding already known things. Novel research is what happens when you find answers to your questions, and you also happen to be familiar enough with the literature to know the problem was open before you found the answer. If it's in any way nice to hear Grant, I, a young but professional research mathematician, find mathematical value in your videos. I'm still really trying absorb your Fourier analysis videos. I still think of the Fourier series in terms of topological groups and homomorphisms, and I've still not been able to distill it down to explain it to someone without a familiarity with group theory and measure theory (So I don't really understand it yet). Keep up the good work.
@markC-888
@markC-888 5 жыл бұрын
Though I very much wanted to learn more about the person behind 3blue1brown, this interview surpassed all expectations. It was phenomenally interesting. Kudos!
@sairshaikh709
@sairshaikh709 5 жыл бұрын
Check out Ben, Ben and Blue. Its 3Blue1Brown's podcast where he chats with two of his friends about Math education.
@TheHumbleSpoon
@TheHumbleSpoon 5 жыл бұрын
I disagree with Grants view that CS should be taught mandatorily in schools and that mathematical subjects such as Calculus should be taught as electives. As was discussed in the video, the quality of math learning resources is fairly dismall as far as textbooks and online resources such as Wikipedia are concerned. CS, on the other hand, has managed to churn out great resources for self teaching programming skills. If someone wants to learn math after secondary education, the barrier to entry is massive because the initial learning curve is fairly steep, whereas someone wanting to teach themselves CS will not only find a wealth of well made materials, but those materials will be made for self study. Because of this, Math needs the helping hand that school will give you whereas CS really doesnt.
@donlansdonlans3363
@donlansdonlans3363 5 жыл бұрын
There are also tons of resources for math
@donlansdonlans3363
@donlansdonlans3363 5 жыл бұрын
I personally think that there are more resources to learn math than cs, there are a lot of resources for learning programming, but beyond that, there are less resources than resources to learn math, yeah, programming is important, but it is just a tool used to implement algorithms, computer science is not about programming, and i think schools that claim to teach cs shouldnt focus so much on programming, or otherwise they shouldnt call their class computer science and directly call it something like programming etc
@VikeingBlade
@VikeingBlade 4 жыл бұрын
School won't give you a helping hand, though, other than making you not have to learn the Pythagorean Theorem because you had to memorize it
@goclbert
@goclbert 4 жыл бұрын
A lot of people in science professions end up having to learn some math later in life and while they may not become experts, online resources certainly help. At least up to the point of multivariable calculus and linear algebra.
@aufdermitte7143
@aufdermitte7143 4 жыл бұрын
Computers are ubiquitous nowadays, undeniably having proficiency with computers is far more important that knowing calculus.
@josemuzval218
@josemuzval218 5 жыл бұрын
That last tips on "how to read a text book" shocked me. I find it very interesting, amazing interview!
@steliostoulis1875
@steliostoulis1875 5 жыл бұрын
This should be on the main channel
@quantumsigmaqed6312
@quantumsigmaqed6312 5 жыл бұрын
And 3b1b as well
@2neutrino
@2neutrino 4 жыл бұрын
@@quantumsigmaqed6312 doesn't fit in with his content, so no
@codahighland
@codahighland 5 жыл бұрын
I appreciate the slower pace. Not because I like it slower myself, but because I have no problems kicking the video up to 1.5x or 2x and following along at the pace that I find comfortable myself, but someone who talks too fast can't be slowed down with any sense of quality. It gives the viewer more control.
@NoriMori1992
@NoriMori1992 5 жыл бұрын
50:00 - 52:49 - That was beautiful, Brady! "There's this _amazing_ thing, and you don't know it, but you _have_ to know it!"
@smoscar
@smoscar 4 жыл бұрын
That taxi driver scenario shows how nice Grant really is. We owe so much to whomever helped him convince himself to go full-time with his channel.
@robinfalk
@robinfalk 5 жыл бұрын
3blue1brown: So I feel like you're saying yeah all the time Numberphile: Yeah.. Wait
@Kram1032
@Kram1032 5 жыл бұрын
that was a very neat interview. Can't wait for the untextbook.
@avi12
@avi12 5 жыл бұрын
Finally, this collaboration happens! Have had been waiting for it!
@benthayermath
@benthayermath 5 жыл бұрын
Brady, You mentioned that your goal in making these videos is just to share cool stuff because great ideas are contagious, not necessarily because you were attempting to inspire people. I think it's worth mentioning at this point that you have inspired us, even if that's not your primary goal. I first discovered your channel in high school (in the U.S.) and I was fascinated by these crazy problems and ideas that I had never heard of in a math class, before I even knew I loved math. I found them absolutely addicting! Now I'm a good way through a math degree, and I think you would want to know that your channel was a contributing factor. Thanks, and keep up the great work, -Ben T. p.s. -- I love the collaborative spirit lately in the world of YT education; it's very exciting! The podcasts have also been great!
@yoavcarmel1245
@yoavcarmel1245 5 жыл бұрын
Marvel: avengers infinity war is the most ambitious crossover ever numberphile: hold my beer
@bigJovialJon
@bigJovialJon 5 жыл бұрын
I *really* love this podcast series! This episode and one with Cliff Stoll were both great.
@MartinPuskin
@MartinPuskin 5 жыл бұрын
Great job with this interview! I had a grin on my face for the whole hour and the 40 minutes of the interview with Hannah Fry before that. These videos somehow manage to both be incredibly wholesome as well as interesting.
@jimmx2
@jimmx2 5 жыл бұрын
These podcasts are bloody brilliant!
@jamesrockybullin5250
@jamesrockybullin5250 5 жыл бұрын
32:55 Wow this guy is an expert interviewer. Steers the conversation right back.
@MK-13337
@MK-13337 5 жыл бұрын
I was always the kid that didn't like math in school but I was good at it nonetheless. In high school I saw the light (so to say) and fell in love with math (only finishing with average grades because school math is boring even if you love real math). Now I'm a mathematician. It's a wonderful subject but before uni/college school does it a disservice.
@tetsi0815
@tetsi0815 5 жыл бұрын
1:00:00 I'm probably not very representative for the majority of people (I studied computer science and am generally interested in math) who turn to Wikipedia to look up a math concept, but I find it interesting that you think the english Wikipedia is horrible at explaining those. As a German native I naturally looked up things in the German version of Wikipedia and generally had to start looking up words from sentence one. Later I found out that the English version of a math related article is in general much easier to understand, less convoluted and has much less jargon than the German one.
@xavierstanton8146
@xavierstanton8146 5 жыл бұрын
Nowadays it's much easier and more trustworthy since scholars look at the articles.
@NoriMori1992
@NoriMori1992 5 жыл бұрын
Wikipedia articles need to be able to explain things in a way that an educated layperson can understand, not just people who have some post-secondary background in the topic, or have already read a bunch of other Wikipedia articles in the same general topic. Most English Wikipedia articles that I've read utterly fail on that front.
@XanderGouws
@XanderGouws 5 жыл бұрын
James Grime next!
@cheesywiz9443
@cheesywiz9443 5 жыл бұрын
YESS PLEASE
@vikaskalsariya9425
@vikaskalsariya9425 5 жыл бұрын
PLEASE!!!A
@yuriiklopovsky
@yuriiklopovsky 5 жыл бұрын
Now you need to get Burkard Polster on!
@gabor6259
@gabor6259 5 жыл бұрын
The battle should continue!
@Artaresto
@Artaresto 5 жыл бұрын
I love Numberphile I love 3b1b This is one of the best things ever Also this gem of a quote: 35:34 "If you're speaking to someone, you WILL output words" Amazing :D
@jan_kulawa
@jan_kulawa 4 жыл бұрын
What a charming introduction to the podcast. I'm already grinning and it hasn't even started.
@sketchyAnalogies
@sketchyAnalogies 5 жыл бұрын
It’s not egotistical to think that way. Your work is not necessarily better than that of others, but it is yours. You built your channel on your personality. Your viewers like your videos because they are made by you. If other people work in them then they are not made by you. Love both of your work. Keep it up. - a high schooler curious in topology, tensors, E&M, and math in general. Thank y’all!
@ChrisHinton42
@ChrisHinton42 5 жыл бұрын
47:18 same here. I was always very quick to understand math, but research seemed like a different beast altogether. No matter, I'm very happy as a graphics programmer.
@alan2here
@alan2here 5 жыл бұрын
You've outdone yourselves with this background :)
@KalikiDoom
@KalikiDoom 5 жыл бұрын
Grant, thank you for giving me that advice. You made my week much better. 53:46
@chronophagocytosis
@chronophagocytosis 5 жыл бұрын
I took a closer look at the eye picture with Inkscape and it turns out, the ratio is pretty close to 1/3. BTW the star/polygon tool is just perfect for this sort of analysis.
@SophiaBZhou
@SophiaBZhou 5 жыл бұрын
Great interview, loved it
@jamcdonald120
@jamcdonald120 2 жыл бұрын
1:01:00 Heather A Moon published a book about Linear Algebra that I found quite readable. It was the only math textbook I could sit down, read, and get a decent understanding of what the topic was. And it uses the same 2 real world problems through out (CRT scanning and Diffusion welding), slowly fleshing out each as you learn techniques to work on them with.
@gaussianvector2093
@gaussianvector2093 2 жыл бұрын
I agree, I found the beauty of math an excelled among state undergrads and community college students. I switched my major, fell back in love with chemistry but it was too late.
@leophoenixmusic
@leophoenixmusic 5 жыл бұрын
In agreement with Brady's point, as a viewer, the thing I really like about Brady's and Grant's videos is the steady pace and long format. If anything I’d rather have longer Numberphile videos! Although I guess that’s what Numberphile 2 content is for :P Also I agree with the idea that Brady and Grant are almost at one with the channels they represent. I just couldn’t imagine what Numberphile would be like without Brady behind the camera. It’s Brady's personality and genuine interest in what he’s making which makes the channel so great.
@Tondadrd
@Tondadrd 5 жыл бұрын
Kurtzgesagt! “Said shortly” “In a nutshell” I had 8 years of German language education. Pronunciation and understandment of that name covers about half of my German skills...
@kingoffire9373
@kingoffire9373 5 жыл бұрын
Awesome, love both channels!
@jeffbyrd6003
@jeffbyrd6003 5 жыл бұрын
Good idea chuckin em on here, I'll switch to the others after these 3 but this is just such a common portal
@tedward191
@tedward191 5 жыл бұрын
Fascinating! Please do a video on how to read math textbooks!
@willmontgomery79
@willmontgomery79 5 жыл бұрын
Just a great idea, I love this Brady
@bernardoabf
@bernardoabf 5 жыл бұрын
I want 20 hours of this, please
@violetasuklevska9074
@violetasuklevska9074 5 жыл бұрын
Two legends
@TapadeepChakraborty
@TapadeepChakraborty 5 жыл бұрын
Thr colab I was waiting for
@uhbayhue
@uhbayhue 4 жыл бұрын
That was one very entertaining and enjoyable hour
@bonesmalin
@bonesmalin 5 жыл бұрын
Early Christmas with this episode!
@ThePharphis
@ThePharphis 4 жыл бұрын
Grant raises a very useful point regarding understanding of statistics (and other things, in general). We really, really place trust in institutions for being honest (probably too much trust) and even when facts are cited accurately, they can be misrepresented (even unintentionally) for a variety of reasons.
@Theraot
@Theraot 5 жыл бұрын
43:30 well, it is 3 blue 1 brown
@robertocastillo1471
@robertocastillo1471 5 жыл бұрын
This makes me really happy
@aurelia8028
@aurelia8028 3 жыл бұрын
Lol I love how his dad would give him a sugar cube for answering correctly, like he was a horse. That's really adorable xD
@finkn
@finkn 5 жыл бұрын
About starting with the questions in a mathematics text book: "Coding the Matrix", by Philip Klein, sort of does that.
@peppybocan
@peppybocan 5 жыл бұрын
I did listen to this podcast... when it came out!
@numberphile2
@numberphile2 5 жыл бұрын
Thank you. I hope you liked it. The plan is to be releasing them here on Numberphile2 in a more contemporaneous way going forward, but didn't want to cause too much confusion at the start and make it appear like it was a video series.
@peppybocan
@peppybocan 5 жыл бұрын
@@numberphile2 yes it was a very pleasant discussion! I was thrilled when you posted photo of Grant on social media and I was holding my breath for Grant's video and brown paper... :D
@Paulo-
@Paulo- 4 жыл бұрын
Grant laughing when Numberphile says that he's maybe inspiring the next generation of mathematicians (41:00), but THAT'S WHAT HE'S ACTUALLY DOING!! This man should get a prize for this, and when in 20 years the one who prooved Riemann's hypothesis will thank him, he will notice it. Maybe is Grant Sanderson really the hope diamond?
@nbme-answers
@nbme-answers 4 жыл бұрын
the way you guys describe your work, so interesting; you're not companies or a Michelangelo workshop, you're writers. the videos are your essays, your voice. the analogy to JK Rowling, very apt 39:20
@raydencreed1524
@raydencreed1524 5 жыл бұрын
59:25 Oh thank god it’s not just me being stupid.
@Moneyisgoodforme
@Moneyisgoodforme 5 жыл бұрын
I look forward to the “untextbook” someday :)
@lucianodebenedictis6014
@lucianodebenedictis6014 5 жыл бұрын
Such crossovers!
@lucasthompson1650
@lucasthompson1650 Жыл бұрын
Love that the ratios in the animation are accurate. =)
@WolfRose11
@WolfRose11 3 жыл бұрын
41:00. 2020: Want to expand what you are doing? Have I got the year for you. 😎
@whzbwkkfu
@whzbwkkfu 5 жыл бұрын
The kaleidoscope effect was blue 3/4 of the time and brown 1/4 of the time, making it 3blue1brown, which is pretty neat.
@SathvickSatish
@SathvickSatish 4 жыл бұрын
30:56 “a curious inspired high schooler” Omg he just described me, and I watch his videos
@grudley
@grudley 5 жыл бұрын
As for the last part, I found wikipedia super useful for me, learning as an undergrad. It sort of sets up this scaffold for me, of different kinds of objects and the connections between objects in kind of a vague way, which makes it much easier to fill in when I actually go and take a course on the subject. It gives me a sense of the landscape at a high level. I think you need to be very comfortable with being in a state of confusion, or knowing that your knowledge of these things is extremely unclear.
@danyaaaa31
@danyaaaa31 4 жыл бұрын
Thanks a lot!
@alurma
@alurma 5 жыл бұрын
You have to dive deep into wikipedia to understand anything from it. But i still read it a whole lot
@evertgarcia-guzman945
@evertgarcia-guzman945 5 жыл бұрын
Ss#sssss
@jamcdonald120
@jamcdonald120 2 жыл бұрын
53:45 when I was in College I took 1 math class each semester while getting a CS major. 1 year before I graduated I realized I was 1 semester of math classes short of a math major. So I got that too
@romanroman8781
@romanroman8781 4 жыл бұрын
Is there anyone here, who could recommend a podcast that is as interesting as this one? :D
@DanielC01000100
@DanielC01000100 4 жыл бұрын
I love Grant's voice
@kevyanuehara
@kevyanuehara 5 жыл бұрын
WE WANT MORE
@telleyout5226
@telleyout5226 5 жыл бұрын
Grey is sounding weird in this HI episode.
@nidhinbenny7975
@nidhinbenny7975 4 жыл бұрын
Its a great point they make about reading wikipedia math articles. Actually I find that online content regarding physics, maths, chemistry can all sound like gibberish until you reach a certain point. For me, once I got to around my last year of undergrad engineering/science was when the articles online really seemed to open up and make sense. Suddenly what used to seem like gibberish was starting to make some sense (especially in maths). So for any student who is reading those things online and wondering if they will ever understand, just a message of hope: hang in there, sometime towards the end of your degree, it will start making sense. This may be little help in doing that assignment that you need done now, but at least at some point you will understand and thats more important than any assignment.
@themathedumacator2611
@themathedumacator2611 5 жыл бұрын
So, are we to take this to mean that you filmed a Numberphile video with Grant, to be released at a later date? On your podcast announcement, it did sound like you were recording the podcasts in addition to the videos.
@RushiScorpin
@RushiScorpin 5 жыл бұрын
Same with my name, Rushikesh, Rishikesh, Hrushikesh Hrishikesh Rshikesh Wholly dependable upon who you are, Maharashtrain, North Indian, South Indian, or Westerner Same here, ask anyone in my school about me, they will say maths student And I studied today computer science...
@theogoix3566
@theogoix3566 5 жыл бұрын
1 hour with 3b1b and numberphile 2? An hour of pleasure.
@azmodanpc
@azmodanpc 3 жыл бұрын
Loved the first bit about the pronounciation.
@AdityakrishnaMr
@AdityakrishnaMr 4 жыл бұрын
Honestly, i would buy ALL the text-books if Grant ever became a writer. I just can't get enough of him...
@nicholasgraham4402
@nicholasgraham4402 5 жыл бұрын
Very much like hello internet, loved it.
@legoblox01
@legoblox01 5 жыл бұрын
What you said about math in school for 4 years, we have to do a minimum of 3 years of math in my school to graduate (though most colleges require 4 years)
@grantstenger6182
@grantstenger6182 4 жыл бұрын
Does anyone know which company Grant interned at? 10:50
@AaronHollander314
@AaronHollander314 5 жыл бұрын
Bloody Brilliant! (Did I use that correctly?)
@leophoenixmusic
@leophoenixmusic 5 жыл бұрын
Grant Sanderson, you MUST write a textbook
@MichaelOnines
@MichaelOnines 5 жыл бұрын
Wow, I didn't lnow Grant was the voice behind the physics and math videos on Kahn Academy, but now that I know I can't "unhear" it. Start looking at the podcast screen looking for the multi-colored figuring.
@HebaruSan
@HebaruSan 5 жыл бұрын
Definitions (and examples) in a text are also essential so the reader can scan back and re-read if they realize later that they didn't understand something. Roger Penrose's _Road to Reality_ illustrates this quite painfully by having almost no definitions or examples; if you get lost, there's no way to catch up, rendering the book mostly unreadable.
@albericponcedeleon2696
@albericponcedeleon2696 5 жыл бұрын
Was that done on purpose or was it some sort of hilarious literary car crash?
@7177YT
@7177YT 5 жыл бұрын
awesome, u both are adorable!
@alexmak3004
@alexmak3004 5 жыл бұрын
It's difficult to realize your works have changed people's life, but I am certainly one of the examples.
@COZYTW
@COZYTW 5 жыл бұрын
Oh my god, Gront Sonderson was at Khan Academy?! I thought his voice sounded familiar! Was he the guy who taught logarithms and second order derivatives?!
@consultant_of_swing2146
@consultant_of_swing2146 5 жыл бұрын
Found it interesting that Brady went with "math" rather than "maths" for this interview. Good journalistic instincts, as always.
@ab8jeh
@ab8jeh 3 жыл бұрын
24:42 that should have come with a warning!
@guywithapplepie
@guywithapplepie 5 жыл бұрын
Gosh I love nothing more than the blue being 3 times as long as the brown.
@rakhuramai
@rakhuramai 3 жыл бұрын
5:00 Kurt's kiss tots 😂
@nakkstar1237
@nakkstar1237 3 жыл бұрын
Please write the textbook!!!
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