The World's Best Mathematician (*) - Numberphile

Поділитися
Вставка
  • Опубліковано 13 бер 2017
  • (*) Among current mathematicians, many people regard Professor Terence Tao as the world's finest... Opinions on such things vary, of course.
    Professor Tao kindly fielded some of our questions, including many submitted by Numberphile viewers.
    EXTRA FOOTAGE: • Terry Tao and 'Cheatin... (and more extras to come)
    The Legend of Question Six: • The Legend of Question...
    Professor Tao's blog: terrytao.wordpress.com/
    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
    We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
    NUMBERPHILE
    Website: www.numberphile.com/
    Numberphile on Facebook: / numberphile
    Numberphile tweets: / numberphile
    Subscribe: bit.ly/Numberphile_Sub
    Videos by Brady Haran
    Patreon: / numberphile
    Brady's videos subreddit: / bradyharan
    Brady's latest videos across all channels: www.bradyharanblog.com/
    Sign up for (occasional) emails: eepurl.com/YdjL9
  • Наука та технологія

КОМЕНТАРІ • 6 тис.

  • @ismailb4334
    @ismailb4334 6 років тому +13625

    - What's your weakness?
    - I forget +c while integrating.

    • @mathgeniuszach
      @mathgeniuszach 4 роки тому +181

      Well said.

    • @aichakaouach9589
      @aichakaouach9589 4 роки тому +52

      u dont need it lol

    • @CarSpotter9
      @CarSpotter9 4 роки тому +501

      Aicha Kaouach Oh you do

    • @Lamb666
      @Lamb666 4 роки тому +289

      Aicha Kaouach it really depends. In definite integrals you don't necessarily need it, but it matters if you have initial conditions and such. It starts to matter a lot more in things like boundary conditions and such.

    • @johnmichaelsaba8893
      @johnmichaelsaba8893 4 роки тому +4

      Hahaha

  • @n00boob89
    @n00boob89 4 роки тому +8951

    I already knew this man was on a different level when the first thing he says is “ I remember my first memory at 2 years old” like bruh what

    • @rokanza2293
      @rokanza2293 4 роки тому +431

      N00BOOB well I remember some stuff when I was 3 years old and it's safe to say that I am not beating this guy in a Math challenge of any sort 🤣

    • @sturpdog
      @sturpdog 4 роки тому +98

      I have clear memories from 6 months and another one at 10 months

    • @vinissues4634
      @vinissues4634 4 роки тому +45

      I can remember one day when I was about 3. I admit; I'm intelligent, but far away from Tao 🤣🤣🤣

    • @n00boob89
      @n00boob89 4 роки тому +5

      VinIssues
      The man is a machine!!!

    • @LostArchivist
      @LostArchivist 4 роки тому +61

      There is some correlation with early memories and exceptional intelligence, but it is not 1 to 1 or always correlated.

  • @redcloudyk
    @redcloudyk 2 роки тому +7522

    A genius, yet so modest. Not a shred of arrogance in him. What a legend.

    • @samnyachiro6942
      @samnyachiro6942 2 роки тому +33

      @Arid Sohan I wish he taught me mathematics I would have solved pi.
      Music and maths are interchangeable, one or the other works fine.

    • @siulapwa
      @siulapwa 2 роки тому +114

      The more you know the more you know what you don't know

    • @Kaan-Yaprak
      @Kaan-Yaprak 2 роки тому +46

      its because when you know youre the best you dont need to act like you are the best ie being arrogant

    • @at7388
      @at7388 2 роки тому +14

      @@siulapwa There is still a long way to go for Tao to get to the level of Socrates who once said, "I know that I know nothing."
      And Socrates was the greatest thinker of all time.

    • @thegreaterconundrum
      @thegreaterconundrum 2 роки тому +26

      Maybe it is the case that having an ego just takes up too much space in our thoughts to be compatible with genius. Maybe whats holding a lot of people back from becoming geniuses is their belief that they are smart, and that they should been seen as smart.

  • @idealrunner5043
    @idealrunner5043 3 роки тому +1941

    I have to say I smiled when he said he hung around kids his age and partied at grad school, nice to see he didn’t let himself get TOTALLY absorbed

    • @hugh_mungus0184
      @hugh_mungus0184 2 роки тому +138

      his mother kept him primary school to do English and P.E. Then he would go to high school to do maths and a couple of other subjects. For this exact reason

    • @akanta5746
      @akanta5746 2 роки тому +244

      apparently he almost failed grad school because he wasted all his time playing civilization 2.
      Even the greatest mathematician of all time is a civ addict irl LOL

    • @nicbentulan
      @nicbentulan 2 роки тому +40

      @@akanta5746 OMG I GOOGLED AND IT'S TRUE XD

    • @gaylordtv561
      @gaylordtv561 Рік тому

      @@akanta5746 jfl

    • @talweiss2128
      @talweiss2128 Рік тому +5

      ​@@akanta5746 well he's not the greatest mathematician of all time,
      Definitely a genius and a cool guy though

  • @eliasm2964
    @eliasm2964 5 років тому +18036

    I used my calculator in my math test today to find 7+11

    • @ericme4767
      @ericme4767 5 років тому +929

      LOL, STOP SHOWING OFF!!

    • @saskiafabrik3751
      @saskiafabrik3751 5 років тому +613

      7+11=18 I don't need to use a calculator for that

    • @ericme4767
      @ericme4767 5 років тому +1726

      @@saskiafabrik3751 👌

    • @nabil731
      @nabil731 5 років тому +79

      @Richard Feynman algebra is easy for me lol

    • @d4shm1r
      @d4shm1r 5 років тому +125

      @@nabil731 My brain need a little of your brain.

  • @vuanhminhle6928
    @vuanhminhle6928 5 років тому +8506

    His CPU is faster than his amplifier. He is getting bottlenecked.

    • @johng7602
      @johng7602 4 роки тому +159

      Vu Anh Minh Le he needs ssd and lots of caching

    • @naota3k
      @naota3k 4 роки тому +77

      This comment is fantastic.

    • @johng7602
      @johng7602 4 роки тому +52

      He’s cpu may not be that different, it’s the operating system that...

    • @yisiang9314
      @yisiang9314 4 роки тому +17

      @@johng7602 ik its a joke but it sounds racist. Maybe thats wad intel peeps think of amd peeps

    • @Munggoon
      @Munggoon 4 роки тому +2

      so right lol

  • @JL-ej3xu
    @JL-ej3xu 2 роки тому +2434

    Had an honor class with him 6 yrs ago when I was an undergrad at UCLA. That was the first higher division math course I took. Could tell he is a very nice person in real life, but to comprehend him during lecture is very very hard. He had a completely different flow compared to other professors. Whole lecture is like listening to him proofing a Lemma in his brain, it’s spontaneous and happens very fast. Taking notes is very challenging: wiring down too many details is risky since if you got lost from his thought process, the rest of the lecture is fucked; too little, you cannot recall them after class. I would say 90% of the students who took his class would think he is not as informative as other professors. But the 10% left could potentially progress very fast.

    • @valentinpoggio5389
      @valentinpoggio5389 2 роки тому +416

      extremely smart people usually have the problem that not even people in the top 5% of intelligence will understand them unless they slow down to an uncomfortable speed for their fast brains. That's why, for most of us, a teacher in top 10% who understands what they're teaching is better than a top 0.01% super brilliant teacher

    • @omphiledirero5622
      @omphiledirero5622 2 роки тому +154

      Highly intelligent people struggle to breakdown concept's

    • @ShaheenGhiassy
      @ShaheenGhiassy 2 роки тому +66

      The curse of knowledge

    • @user-rc7cv3on3n
      @user-rc7cv3on3n 2 роки тому +120

      @@omphiledirero5622 they struggle to help others understand concepts in a way as deep as them

    • @wyerscor5599
      @wyerscor5599 Рік тому +157

      I always think of teaching abilities as a trait of character rather than a trait of intelligence. But when both fall into the same person it can be truly fascinating… just saying: Richard Feynman.

  • @l75rd83
    @l75rd83 3 роки тому +2489

    I’m eating jam sandwiches for the rest of my life.

    • @nicbentulan
      @nicbentulan 3 роки тому +14

      if i do the same (at least for breakfast), then i wanna choose the type of jam!!!

    • @pankakotakismegalomavropou3355
      @pankakotakismegalomavropou3355 3 роки тому +46

      I eat placenta of east asians for daily iq boost

    • @kenneth9142
      @kenneth9142 2 роки тому +6

      @@pankakotakismegalomavropou3355 😂

    • @maxwellsequation4887
      @maxwellsequation4887 2 роки тому +3

      @@nicbentulan hey I saw u at several chess channels, you like mathematics too?

    • @nicbentulan
      @nicbentulan 2 роки тому +3

      @@maxwellsequation4887 oh thanks for mentioning. i have a master's in applied maths.

  • @QLY.
    @QLY. 4 роки тому +13892

    His brain 240 FPS, his mouth 60 hz

    • @QLY.
      @QLY. 3 роки тому +301

      @William Darko jokes can't be explained but hz receiver, pfs sender.

    • @solomon2532
      @solomon2532 3 роки тому +442

      @William Darko dude... his joke makes sense

    • @cheetodeleto9432
      @cheetodeleto9432 3 роки тому +243

      William Darko the are. If you have 60hz display you canny show anything above 60fps. Learn how computers and their displays behave.

    • @QLY.
      @QLY. 3 роки тому +99

      @@cheetodeleto9432
      and basically, this is the joke itself!

    • @gamingonly6133
      @gamingonly6133 3 роки тому +7

      @William Darko there are

  • @tarikvaljevac7297
    @tarikvaljevac7297 5 років тому +6606

    -So what did you eat for breakfast?
    -Jam sandwich.
    -You had a sandwich?
    -Yeah.
    -A jam sandwich?
    -Yeah...
    Best. Conversation. Ever.

    • @Ampz55
      @Ampz55 5 років тому +327

      The guy asking questions was taking notes so he can increase his skill in mathematics.
      Jam + Sandwich = Mathskillz

    • @haretztj4682
      @haretztj4682 5 років тому +13

      its like an echo xD

    • @aeo17948
      @aeo17948 4 роки тому +5

      Balkanac ne vjerujem

    • @VoidFame
      @VoidFame 4 роки тому +10

      Honestly made me want a pb and J

    • @orangeiceice12
      @orangeiceice12 4 роки тому +1

      I got that crunchy and raspberry ham right nao

  • @TacSprint
    @TacSprint Рік тому +220

    The stars really aligned for this guy lol
    He had an affinity for math early on, had access to mentors that could help develop his skills, and just went with it.

  • @AuCeVi
    @AuCeVi 3 роки тому +2871

    He looks exactly as what you'd imagine the world's greatest mathematician would look like.

    • @supertester23
      @supertester23 3 роки тому +51

      The best is Grigori Perelman

    • @wiserhuman21
      @wiserhuman21 3 роки тому +130

      Because he is the best one, and that's why he looks exactly like the best one

    • @mr.scientist1469
      @mr.scientist1469 3 роки тому +5

      No gauss or euler is the greatest

    • @TheGrafton12
      @TheGrafton12 2 роки тому +37

      If Stephen Hawking never got ALS, they'd hang out and have a similar look...

    • @dfsfssdfsdfs3084
      @dfsfssdfsdfs3084 2 роки тому +6

      @@supertester23 sources?

  • @stefankaiser960
    @stefankaiser960 4 роки тому +5856

    3 year old Terence to his mom: "Mom, why are the books only about integer-dimensional manifolds?"
    Mom: What?

    • @giobrach
      @giobrach 4 роки тому +727

      Stefan Kaiser
      Mom: “Because topological manifolds cannot have non-integral dimension, unless you modify your notion of manifold”

    • @GamingPotatoHD
      @GamingPotatoHD 4 роки тому +137

      Mom: yes

    • @dibbidydoo4318
      @dibbidydoo4318 4 роки тому +216

      His mom had a math degree.

    • @mayankdeshpande7212
      @mayankdeshpande7212 4 роки тому +94

      @@giobrach that's actually a reasonable explanation.

    • @evalsoftserver
      @evalsoftserver 4 роки тому +16

      Anyone ever heard of the Geometrization and Poincare Conjecture??

  • @Hoodratliker
    @Hoodratliker 4 роки тому +4705

    "Whats your weakness?"
    "Algebra Topology"
    never heard of it.

    • @Richvern1
      @Richvern1 4 роки тому +361

      I think he said, "Algebra and Topology", cuz he continued referencing "those".

    • @user-hr8uj4qw4k
      @user-hr8uj4qw4k 4 роки тому +157

      Cesar M. I think algebraic topology is what he meant to say.

    • @hoangtudaden1304
      @hoangtudaden1304 4 роки тому +97

      Algebraic Topology is using abstract algebra concept/structure to study Topology

    • @OwenDLC
      @OwenDLC 4 роки тому +74

      Algebraic Topology is somewhat difficult. But then again, I only took it in undergrad. This dude is something else.

    • @pengfei5750
      @pengfei5750 4 роки тому +87

      Algebra and topology are two big branches of mathematics. There is no such thing called Algebra topology but there is one field of mathematics called algebraic topology. Just FYI. There are many big branches in mathematics like algebra, geometry, analysis and so on. Sometime we can use technics in one branch to solve problems in another branch and this will lead to a new field of study in mathematics. Normal the technic will become an adjective and appears first in the name. Algebraic topology is the studies of topology in the context of algebra or with tools developed in algebra.

  • @SalesforceUSA
    @SalesforceUSA 3 роки тому +438

    We need more of Terry Tao on Numberphile, I would listen to him for hours.

  • @kcstevens7532
    @kcstevens7532 2 роки тому +164

    Key take-away - how T was raised by parents recognizing and learning how to feed his gift. Thank you for sharing.

  • @apprentice500
    @apprentice500 5 років тому +3232

    Its so nice when a prophesied genius fulfils their potential.

    • @koraptd6085
      @koraptd6085 4 роки тому +88

      there's no such a thing as a prodigy... it's all about his mentality and people that he has met on his path.
      Polgar sisters are one of the best examples of the true nature of so called "talented kids".

    • @BLUDDYknucklez
      @BLUDDYknucklez 4 роки тому +106

      @@koraptd6085 nothing is pure nature nor pure nurture. It is always a mix of both, and this applies to many aspects of our existence.

    • @Johncornwell103
      @Johncornwell103 4 роки тому +4

      @@koraptd6085
      Tell that to William Sidis.

    • @stevo7220
      @stevo7220 4 роки тому +11

      @@koraptd6085 You can do definitely that but the problem is there is deferences in IQ and if one kid gets expert in one field like Judit polgars but if the kid is also gifted he could first get faster there be better and also be successful in multiple areas so yes there are gifted children

    • @ELgeneral-pl9yg
      @ELgeneral-pl9yg 3 роки тому +14

      @@koraptd6085 keep coping

  • @LOTUSELISE340R
    @LOTUSELISE340R 4 роки тому +2937

    Did anyone else's jaw drop at the fact he had a PHD in Mathematics...AT 20!! From Princeton! And was teaching by 24. What a brilliant man.

    • @uduehdjztyfjrdjciv2160
      @uduehdjztyfjrdjciv2160 3 роки тому +120

      ramanujan didnt had university education

    • @ThomasJr
      @ThomasJr 3 роки тому +24

      nEW JERSEY IS really boring. I wonder how he survived Princeton.

    • @negropedro1497
      @negropedro1497 2 роки тому +200

      Gold medal at 12 at IMO is more impressive

    • @mdbahrozbaburali
      @mdbahrozbaburali 2 роки тому +5

      @@uduehdjztyfjrdjciv2160 yeah but he is someone who geniuses study.

    • @huzi37709
      @huzi37709 2 роки тому +64

      This really put it into perspective for me as I will be 20 in a few months and I'll be at the stage to just _apply_ for a PhD when I am 24! That's also not even to say if I will even get onto a PhD, never mind it being somewhere like Princeton. Insane

  • @lovalalova
    @lovalalova Рік тому +53

    I love how he and Zvezdelina both remember how they met over question 6 at the australian olympiad.

    • @OwlRTA
      @OwlRTA Рік тому +8

      He misremembered her nationality though lol

  • @ashutoshkumarjha41
    @ashutoshkumarjha41 3 роки тому +76

    The thing I love about Mr Terry is that he is honest and hardworking that can be understood by this interview. Still trying to know more about you by watching your clips.

  • @rayyoshida7963
    @rayyoshida7963 4 роки тому +3351

    One of the most intelligent person in the world but how humble is he. I really like him

    • @gibsonc22
      @gibsonc22 3 роки тому +8

      Yeah , I really liked how earnestly he consider the questions.

    • @aarohansharma4551
      @aarohansharma4551 3 роки тому +45

      they usually are....bowed down by knowledge

    • @sarthakjain1824
      @sarthakjain1824 3 роки тому +113

      Yes intelligent people are very humble. Thats why tiktokers are egoistic and not humble at all

    • @Ali_7.8.6
      @Ali_7.8.6 3 роки тому +45

      If you're really capable then you don't have to sell yourself to others, you let your work speak for itself

    • @ThomasJr
      @ThomasJr 3 роки тому +4

      ONE OF THE MOST YES, BUT THERE ARE BETTER ONES. FEYNMAN AND JOHN NEUMAN FOR EXAMPLE. TAO DOESN'T WOW! THESE ONES I CITED DO.

  • @Zack-xz1ph
    @Zack-xz1ph 6 років тому +667

    "Then I partied, and so forth"
    Wow those parties must have been off the chain

  • @143vby
    @143vby 3 роки тому +284

    imagine first day of school from summer and your first math class this dude walks in but he is 13 years old ”Hi im your new mathteacher”

  • @Mutual_Information
    @Mutual_Information Рік тому +23

    This is a beautiful video. I come back to it every once and awhile for motivation and it never disappoints.

  • @man9783
    @man9783 4 роки тому +4358

    PhD in maths at 20. I'm here struggling with highschool math.

    • @f3ralp1g3on6
      @f3ralp1g3on6 3 роки тому +184

      This is actually a point where i stoped watching. There are prodigys and suckers. And i am not a prodigy.

    • @xmathematician.5337
      @xmathematician.5337 3 роки тому +24

      But why?My dream is to do PhD in maths.What should I do?can you suggest me something?

    • @jeffreywong7244
      @jeffreywong7244 3 роки тому +159

      x Mathematician. Study more lol

    • @xmathematician.5337
      @xmathematician.5337 3 роки тому +75

      @@jeffreywong7244 right thanks brother.

    • @jeffreywong7244
      @jeffreywong7244 3 роки тому +20

      x Mathematician. Np

  • @shuneughu4244
    @shuneughu4244 3 роки тому +2886

    Math is something I’ve never enjoyed doing but always admire people who can do it well

    • @princeofexcess
      @princeofexcess 2 роки тому +140

      Math is so vast you might not even know about math you would enjoy. I think most people learn to hate math because of what math they are taught and what they are taught math is.
      It also takes some time to enjoy math. Once you're proficient it's hard not to like it.

    • @shuneughu4244
      @shuneughu4244 2 роки тому +10

      @@princeofexcess yea and see that’s so far over my head that I’ll likely never get it down

    • @princeofexcess
      @princeofexcess 2 роки тому +33

      @@shuneughu4244 You dont have to :) But likely you are using some sort of math concepts and enjoying it from time to time you just dont know its math.
      In another life you could like math its all about experiences.

    • @hisajabness6946
      @hisajabness6946 2 роки тому +2

      Surprising I like maths but maths absolutely hates! I have failed miserably in every math test I have ever done. Now as a business even addition and subtraction is hard and I make mistakes and come to realize when I have already conned myself of hard earned money!

    • @philadellphhia
      @philadellphhia 2 роки тому +6

      I enjoy math only when i was in elementary school

  • @erikgordon4783
    @erikgordon4783 3 роки тому +58

    8:58 - what an absolutely solid answer that transcends far more than mathematics.

  • @mordecairugag9873
    @mordecairugag9873 2 роки тому +73

    8:57 Fun fact: That man on the right is Grigori Perelman a math genius who solved one of the world’s most challenging mathematical problems but turned down a prestigious medal and a $1 million prize that went with it.
    I heard a story about him and I could not help but wonder what this man was thinking and how he view things in this world

    • @blockland30
      @blockland30 11 місяців тому +6

      Most geniuses have a little madness. I can’t imagine any normal person turning down that much money

    • @jygb7092
      @jygb7092 10 місяців тому

      Yes because normal people are greedy, selfish degenerates.

    • @trumptookthevaccine1679
      @trumptookthevaccine1679 6 місяців тому

      Why

    • @cg8397
      @cg8397 6 місяців тому +6

      ​@@blockland30Perelman lives in Moscow, that money would make him the target of gold diggers and kidnappers.

    • @barneyronnie
      @barneyronnie 6 місяців тому +2

      He became disillusioned when other mathematicians claimed that they had developed the proof. Mathematics which, for the most part, is pursued by humans who are dedicated to truth and possess integrity has become tainted by societal rot!

  • @John.Smith007
    @John.Smith007 5 років тому +1066

    "My boy is wicked smart".

  • @cloudsleyfalconbridge
    @cloudsleyfalconbridge 5 років тому +3272

    Oh, he would do some real damage if he stepped into a casino.

  • @WalrusRiderCycling
    @WalrusRiderCycling Рік тому

    Hey Terence. Do you remember Basil Chin from your days at Flinders University? He was my brother-in-law and used to talk about you..

  • @Bell1cross
    @Bell1cross 2 роки тому +44

    Love watching Terrence Tao's interviews. The answer most people seem to avoid is how much love they received from their community to succeed. Did teachers take time to teach him the concepts? Were the parent's attending teacher parent conferences? Did he have tutors? Was public school beneficial or did he go to private school? Did he teach his fellow students or just keep to himself? Does he have a photographic memory and if so much of the questions before are irrelevant now. Very important questions that a lot don't think of when looking over geniuses. Even the place he was raised can have a profound effect on how likely he is to succeed.

  • @bhargavbaruah7870
    @bhargavbaruah7870 7 років тому +1967

    Terence Tao .The man who inspired me to give up mathematics

    • @kennethsinger561
      @kennethsinger561 4 роки тому +54

      LOL!

    • @j.dragon651
      @j.dragon651 3 роки тому +18

      I feel that way about some guitar players but I been plugging away for fifty five years at it.

    • @UmarTahir
      @UmarTahir 3 роки тому +15

      Damn, I know how you feel. This video definitely scared me, seeing how easily everything comes to him...

    • @darthmath1071
      @darthmath1071 3 роки тому +107

      I used to think that way. But now I see things differently. Some people are born taller, faster, and maybe some are born "smarter". But unlike in sports, in mathematics, science, literature, etc. you can always bring something new to the table, or be the lucky one who realizes something important. So just do what you like to do and don't compare yourself to others :)

    • @bhargavbaruah7870
      @bhargavbaruah7870 3 роки тому +51

      @@darthmath1071 The comment is 3 years old , and I think like you nowadays.....Life is better.

  • @Mizar88
    @Mizar88 6 років тому +2070

    he's like overclocked

  • @TCUsouthpaw
    @TCUsouthpaw Рік тому +26

    “One of my earliest memories is from when I was two years old” that alone says something lol.

  • @DzzO
    @DzzO 2 роки тому +22

    I love how he talks about speaking things out loud to help him think more precisely.

  • @xiejackson3983
    @xiejackson3983 5 років тому +1598

    " My earliest memory is 2 years old"!!!!!!! I can remember nothing before 10

    • @yreina
      @yreina 5 років тому +347

      I think u got alzheimers bro

    • @Trumpophone7
      @Trumpophone7 5 років тому +30

      I remember a random unimportant time from when I was 1, but my next oldest after that is like when I was 4 lol

    • @MrHumes-nv1zr
      @MrHumes-nv1zr 5 років тому +76

      Lol. My earliest memory was when i was born, it was a sunday, 5 people were in the r r r r room, 3 males 2 females. I believe i weighed 7lbs 6.23oz.

    • @clank2269
      @clank2269 4 роки тому +5

      That's normal...I have many memories when I was 2 and 3

    • @magichands135
      @magichands135 4 роки тому +6

      (and I'm 9)

  • @eva00r
    @eva00r 4 роки тому +1904

    As you may not think, HE is 44. - Math made him a few decades younger.

    • @GerstBladeworks
      @GerstBladeworks 4 роки тому +213

      That's the initial thought I had. He looked like he was 12 when he was a professor at UCLA and now he looks like a college student when he's 44. Crazy.

    • @krono8125
      @krono8125 4 роки тому +2

      I commented on ur 44th like.

    • @EpicGameJunkies
      @EpicGameJunkies 4 роки тому +26

      How can’t you see his age lol :D

    • @MIbra96
      @MIbra96 4 роки тому +110

      @@GerstBladeworks What?? College student? XD
      He definitely looks like around 40.

    • @vinesthemonkey
      @vinesthemonkey 4 роки тому

      Math

  • @thePyiott
    @thePyiott 2 роки тому +4

    The way he describes he couldn't understand the why of mathematics at younger age is very relatable, disregarding the mathematics I think we all experience new dimensions of clarity the older we get.

  • @nicbentulan
    @nicbentulan 3 роки тому +118

    5:06 I've learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel. - maya angelou misattributed
    'I don't remember much about, um, our conversation, except I remember (...) I really felt like I was being treated like an equal.'

  • @mathsmoica
    @mathsmoica 7 років тому +1551

    *Once, during a Lebesgue measure theory, our teacher spoke about Terence Tao. He had stars in the eyes while he was speaking*

    • @idjles
      @idjles 7 років тому +95

      Maths moi ça ! I had the pleasure of sitting next to Terry in class - and was very proud when I solved a problem faster than him!

    • @sadhlife
      @sadhlife 7 років тому +66

      Idjles Erle Really? I genuinely envy you!
      I think i can do a lot better in studies ( I'm called geek everywhere already), but I procrastinate, A LOT. like, full final exam studies on last day. I imagine what I could do if all the laziness went away.

    • @zannettos
      @zannettos 7 років тому +158

      so basically you are just a smart lazy person. Welcome to the club

    • @1nsomnio
      @1nsomnio 7 років тому +73

      It doesn't go away. You train it away

    • @learningsuper6785
      @learningsuper6785 7 років тому +31

      Same when my math professor (phd from MIT) talked about Tao one time when I was in his office.

  • @WalrusRiderCycling
    @WalrusRiderCycling 4 роки тому +3057

    I remember Terry very well at Flinders University in Adelaide. Child genius.

    • @Georgey0121
      @Georgey0121 3 роки тому +176

      I dont think you do to be honest, i checked the roster and you wasnt on the list there, you attended jerkyjunk town univershitty and it showed that you passed the ballistical textbook pumpuff modules

    • @Georgey0121
      @Georgey0121 3 роки тому +82

      @Nicholas Saris you was in detention most of the time.. you wouldnt know

    • @Error-xo9df
      @Error-xo9df 3 роки тому +80

      @@Georgey0121 You were smoking weed outside of school, almost every day!

    • @uniquelykenan
      @uniquelykenan 3 роки тому +16

      @@Georgey0121 I second that!

    • @adamfattal468
      @adamfattal468 3 роки тому +8

      @acidtooth Wait you were dealing my product to a bunch of students?

  • @yetanotherjohn
    @yetanotherjohn Рік тому +3

    I am so happy that he enjoys collaborating, like musicians, who have to admire each other, and be fun company.

  • @Thanos-hp1mw
    @Thanos-hp1mw 2 роки тому +21

    What an intelligent and humble guy. I really wish I had the intelligence he possesses. He's my idol and inspiration now. 💕

  • @JimmyIsTheBest1
    @JimmyIsTheBest1 7 років тому +686

    That guy is so good at maths and so forth

    • @dreamsincosmos
      @dreamsincosmos 6 років тому +39

      a-a-nd y-yea

    • @alephnull5662
      @alephnull5662 5 років тому +16

      And he had a jam sandwich at breakfast.
      Yeah.
      A jam sandwich.
      Yeah.

  • @wieter4094
    @wieter4094 7 років тому +1013

    "my weaknesses are algebra and topology"
    me: oooh maybe i'm better at that than him
    inner me: dude no

    • @DeathBringer769
      @DeathBringer769 5 років тому +238

      His personal standards for "weaknesses" are still way higher than the skill of most of us average mortals, lol...

    • @DraoxxMusic
      @DraoxxMusic 5 років тому +232

      By algebra, I think he means abstract algebra (group theory and stuff), not the high school algebra everyone learns

    • @cgme9535
      @cgme9535 5 років тому +14

      HAHAHAHAHAHAHA! "Dude, no"

    • @danpt2000
      @danpt2000 5 років тому +2

      what is group theory?

    • @6subswith0vids80
      @6subswith0vids80 5 років тому +32

      @@danpt2000 stuff

  • @michaelfavata2720
    @michaelfavata2720 3 роки тому +9

    4:45 the comments on Erdos correspond with the general picture of him i gathered from a wonderful biography of him "The Man Who Only Loved Numbers." He was known to have a huge knowledge of a range of mathematical subjects and part of his brilliance was as a collaborator. He could always find problems that were appropriate for the level of his interlocutor and productive for them to work out together as equals. A great team player.

  • @toshinakae6397
    @toshinakae6397 2 роки тому +93

    "If we all thought the same way, we all had similar philosophy, we would be much poorer" great quote!

  • @raygunn.
    @raygunn. 5 років тому +902

    You know the Riemann hypothesis is hard to solve when the best mathematician doesn’t want to solve it.

    • @magicmulder
      @magicmulder 4 роки тому +58

      Ray Gun He‘s close. RH requires Lambda = 0, so in his words, if RH holds then „just ever so slightly“.

    • @wavemaker2077
      @wavemaker2077 4 роки тому +27

      I have to use google to find out what that is.

    • @dibbidydoo4318
      @dibbidydoo4318 4 роки тому +116

      I think you need to re-watch the video, he says it doesn't work like that. It's not that he doesn't want solve it but that mathematics is built on the works of other mathematicians and that the mathematical tools aren't there yet as far as any mathematician can see and that he'd be the first to go for it when the right tools shows up.

    • @Arkayjiya
      @Arkayjiya 4 роки тому +81

      @Mr. H "He could be the one to invent the tools though"
      You can't always purposefully invent the tools, especially not for such a famous problem. If we knew how to do that, we'd also know how to solve it because in this case inventing the tools would be equivalent to finishing the reasoning. For complex problems like that tools might invented by pure chance when solving something completely unrelated. Then someone suddenly realize that this new thing can be applied to a part of another problem like this one, and solve a bit more of it or if everyone's lucky, the rest of it.

    • @nirorit
      @nirorit 4 роки тому +6

      @Mr. H Are you offended? Grow up.

  • @piseykim3170
    @piseykim3170 4 роки тому +715

    His brain working faster than the speed of his mouth.

    • @yungboomer6467
      @yungboomer6467 3 роки тому +9

      And so forth

    • @carljohn-cena2726
      @carljohn-cena2726 3 роки тому +5

      That's because he is not a rapper

    • @edwardspencer9397
      @edwardspencer9397 2 роки тому +6

      Please don't make fun of him. I see a lot of people here making fun of his speech. As a stutterer myself, I can tell he has a stuttering problem yet he is trying his best not to stutter. It takes immense work to not stutter when you have a stutter. It is like being blind but showing people you are not. I know this from personal experience. Just the fact that he is speaking without any of you noticing his obvious stutter is so awesome.

    • @piseykim3170
      @piseykim3170 2 роки тому +12

      @@edwardspencer9397 I do not know about that fact and I was not making fun of him. I really thought that way. I thought It should be the same way when our handwriting is bad because our brain goes faster. Sorry if what I said sounds offensive. But I am his huge fan! :)

    • @abhirajarora7631
      @abhirajarora7631 2 роки тому +5

      @@edwardspencer9397 No one is making fun of him.

  • @oscarsanchez3201
    @oscarsanchez3201 2 роки тому +2

    Bringing things from field x to y. Is really how mathematical discoveries and solutions are made. All great things are done in teams

  • @crazyrobots845
    @crazyrobots845 2 роки тому +1

    wish I could like this twice, great interview

  • @procrastinateurreformateur5968
    @procrastinateurreformateur5968 6 років тому +278

    Very Humble person.

  • @cianreyes8820
    @cianreyes8820 3 роки тому +784

    This dude remembers things from when he was two years old. Meanwhile I can't remember what I eat for lunch today.

    • @leedlbagginshield8492
      @leedlbagginshield8492 3 роки тому +48

      short term memory and long term memory have to be viewed seperately. I can remember a short scene in my life in which I was a toddler

    • @aarohansharma4551
      @aarohansharma4551 3 роки тому

      thats short term memory.

    • @vincenttan6303
      @vincenttan6303 2 роки тому +5

      Sometimes I can't remember what I said 10 seconds ago... it's especially awkward during interview...

    • @kdjshfihekls
      @kdjshfihekls 2 роки тому +13

      Maybe it was a jam sandwich

    • @dielaughing73
      @dielaughing73 2 роки тому +3

      I forgot to eat lunch today

  • @joebloggsparent3098
    @joebloggsparent3098 Рік тому +1

    Brilliant man and comes across very well, humble and lovely too!

  • @JK-bx1ut
    @JK-bx1ut 2 роки тому +1

    What a nice guy! So humble and warm.

  • @stormysamreen7062
    @stormysamreen7062 5 років тому +724

    Teacher: Why didn't you solve this problem?
    Me: 9:41 to 10:15
    Teacher: That's not an excuse, that's another F.

  • @nickgibson2123
    @nickgibson2123 3 роки тому +177

    His voice satisfyingly resonates in my ears while wearing headphones.

  • @tryAGAIN87
    @tryAGAIN87 2 роки тому

    By any change, does the solution a^2+b^2 = c^2 help with the question 6 problem? It almost seems to me that the only number the solution works for is 1 and if c^2 = ab+1 then that implies the value of ab is 0.

  • @gerryfromthevoid8986
    @gerryfromthevoid8986 3 роки тому +94

    I find him fascinating in the same way you find a great athlete fascinating. It's like, someone who has this brilliance and natural ability at what they do, even though I don't understand how they do it.

  • @barjuandavis
    @barjuandavis 7 років тому +262

    I thought this video is at 1.5x speed...

  • @Freakybananayo
    @Freakybananayo 6 років тому +1638

    Terry Tao more like Terry 2π

    • @xcarnage8632
      @xcarnage8632 5 років тому +3

      haha nice

    • @jade-jm6xw
      @jade-jm6xw 5 років тому +6

      👏👏

    • @tobblesmash6193
      @tobblesmash6193 5 років тому +15

      Freakybananayo more like Terry 2 pi? I don’t get it

    • @yogos360
      @yogos360 5 років тому +70

      @@tobblesmash6193 The greek letter Tau τ = 2π.

    • @tobblesmash6193
      @tobblesmash6193 5 років тому +9

      DeathByFist ahhhh, did not know that, thanks

  • @theradiantdadmaster5463
    @theradiantdadmaster5463 Місяць тому +1

    "My earliest memory is when I was 2 years old."
    That alone explained the gulf between his brain and mine. I barely remember 2 years ago

  • @CuriousCyclist
    @CuriousCyclist 8 місяців тому +5

    After watching this video, I immediately went looking for the video about the legendary Question 6 which stumped Terence. The mathematicians who aced that were great too. Mathematics is fun and the human brain is just incredible.

  • @SamuelHauptmannvanDam
    @SamuelHauptmannvanDam 7 років тому +783

    The most awesome thing is how he has the comfort to call mathematics tricks, like he feels empowered by math rather than fearing it and I truly believe this is what is holding too many of us back. That a lot of people fear math. It's like swimming.
    If you can swim comfortably, it doesn't matter how deep or vast it is as long as it is calm of course. But if you can't swim, even the pool can be freaky and even dangerous.

    • @sadhlife
      @sadhlife 7 років тому +9

      Great explanation bro, +1

    • @234pg786
      @234pg786 7 років тому +5

      Samuel Hauptmann van Dam Why would anyone be afraid of math? Is the underlying fear the fear of being wrong, or having an incomplete understanding of it? Then that's an academic problem. Unfortunately, too many people are discouraged in today's academic spaces.

    • @SamuelHauptmannvanDam
      @SamuelHauptmannvanDam 7 років тому +5

      I think there is a lot to it.
      Honestly, a lot of teachers that isn't math teachers, which is most teachers, just doesn't appreciate math and for those who do, I think math is like truth and doesn't really care if others believe it?
      Like, you could disagree but I am actually using it to get to the moon and you won't get their either without me no matter how much you disagree.
      I think a lot of it is in the lack of appreciation and how to perceive math - like you said, though you had the negative angle on it. I think a lot of people sees math as a barrier to in between themselves and what they want rather than a tool to increase the speed of how you are getting there. Like the mountain or the sea.
      A lot of people have said it before but the why is just as important as the how. Especially when you have to get comfortable with the journey.

    • @SamuelHauptmannvanDam
      @SamuelHauptmannvanDam 7 років тому +1

      Thanks! Makes me all proud. :D

    • @learningsuper6785
      @learningsuper6785 7 років тому +1

      Of course he doesn't fear. People with IQ lower than 120 fear math.

  • @notthemlgtom494
    @notthemlgtom494 4 роки тому +1858

    If you play this video on 0.75X he will sound like a normal person.

    • @commentfreely5443
      @commentfreely5443 4 роки тому +75

      i play everything 1.75x

    • @kdjshfihekls
      @kdjshfihekls 4 роки тому +77

      He sounds like he just smoked a joined and started to relax after I set the speed 0.75

    • @Arkayjiya
      @Arkayjiya 4 роки тому +27

      And if you slow down his brain to 0.75* he'll still be way smarter than a normal person.

    • @IsaacAsimov1992
      @IsaacAsimov1992 4 роки тому +3

      What I can say is that he must have a great singing voice (rich and resonant).

    • @dariacostea3278
      @dariacostea3278 4 роки тому +2

      Lol he speaks so fast that youvdont hear that disorhated sound

  • @ahmedayesh3728
    @ahmedayesh3728 3 роки тому +2

    it is an amazing meeting you asked him all the question that I would ask.

  • @promathgeek7569
    @promathgeek7569 2 роки тому +3

    Terence tao is deeply engulfed in the world of mathematics,his reasoning is out of this world, furthermore, he's humble to the core.😇🤸💯

  • @AThomasKent
    @AThomasKent 7 років тому +605

    Just got into UCLA for math. Looking forward to the chance to take a class from Tao :-)

    • @ananyaupadhya1974
      @ananyaupadhya1974 5 років тому +11

      That's amazing.

    • @ananyaupadhya1974
      @ananyaupadhya1974 5 років тому +9

      How has it been?

    • @gatoradeee
      @gatoradeee 5 років тому +249

      famous last words

    • @heleng3450
      @heleng3450 5 років тому +2

      @Jeff Ahn ahahaha

    • @muhammadputera6593
      @muhammadputera6593 5 років тому +69

      he's a brilliant teacher, really takes the time to explain the material well and is actually available for office hours. I sat in a class he taught once. (Never took a class with him though -- I did physics, not math, and he only taught grad courses.) Cool guy.

  • @MagnusAnand
    @MagnusAnand 7 років тому +195

    "You win some, you lose some"

    • @jamesl9040
      @jamesl9040 5 років тому +9

      OH BOY...he hits a moment there. It's like he's having flashbacks to a warzone🤣🤣🤣

  • @skysetblue9578
    @skysetblue9578 2 місяці тому

    He seems so humble. 👍🏻 thank you Tao

  • @CastawayJadee
    @CastawayJadee 4 місяці тому +5

    " What's 5 + 5? "
    "It's 10"
    "Hold up let me go check my calculator"

  • @sergioacostaesquivel9776
    @sergioacostaesquivel9776 3 роки тому +254

    imagine that just one of your flexes is that Erdös wrote you a letter of recomendation for Princetone ☠️

    • @pjaxy
      @pjaxy 3 роки тому +7

      Super badass

    • @ORNAMENTS_CLO
      @ORNAMENTS_CLO 3 роки тому +2

      Yeah but he's more intelligent than Erdos. His iq is higher than his. So nothing to be impressed about.

    • @mikedelhoo
      @mikedelhoo 2 роки тому +37

      @@ORNAMENTS_CLO "So nothing to be impressed about." That's pretty funny.

    • @dielaughing73
      @dielaughing73 2 роки тому +23

      @@mikedelhoo who cares which has the higher IQ anyway

    • @mikedelhoo
      @mikedelhoo 2 роки тому +6

      @@dielaughing73 "who cares which has the higher IQ anyway" You'll have to ask Kicks.

  • @markhansen4258
    @markhansen4258 5 років тому +407

    He seems like a well adjusted guy. Not the sort of introverted eccentric you might expect.

    • @TheOne-jm6tg
      @TheOne-jm6tg 4 роки тому +90

      That’s clearly a stereotype

    • @themandalorian7352
      @themandalorian7352 4 роки тому +12

      He doesn't feel naturally comfortable answering a lot of questions but I got a feeling like he's humble and he wants to give back even though he may really hate interviews.

    • @edswings6343
      @edswings6343 4 роки тому +1

      @@TheOne-jm6tg Not so much, i've been to a couple meetings where there are a bunch of geeks and they generally turn out to be assholes

    • @animefightlover4686
      @animefightlover4686 2 роки тому +1

      He probably learnt a lot about his weaknesses while growing up rather than being conceited about his strengths.

  • @jamesstanley11
    @jamesstanley11 Рік тому +6

    I remember this small kid walking the corridors of Blackwood high school. I wondered what he was doing there. I later was told it was Terence Tao learning high school level maths. 👍

  • @kekero540
    @kekero540 2 роки тому +1

    This is why great teachers matter, every great man has had a great teacher guiding him while he was young.

  • @ryan2128
    @ryan2128 4 роки тому +362

    2:48 "AND THEN I PARTIED AND SO FORTH".... had a Pepsi

  • @maximilianbur2560
    @maximilianbur2560 4 роки тому +396

    "I was 2 years old"...when I finished calc 3

  • @Tondadrd
    @Tondadrd 3 роки тому +5

    The first mathematician I heard of, who mentioned climbing! Nice!
    9:50 I think Tao was talking about rock climbing, not ice climbing (ice climbing was shown in visualisation).
    We (rock climbers) don't use spiked shoes and ice axes, only rubber boots and our hands. That's why he said: "10 meeters without any *hand* holds".

  • @klaushermann6760
    @klaushermann6760 2 роки тому +1

    Long live to Terence Tao, he can improve our understanding of the Universe by each day he lives.

  • @dvlarry
    @dvlarry 4 роки тому +325

    So often the smartest genius is humble and acts not the most clever.

    • @Oblivion1407
      @Oblivion1407 3 роки тому +21

      You will know more things that you don’t know when you know more

    • @geometricart7851
      @geometricart7851 3 роки тому +19

      @@Oblivion1407 I always eat more things that I don't eat when I eat more.

    • @Yasmin-xt2rj
      @Yasmin-xt2rj 3 роки тому

      geometric art why did I laugh 😹

    • @ThomasJr
      @ThomasJr 3 роки тому

      not all of course, we can't generalize

    • @kasajizo8963
      @kasajizo8963 3 роки тому +5

      Often, but not always. Gauss was very arrogant.

  • @djdunfee6775
    @djdunfee6775 7 років тому +2300

    Releasing a video about a guy named Tao on pi day? I think numberphile is run by taoists lol

    • @djdunfee6775
      @djdunfee6775 7 років тому +65

      ender_scythe You see, it's called a joke. You can tell by the lol at the end

    • @fossilfighters101
      @fossilfighters101 7 років тому

      +

    • @ITR
      @ITR 7 років тому +58

      Taoist... Tauist... Tau...
      τ > π confirmed

    • @msolec2000
      @msolec2000 7 років тому +43

      "τ > π confirmed"
      We already knew that. It's a fact.

    • @ToastyBoy17
      @ToastyBoy17 7 років тому +9

      But why the animosity, Jumbo?

  • @alexjbriiones
    @alexjbriiones Рік тому +14

    I would love for Terence to do some retrospective views on mathematicians like Ramanujan, Gauss, and David Hilbert. Also, how to use AI in mathematics

  • @user-hp1mt9du6t
    @user-hp1mt9du6t 7 місяців тому +4

    Yup, he's great! His solution of 3x+1 works great in physics. Great Man! Sorted out many of my own mathematical concerns just like that. Thank you Mr. Tao! All best from SpaceMan! 👾

  • @fabiocastro9271
    @fabiocastro9271 5 років тому +719

    He looks exactly how I thought the greatest mathematician would look like, for some reason.

    • @kennethhill613
      @kennethhill613 3 роки тому +24

      He probably knows Karate.

    • @stan6477
      @stan6477 3 роки тому +1

      @@kennethhill613 lol

    • @suyashshandilya9891
      @suyashshandilya9891 3 роки тому +40

      That's racist

    • @-BuddyGuy
      @-BuddyGuy 3 роки тому +2

      He's also the world champion at arcade dancing games

    • @liquidbraino
      @liquidbraino 3 роки тому

      If I was making a movie about the best mathematician I'd cast him as the lead actor.

  • @beatrizalmeida2898
    @beatrizalmeida2898 3 роки тому +28

    Love this channel!! so interesting that you brought a more personal interview about such a incredible person!!

  • @ankit619
    @ankit619 2 роки тому

    What's the music at the beginning. I know it's very famous but don't know what it is called?

  • @CH-zj9pf
    @CH-zj9pf Рік тому +1

    thoroughly enjoyed this video.

  • @NingMcKenzie
    @NingMcKenzie 7 років тому +265

    The "Romanian woman" whom he mentions as solving the problem is Zvezdelina Stankova (my professor of two semesters, and is actually Bulgarian).

  • @mrnarason
    @mrnarason 7 років тому +902

    Very interesting look into the math mind of a genius. Anyway when he says he "struggles with algebra", I'm certain he means abstract algebra.

    • @cappucino7908
      @cappucino7908 7 років тому +157

      No one distinguishes "abstract" algebra from the excuse of numeric manipulation people mistakenly call algebra in high school in university.

    • @Quantiad
      @Quantiad 7 років тому +25

      Are you 'certain' though...?

    • @uamdbro
      @uamdbro 7 років тому +58

      Okay, but not everybody watching Numberphile will know the difference.

    • @TIMS3O
      @TIMS3O 7 років тому +50

      Victor P. He said algebraic topology, not abstract algebra. Pretty much any field incorporates abstract algebra in some way so it would be pretty dull to think that he struggles with it. Algebraic topology uses algebraic methods to solve problems in topology, for example constructing the fundamental group for a given topological space or breaking it down in smaller parts with CW-complexes. From my small experience with is that it is a really technical area and is for me pretty hard to grasp.

    • @bronzenrule
      @bronzenrule 7 років тому +124

      +TIMS3O Actually, Tao said "algebra *_and_* topology" are his weakest areas, not "algebraic topology". " *_Those_* have always been my weakest *_areas_* ." 7:40

  • @a3axon
    @a3axon 3 роки тому +38

    I need this man to teach me how to complete the square

  • @sweepingtime
    @sweepingtime 2 роки тому +2

    I like the idea that talking out what's in your head to one's collaborator makes one more organized. To put it simply I must feel like an expert on some topic- in my head, but the moment it comes out it's all a mess and people don't understand what I'm getting at at all.

  • @joaohonradodasilva2003
    @joaohonradodasilva2003 7 років тому +7

    I was waiting for a Terence Tao interview on Numberphile for so long.

  • @dipro001
    @dipro001 7 років тому +6

    It is very satisfying to get such humble opinion from such a capable mathematician. Thank you for making this video.

  • @JayZoop
    @JayZoop 4 місяці тому +3

    Talking to yourself does help to organize thoughts when a lot is going on in your head.

  • @kingraijun9908
    @kingraijun9908 2 роки тому +1

    I was also in an academe before and wrote papers but didn’t make them to being published until I went on joining the corporate world. I stopped writing scientific papers from then on. I remembered from the uni I was in before that for one to level up his stature, he should be the main author of the researches. I’m kinda fascinated when Dr Tao mentioned that he enjoyed joint works/collaboration with co-Mathematicians. And further amazed on the screenshots of the titles shown in the vid - not because of the titles but on him not as main author on majority of them. I’m not generalizing it based on the ones shown in the vid though. Is it still a thing for universities or scientific community to profile a professional base on the authorship of the paper?
    P.S. i’m just curious since I am not part of any scientific communities for almost a decade now.

  • @RicoCordova
    @RicoCordova 4 роки тому +267

    I found this very interesting. He breaks down so many walls to the "magic" behind high level mathematics. It's refreshing to hear him concede that some problems are just beyond our current tool set no matter how "strong" you are. That's quite insightful and gives me pause because I now realize the depths of his genius (and others like him) is due to a strong work ethic. I strive to be so diligent.

    • @UmarTahir
      @UmarTahir 3 роки тому +1

      Well said!

    • @georget8008
      @georget8008 3 роки тому +1

      Godell's incompleteness

    • @hybmnzz2658
      @hybmnzz2658 3 роки тому +9

      @@georget8008 unrelated

    • @fzxfzxfzx
      @fzxfzxfzx Рік тому +4

      It just makes me want to give up

  • @theyugijoker5856
    @theyugijoker5856 5 років тому +4

    One of my Professors in Germany worked for quite some time with Terence Tao together. Such an honor to recieve lectures from such a man! I am so happy!

  • @minsapint8007
    @minsapint8007 2 роки тому

    Wonderful interview.