I taught my 7yo niece to count in binary. I framed it as "I can count to a thousand on my fingers". Then I put stickers on each finger with the numbers 1, 2, 4, 8, ... and showed that you can make any number by adding up the fingers that are touching the table. She enjoyed telling me which fingers I should put on the table to make different numbers.
I love that aside from the hazard of your niece trying to count in binary on her own and learning that other people seem to have Strong aversions to the numbers 4 and 5...
Great conversation! Regarding communication between disciplines: When I was a PhD student in music theory, I taught several undergraduate music theory courses. A senior math professor asked to sit in on my class because he liked music. For the first few weeks, he was catching up on the music jargon and some notational issues. Once he understood that, I was amazed at how insightful he was at looking at music theory problems in different (and often more efficient) ways. Similarly, I don't have any formal training in math beyond basic high school classes. However, I took a PhD seminar on music and computation/math where we analyzed and composed music using various math techniques (some stats, combinatorics, etc.). It took me a while to get used to the jargon and notation of math and computer science, but once I did it felt like a whole world opened up, and now I work as a machine learning scientist for speech and audio understanding. I think there is so much different disciplines can contribute to each other, and I love that both of you and others are calling for better ways of stepping into and understanding jargon that prevents so many people from understanding a topic.
Whoa, this is so great ! Can you please elaborate how exactly you picked up the relevant math and stats/ ML skills ? For instance, how were you able to take classes on Statistics, ML, Linear Algebra in order to prepare for such a change of career ?
@@SayakKolay I was very interested in math and music, so I learned a lot of math independently online. I also had a music professor who also had a math degree. He taught me a lot and pointed me towards several resources. Perhaps the biggest thing is that I learned a ton of math by learning to code. A lot of things became very intuitive when I wrote them in code rather than mathematical notation. Also, with high-level programming libraries like sklearn, keras, and pytorch, you can build some basic ML without knowing all the math. I did that and then learned the math behind all the operations once I had some intuition about how things worked. It turns out that ML doesn't really require very advanced math, and modern coding libraries take care of the details so you can focus on the big picture.
Grant is actually a great interviewer, how he confronts the earlier answers with future points Alex make to formulate the questions is so engaging and fun to watch, had me hooked trough the whole episode, im loving this podcast keep it up
I'm a senior in undergrad. I remember having to learn LaTeX freshman year and proof writing at the same time. But never have I heard of Lean. I took a comp. sci. class that introduced me to Standard ML, my first functional language. After checking Lean out, I'm super excited to try and work with it as I round out my senior year.
I just realised that Alex is constantly smiling through the whole interview, this plus the fascinating discussions : no wonder I was so enthusiastic and happy watching this podcast ! Thank you for this :)
Prof Alex Kontorovich has a channel too where he has lectures on complex analysis, number theory and more. 5 min in the complex analysis lectures, and i was like , wow. He explains why of things , not like just the math but also math history and good stories.
@@playerscience well yeah, but the problem is I don’t yet have the background to understand the proof of that theorem. A 3blue1brown video would at least give an intuitive explanation.
i think that that particular topic was to be given at a talk at the 2021 IMO (International Math Olympiad), and not meant for a specific video. (sorry to burst your bubble)
The classic proof of the Abel-Ruffini theorem uses pages and pages of algebra and is a bit of a tedious slog. The modern proofs, using Galois theory, are much nicer and much more general, but they are also much less accessible. For most people, it takes at least two semesters of intro abstract algebra to work up to a full understanding of that proof. I don't think I've ever seen an accessible presentation of that proof, and I'm skeptical whether it's possible.
I was just binge listening to podcasts on Spotify in search of something interesting and you drop this! Looking forward to listen to this before bed :)
Dear sir Grant , can i just say that i love you? Thanks a lot for your gift to mankind , the channel 3blue1brown and this new podcast too! You are the most inspiring educator i have ever seen .
An engineering student now. My parents are immigrants (who moved to the UK) and we were quite poor and back in their home country of origins they weren't really educated especially after the devastating impacts of war and famine that held back our people for many years and so Mathematics, Science, and Engineering isn't something I found a love for or really understood until the last year of middle school where I started to teach myself Mathematics and Science in an already muddled, rubbish curriculum, that didn't teach help children find what they love and help them understand it, but just taught children for the sake of passing the exam. So, teaching myself and understanding the beauty was the catalyst for everything up to now. I also quite envied children who did have parents and role models that helped them understand the importance of knowledge, learning, and education (especially if it was Maths and Science) but at the same time I am really grateful for my parents for bringing me up and putting food on the table and always caring for me. Only thing one can do is move forward and keep striving for the ability to see the beauty in things!
I absolutely love this guy and his ideals based on this podcast, especially the experimental math that i didnt even know existed. The thing that made me like physics over math is that you can just do experiments if you don't know something and work your way back. To know you can do the same in mathematics is pretty cool.
It's probably his main channel, I mean like the channel that was created with his account. And when he wanted to post videos he created another channel linked to the same account and called it 3blue1brown.
"You need problems to excite you, and then you need the skills that we teach in school whose sole purpose is to make thinking obsolete" - and we are labelled as "intelligent" if we excel in the very skills whose purpose is to make thinking obsolete!
As someone who excels in those skills and so does well academically, this thought often gives me imposter syndrome in the sense that I feel a far worse mathematician than most the people around me at uni, despite generally doing well in exams
Nonsense. These skills are the alphabet of mathematics. Alone, they are not enough to get you good grades in class. It's that most students are so bad at math that they are struggling with the basic stuff that they can't even see the creative aspect of problem solving which is required for the best grades.
Talking about steering mathematicians to do certain things: Alan Turing and the enigma is a good example of a very good pure mathematician being forced to work on a very concrete applied problem, and producing some moderately important outcomes.
My most profound thanks to Grant and Alex for this informative talk. As an aspiring professor, it was great to see that I share a lot of opinions with Alex.
This was an absolutely great conversation and kudos for the podcast initiative Grant, Thank you! If I had access to this kind of content 10 years ago when I was in undergrad, my choice of curriculum would have probably been different.
Find it on all the usual podcast apps: iTunes: podcasts.apple.com/us/podcast/the-3b1b-podcast/id1576951213 Spotify: open.spotify.com/show/74ZzyhJx8NL5OBmv2RWXnB Google Podcasts: www.google.com/podcasts?feed=aHR0cHM6Ly9hbmNob3IuZm0vcy82MzZiNDgyMC9wb2RjYXN0L3Jzcw== RSS: anchor.fm/s/636b4820/podcast/rss
I realised the awesomeness of math in the last year of high school. Before that I had very bad math teachers at school, who literally didn't teach anything, they just made students like me to just memorize the math problems and spit it out in exams. But when I came to college, new teachers came who taught me in the right way! and then my curiosity towards math grew up.
Grant. This is a great yeoman service you re performing. In hinduism, math especially infinities is considered the language of the gods. I especially lked your videos on the infinities and series in general and the intuitive thinking you tend to provoke. THANK YOU.
Also, assuming everyone watching is a unique person, then that means a 84% viewer-subscriber ratio, which is incredibally high for such ratio. Normally I see a 10% ratio of viewer-subscriber ratio.
As a subscriber, I can assure you his subscribers have subscribed for a reason! And I’m always excited for the next episode.. These are genuinely *asset for the education system*. And one of the things that keep me coming back to this channel is how grant is truly trying to make the world a better place. I mean, look at him, *he has like almost everything* yet he performs more projects just for the sake of making math/education better. Honestly speaking, he needs to be in the education ministry. And he deserves so much more. My love and prayers are for him
This is much better than Roe Jogan Edit: I appreciate Rogan interviewing many high-level STEM guests but the conversation depth can only go so far. Would love to see many of the same interviews with Grant as host.
Great first pod, Grant! One small suggestion: it might be useful to put time stamp of all important points/question in the description. As a viewer, sometimes it’s useful to directly jump to interesting discussion rather than listening to whole thing.
When alex said abaut the soviet system being ahead of the American , I had the same experience when I came to america from italy so its nice too see I wasn't the only one that had it that way
I used to live in India and the math curriculum there is way more ahead and rigorous than in the US. I remember set theory and graph theory were taught in high school.
I am curious, is Alex related in some way to the famous russian mathematician Kantorovich who worked in the field linear programming? His models are taught in universities here in Russia. I am very curious!
Podcast from artist itself is reasonable thing to get ideas and learn from these wise minds. First podcast is lucid, it try to clear the narrows gap between school/college learning and actual field work. It always gets encouragement even anyone can merely used math everyday. Well, good luck for future interactions.
Please keep going with this podcast. It's hard to find good podcasts in technical and scientific areas where the conversations are still accessible and entertaining.
I’ve been to the Mo Math Museum in NYC. I have a photo taken of me sitting on a turning chair with red and yellow lines that form an hour glass shape as you wind around.
I got interested in math when I was very young. For some reason, I loved finding patterns and numbers and geometric shapes and puzzles and logic, and also science, especially physics and basic programming. It's kinda complicated to explain why I like numbers and patterns and doing puzzles; it's just that they're intriguing and beautiful and all... and that's what made me get hooked into math when I was younger.
@@gaous Lmao. I just looked up how old RSS was so I could tell you I'm younger than it, but I'm older by 2 years. In any case, I'm not 40. Why shouldn't I use RSS? For me, it is more convenient. It's open, not dictated by some big company. Why should I need to install a spyware app to listen to podcasts?
It's always fun, exciting and a lot more adventurous to listen to someone who has played at the beach and swam in the ocean when u have just built balls of sand at the river banks n found joy in throwing them into the water!❤️❤️
I love the podcast and am excited for the coming episodes. Would it be possible to add chapters to the video and the audio version? These would be immensely helpful and appreciated :)
I find the discussion on pushing mathematicians towards "important" problems to be very fascinating. I often think about what kind of society we could have if extremely strong problem solvers were not economically incentivized to get people to scroll a newsfeed 0.001% longer, or eke out a 0.001% stronger advantage in the stock market. Of course if that were the case, who gets to be the arbiter of important problems? The NSF?
About an hour in Kontorovich mentions two people who wrote a book where on the five hundredth-about page they prove the theorem (1+1)=2 and attributes one of the authors as Tarski, I believe he's talking about Principia Mathematica by Whitehead and Russell. For completeness I wanted to note this in the comments
Wow finally a math podcast! You could make a channel with cuts of your podcast, will be good cause i can see the clips in the interval of work. Thanks a lot, from 🇧🇷
I saw he video was 1.5 hrs long and I thought to myself "oof that's way too long". I was only going to watch the first 5 min to see what it was about but it was so interesting I ended up watching the whole thing
Hey Grant, very nice podcast! All the episodes so far have been stellar. I'm listening on one of the nice podcasting apps (not you Spotify, not you Apple). I'm just dropping in here to see what your guests look like Poggers
There is so much interesting stuff out there but the signal to noise ratio is low in journals etc so it would be nice have a map of universalities and the top teaching resources, like a Wikipedia stack-exchange UA-cam mashup.
The problem with cell towers at around the 50:00 minute mark reminded me of an engineering video I watched about culverts; there are many ingenious designs to improve flow rate, but often the best and cheapest solution is just to make a slightly bigger culvert.
1:09:12 Alex is thinking of Alfred North Whitehead and Bertrand Russell and their multi-volume opus Principia Mathematica. They had three goals (see Wikipedia for details), but the key one had to do with resolving the paradoxes that (ironically) Russell discovered in set theory. These paradoxes appear due to self-referential constructs (see Russell's Paradox). A more accessible paradox that Russell himself used to illustrate the issue without involving advanced math concepts (just logic) is known as the Barber Paradox ("If a barber shaves all those, and those only, who do not shave themselves, does the barber shave himself?"). Whitehead and Russell do indeed take 300+ pages to prove that 1 + 1 = 2 (an "occasionally useful" proposition, as they called it). To do that they first invent a system for describing any statement, formula, equation, etc. in notational form. The goal being to prove that mathematics, as we know it, is consistent and to resolve the paradoxes. In 1930 and 1931 Gödel proved that no mathematical system can be both consistent and complete (and that our math is consistent, but incomplete). Indeed, he used Whitehead's and Russell's notation in his proofs. (An incomplete system cannot be used to prove all its propositions, rather, there must be at least one true proposition that cannot be proven--an axiom.) How he constructed his argument is fascinating in its own right and worth exploring. "I'm a Strange Loop" details the paradoxes, Whitehead's and Russell's attempt at resolving them, and Gödel's proof in a highly accessible and readable form. But for the impatient who would like to get the half-hour version of things (instead of 400 pages), see Veritasium's ua-cam.com/video/HeQX2HjkcNo/v-deo.html
God that early example about fluency vs abstract thinking was my second year of uni doing vector calculus and complex analysis. Every example of a complex integral I was given just boiled down to the lecturer saying "just use Cauchys theorem here..." to the point where by the end of the class I didn't know how to actually integrate a complex integral. Like, at all. It took years later and rediscovering parameterisation and stuff like that before I could even make sense of a contour integral because I was just bombarded with theory and no rote learning. Vector calculus was the same. Green's theorem this, divergence theorem that. I just wanted to *do* the integrals, god dammit!
can't believe I spent one hour watching this (watching it at 1.5x speed). don't regret it a bit! love you guys (well, i don't mean it that way :P, old guy here, working in a math-related field, graduated in a former communist country too). edit: "the second second tower" - the drama of my life... people are hard to change. Kudos!
One thing about Lean and Coq - how do you proof that there is no mistake in checker itself? Like, for example, Rust programming language were claiming that it is memory safe if you don't use "unsafe" blocks. But then, counter example appeared, without unsafe blocks but leaking memory.
1:05:00 I know nothing of the progress of automated proofs. Are we to the level where we will build a database of all papers with formalised proofs and use those very simply to guide complex demonstrations? Or is it just a basic software with only a standard library of common theorems?
Well I can speak for mathlib in Lean at least. Some areas of mathematics are well into formalization (number theory, category theory...) and others aren't (analysis (it's very advanced, but the low level stuff is hardly usable because everything is so general. We are still lacking specific theories, like real and complex analyses), combinatorics...). A good indicator we keep track of is whether we can give a standard paper to a Lean-trained undergrad and have them formalize it without needing to formalize even more basic theory. We also sometimes formalize IMO problems, but of course the maths involved are pretty limited. But really mathlib is a big monolith of mathematics that everyone expands in a different direction. People push for improvement in diverse areas of maths and if something hasn't been formalized yet it's most likely that nobody has yet been interested in it enough.
As a chessplayer (IM and pretty close to GM at some point in time ) I find pretty normal that chess programs learn more from their own playing than from a human chess database. Humans apply general rules and principles while computers go straight by shear computing power. A computer will always play the best move but humans will generally play the safest move. As Kasparov described Karpov once , he plays " a pretty good move". For a computer there's no point in studying strategy separated from tactics (as humans do) cause there is no any difference on how computer operates.
I once heard a lecture on number theory, it was how some GPS problem was solved with Chinese remainder theorem, it was far beyond my level, I was in calc 1, as a result I really don’t remember it. If you’re looking for an insight of abstract , mostly theoretical seeming mathematics can have practical real applications.
"This is the amazing thing about kids and by kids I mean PHD students they don't know what hard"
I want to call that the SiFi amorphous condensation visualisation ability. (?)
I taught my 7yo niece to count in binary. I framed it as "I can count to a thousand on my fingers". Then I put stickers on each finger with the numbers 1, 2, 4, 8, ... and showed that you can make any number by adding up the fingers that are touching the table. She enjoyed telling me which fingers I should put on the table to make different numbers.
I love that aside from the hazard of your niece trying to count in binary on her own and learning that other people seem to have Strong aversions to the numbers 4 and 5...
Great conversation! Regarding communication between disciplines:
When I was a PhD student in music theory, I taught several undergraduate music theory courses. A senior math professor asked to sit in on my class because he liked music. For the first few weeks, he was catching up on the music jargon and some notational issues. Once he understood that, I was amazed at how insightful he was at looking at music theory problems in different (and often more efficient) ways.
Similarly, I don't have any formal training in math beyond basic high school classes. However, I took a PhD seminar on music and computation/math where we analyzed and composed music using various math techniques (some stats, combinatorics, etc.). It took me a while to get used to the jargon and notation of math and computer science, but once I did it felt like a whole world opened up, and now I work as a machine learning scientist for speech and audio understanding.
I think there is so much different disciplines can contribute to each other, and I love that both of you and others are calling for better ways of stepping into and understanding jargon that prevents so many people from understanding a topic.
Whoa, this is so great !
Can you please elaborate how exactly you picked up the relevant math and stats/ ML skills ? For instance, how were you able to take classes on Statistics, ML, Linear Algebra in order to prepare for such a change of career ?
@@SayakKolay I was very interested in math and music, so I learned a lot of math independently online. I also had a music professor who also had a math degree. He taught me a lot and pointed me towards several resources.
Perhaps the biggest thing is that I learned a ton of math by learning to code. A lot of things became very intuitive when I wrote them in code rather than mathematical notation.
Also, with high-level programming libraries like sklearn, keras, and pytorch, you can build some basic ML without knowing all the math. I did that and then learned the math behind all the operations once I had some intuition about how things worked. It turns out that ML doesn't really require very advanced math, and modern coding libraries take care of the details so you can focus on the big picture.
Your story is similar to mine and inspirational. I had that first exposure during undergrad software engineering classes.
Grant is actually a great interviewer, how he confronts the earlier answers with future points Alex make to formulate the questions is so engaging and fun to watch, had me hooked trough the whole episode, im loving this podcast keep it up
Yes, and also this conversation wanted to be as useless as possible through the whole hour and a half
For my Master’s thesis, I had to look at a couple of his papers. Was quite a shock to see someone I ‘know’ on this channel!
I'm a senior in undergrad. I remember having to learn LaTeX freshman year and proof writing at the same time. But never have I heard of Lean. I took a comp. sci. class that introduced me to Standard ML, my first functional language. After checking Lean out, I'm super excited to try and work with it as I round out my senior year.
are you from CMU?
Whats lean ?
I just realised that Alex is constantly smiling through the whole interview, this plus the fascinating discussions : no wonder I was so enthusiastic and happy watching this podcast ! Thank you for this :)
indeed , i just want to spam a hundred thank yous in the comment section, lol.
Prof Alex Kontorovich has a channel too where he has lectures on complex analysis, number theory and more. 5 min in the complex analysis lectures, and i was like , wow. He explains why of things , not like just the math but also math history and good stories.
As a phd student in math this is EXACTLY the content I was looking for. Ty!
40:16 YESSSS HE’S DOING THE UNSOLVABILITY OF THE QUINTIC!!! I’ve wanted to understand that for so long. I can’t wait for that video!
There is a theorem called "Abel-Ruffini" theorem, which explains it.
@@playerscience well yeah, but the problem is I don’t yet have the background to understand the proof of that theorem. A 3blue1brown video would at least give an intuitive explanation.
i think that that particular topic was to be given at a talk at the 2021 IMO (International Math Olympiad), and not meant for a specific video. (sorry to burst your bubble)
@@spegee5332 :o dang. Is there a video of that talk somewhere?
The classic proof of the Abel-Ruffini theorem uses pages and pages of algebra and is a bit of a tedious slog. The modern proofs, using Galois theory, are much nicer and much more general, but they are also much less accessible. For most people, it takes at least two semesters of intro abstract algebra to work up to a full understanding of that proof. I don't think I've ever seen an accessible presentation of that proof, and I'm skeptical whether it's possible.
3 years after this conversation (late bloomer 😅): lovely to see big smile & inspired eyes speaking what they're passionate about
I was just binge listening to podcasts on Spotify in search of something interesting and you drop this! Looking forward to listen to this before bed :)
Dear sir Grant , can i just say that i love you? Thanks a lot for your gift to mankind , the channel 3blue1brown and this new podcast too! You are the most inspiring educator i have ever seen .
An engineering student now. My parents are immigrants (who moved to the UK) and we were quite poor and back in their home country of origins they weren't really educated especially after the devastating impacts of war and famine that held back our people for many years and so Mathematics, Science, and Engineering isn't something I found a love for or really understood until the last year of middle school where I started to teach myself Mathematics and Science in an already muddled, rubbish curriculum, that didn't teach help children find what they love and help them understand it, but just taught children for the sake of passing the exam. So, teaching myself and understanding the beauty was the catalyst for everything up to now.
I also quite envied children who did have parents and role models that helped them understand the importance of knowledge, learning, and education (especially if it was Maths and Science) but at the same time I am really grateful for my parents for bringing me up and putting food on the table and always caring for me.
Only thing one can do is move forward and keep striving for the ability to see the beauty in things!
Inspirational story dude ! Glad you found the passion for Math.
I was very happy to see you got Dr. Kontorovich to sit down for a chat. I enjoy listening to him.
I love the way how Grant addresses people as "This Human".
I absolutely love this guy and his ideals based on this podcast, especially the experimental math that i didnt even know existed.
The thing that made me like physics over math is that you can just do experiments if you don't know something and work your way back. To know you can do the same in mathematics is pretty cool.
Thank you, I like this a lot. Looking forward to future episodes. For the ultimate math interview podcast crossover you could have Brady on ;)
This channel exists since 2011 and after 10 years you uploaded your first ever video. See you all in the next video in 2031!
I'm sure it has more videos but they are unlisted or so
It's probably his main channel, I mean like the channel that was created with his account. And when he wanted to post videos he created another channel linked to the same account and called it 3blue1brown.
@@xXDarQXx yup this is probably his "personal" channel
I'm very glad to hear a discussion of computational fluency 🙏
Nowadays everything has become so interesting that you can't be focused anymore 😓🙂
So true!
It can be helpful to have a make a game plan following undergraduate syllabus and choosing textbooks. Check out Math Sorcerer on UA-cam.
"You need problems to excite you, and then you need the skills that we teach in school whose sole purpose is to make thinking obsolete" - and we are labelled as "intelligent" if we excel in the very skills whose purpose is to make thinking obsolete!
Asa ahe ka...waah , 😂
As someone who excels in those skills and so does well academically, this thought often gives me imposter syndrome in the sense that I feel a far worse mathematician than most the people around me at uni, despite generally doing well in exams
Nonsense. These skills are the alphabet of mathematics. Alone, they are not enough to get you good grades in class. It's that most students are so bad at math that they are struggling with the basic stuff that they can't even see the creative aspect of problem solving which is required for the best grades.
Thank you so much for this Sir! Would love to know more about such inspiring people from the educational domain
Talking about steering mathematicians to do certain things: Alan Turing and the enigma is a good example of a very good pure mathematician being forced to work on a very concrete applied problem, and producing some moderately important outcomes.
Timestamps with conversation topics would be great for future videos
My most profound thanks to Grant and Alex for this informative talk. As an aspiring professor, it was great to see that I share a lot of opinions with Alex.
I love your channel! Regards from Argentina 🇦🇷 .
Congrats on the Copa America
This is amazing, probably the highest quality math-centric podcast I've seen so far!
This was an absolutely great conversation and kudos for the podcast initiative Grant, Thank you! If I had access to this kind of content 10 years ago when I was in undergrad, my choice of curriculum would have probably been different.
Find it on all the usual podcast apps:
iTunes: podcasts.apple.com/us/podcast/the-3b1b-podcast/id1576951213
Spotify: open.spotify.com/show/74ZzyhJx8NL5OBmv2RWXnB
Google Podcasts: www.google.com/podcasts?feed=aHR0cHM6Ly9hbmNob3IuZm0vcy82MzZiNDgyMC9wb2RjYXN0L3Jzcw==
RSS: anchor.fm/s/636b4820/podcast/rss
New channel! Awesome!
Tip: it looks like your camera Auto White Balance is a bit too aggressive, you may get a better result by locking it in to a single value.
I realised the awesomeness of math in the last year of high school. Before that I had very bad math teachers at school, who literally didn't teach anything, they just made students like me to just memorize the math problems and spit it out in exams.
But when I came to college, new teachers came who taught me in the right way! and then my curiosity towards math grew up.
one and only one word : Inspiring!
Grant. This is a great yeoman service you re performing. In hinduism, math especially infinities is considered the language of the gods. I especially lked your videos on the infinities and series in general and the intuitive thinking you tend to provoke. THANK YOU.
This is great! You making podcasts is the thing I never knew I needed, thank you for creating such awesome content:)
Also, assuming everyone watching is a unique person, then that means a 84% viewer-subscriber ratio, which is incredibally high for such ratio. Normally I see a 10% ratio of viewer-subscriber ratio.
some channels that spam videos have over 100% ratio
@@aphraxiaojun1145 that's a youtube bug
@@30IUA-cam I mean he is a big creator already
The fallacy here is that not all subscribers watch all the videos
As a subscriber, I can assure you his subscribers have subscribed for a reason! And I’m always excited for the next episode..
These are genuinely *asset for the education system*.
And one of the things that keep me coming back to this channel is how grant is truly trying to make the world a better place.
I mean, look at him, *he has like almost everything* yet he performs more projects just for the sake of making math/education better.
Honestly speaking, he needs to be in the education ministry. And he deserves so much more. My love and prayers are for him
This is much better than Roe Jogan
Edit: I appreciate Rogan interviewing many high-level STEM guests but the conversation depth can only go so far. Would love to see many of the same interviews with Grant as host.
Not being dumb enough to invite conspiracy theorists to your show is a low bar, lol
Great first pod, Grant!
One small suggestion: it might be useful to put time stamp of all important points/question in the description. As a viewer, sometimes it’s useful to directly jump to interesting discussion rather than listening to whole thing.
When alex said abaut the soviet system being ahead of the American , I had the same experience when I came to america from italy so its nice too see I wasn't the only one that had it that way
I used to live in India and the math curriculum there is way more ahead and rigorous than in the US. I remember set theory and graph theory were taught in high school.
Re that last question: Veritasium uploaded on Collatz today - it featured Alex extensively.
yeah
My life just got better, thanks to you
Thanks Grant for these podcasts.. They are really helpful for PhD student like me..Please Keep on making these kind of videos..
I am curious, is Alex related in some way to the famous russian mathematician Kantorovich who worked in the field linear programming?
His models are taught in universities here in Russia.
I am very curious!
I have had this question for so long!!
isn't he Kantorovich? idk if the spelling matters that much
@@flatmodule839 Well, it might matter but the possibility is rather small I would say.
Yeah he is his son from another dimension.
Podcast from artist itself is reasonable thing to get ideas and learn from these wise minds. First podcast is lucid, it try to clear the narrows gap between school/college learning and actual field work. It always gets encouragement even anyone can merely used math everyday. Well, good luck for future interactions.
"... and by kids I mean phd students" got me good! Great podcast!
Please keep going with this podcast. It's hard to find good podcasts in technical and scientific areas where the conversations are still accessible and entertaining.
Really great first episode! I'd love to see figures like Edward Witten and Sean Carroll on the podcast in the future!
this conversations are pure gold!
I’ve been to the Mo Math Museum in NYC. I have a photo taken of me sitting on a turning chair with red and yellow lines that form an hour glass shape as you wind around.
kind of off topic but grant’s voice is so deep and raspy and perfect to listen to
I would LOVE to learn more about Soviet mathematics, either the history of, Soviet mathematics pedagogy, etc. etc.
I'm so happy you started this podcast. I don't know if it is a popular opinion, but I'd rather watch the uncut material. Cheers mate c:
I got interested in math when I was very young. For some reason, I loved finding patterns and numbers and geometric shapes and puzzles and logic, and also science, especially physics and basic programming. It's kinda complicated to explain why I like numbers and patterns and doing puzzles; it's just that they're intriguing and beautiful and all... and that's what made me get hooked into math when I was younger.
Thank you for providing an RSS feed. So many podcasts don't these days
maybe I not 40 years old yet to understand. But why do you need RSS for?
@@gaous Lmao. I just looked up how old RSS was so I could tell you I'm younger than it, but I'm older by 2 years. In any case, I'm not 40.
Why shouldn't I use RSS? For me, it is more convenient. It's open, not dictated by some big company. Why should I need to install a spyware app to listen to podcasts?
@@MarcelRobitaille Good to know that :)
Such a fantastic interview! Thank you for this, and for all the other amazing videos on your channel.
Finally a dedicated podcast! Thank you!!!
999 subscriber
Me : clicks subscribe becoming 1000th subscriber
That Power is unmatched
The satisfaction LOL 😂
Respect +++++
So excited for this new, fresh content. Godspeed, Grant.
Awesome guest! So positive and expressive!
Absolutely fascinating, can’t wait for next week!
It's always fun, exciting and a lot more adventurous to listen to someone who has played at the beach and swam in the ocean when u have just built balls of sand at the river banks n found joy in throwing them into the water!❤️❤️
Does his last name relate to contours?
Underrated comment
I love the podcast and am excited for the coming episodes. Would it be possible to add chapters to the video and the audio version? These would be immensely helpful and appreciated :)
I find the discussion on pushing mathematicians towards "important" problems to be very fascinating. I often think about what kind of society we could have if extremely strong problem solvers were not economically incentivized to get people to scroll a newsfeed 0.001% longer, or eke out a 0.001% stronger advantage in the stock market. Of course if that were the case, who gets to be the arbiter of important problems? The NSF?
About an hour in Kontorovich mentions two people who wrote a book where on the five hundredth-about page they prove the theorem (1+1)=2 and attributes one of the authors as Tarski, I believe he's talking about Principia Mathematica by Whitehead and Russell. For completeness I wanted to note this in the comments
And ofc, "by kids I mean phd students" is a gold line
Thank you for this excellent podcast promoting maths as an exciting activity.
Hope its not too late for a podcast with Tai-Danae Bradley, perfect fit for this podcast imo
I'm maths student and really loved this vid 👍
A real pleasure. Thanks!
Both maintain a smile throughout the interview making em even more likeable..maybe I should smile often while i speak and hope ppl like me better😅
Wow finally a math podcast!
You could make a channel with cuts of your podcast, will be good cause i can see the clips in the interval of work. Thanks a lot, from 🇧🇷
I'm 628th subscriber.
Btw 3blue 1brown is like that channel which will open your mind in different thinking skills.
Fantastic podcast! Thanks for this.
SO excited for this podcast finally can’t wait to see where it goes!! I love the long form math discussions so this is literally perfect
Hope you do lots of these!
Great show! Ive wanted a nice podcast about maths for so long :)
great talk! thank you!
I saw he video was 1.5 hrs long and I thought to myself "oof that's way too long". I was only going to watch the first 5 min to see what it was about but it was so interesting I ended up watching the whole thing
it will be very interesting to see if complex & Fourier analysis can be codified into Lean
Hey Grant, very nice podcast! All the episodes so far have been stellar. I'm listening on one of the nice podcasting apps (not you Spotify, not you Apple). I'm just dropping in here to see what your guests look like Poggers
That intro is just stunning!
There is so much interesting stuff out there but the signal to noise ratio is low in journals etc so it would be nice have a map of universalities and the top teaching resources, like a Wikipedia stack-exchange UA-cam mashup.
The problem with cell towers at around the 50:00 minute mark reminded me of an engineering video I watched about culverts; there are many ingenious designs to improve flow rate, but often the best and cheapest solution is just to make a slightly bigger culvert.
FEEDBACK: Provide time-lapse of topics discussed in videos. 😊
This was incredibly interesting. Thank you.
1:09:12 Alex is thinking of Alfred North Whitehead and Bertrand Russell and their multi-volume opus Principia Mathematica. They had three goals (see Wikipedia for details), but the key one had to do with resolving the paradoxes that (ironically) Russell discovered in set theory. These paradoxes appear due to self-referential constructs (see Russell's Paradox). A more accessible paradox that Russell himself used to illustrate the issue without involving advanced math concepts (just logic) is known as the Barber Paradox ("If a barber shaves all those, and those only, who do not shave themselves, does the barber shave himself?").
Whitehead and Russell do indeed take 300+ pages to prove that 1 + 1 = 2 (an "occasionally useful" proposition, as they called it). To do that they first invent a system for describing any statement, formula, equation, etc. in notational form. The goal being to prove that mathematics, as we know it, is consistent and to resolve the paradoxes.
In 1930 and 1931 Gödel proved that no mathematical system can be both consistent and complete (and that our math is consistent, but incomplete). Indeed, he used Whitehead's and Russell's notation in his proofs. (An incomplete system cannot be used to prove all its propositions, rather, there must be at least one true proposition that cannot be proven--an axiom.) How he constructed his argument is fascinating in its own right and worth exploring. "I'm a Strange Loop" details the paradoxes, Whitehead's and Russell's attempt at resolving them, and Gödel's proof in a highly accessible and readable form. But for the impatient who would like to get the half-hour version of things (instead of 400 pages), see Veritasium's ua-cam.com/video/HeQX2HjkcNo/v-deo.html
Amazing! Looking forward to this
God that early example about fluency vs abstract thinking was my second year of uni doing vector calculus and complex analysis. Every example of a complex integral I was given just boiled down to the lecturer saying "just use Cauchys theorem here..." to the point where by the end of the class I didn't know how to actually integrate a complex integral. Like, at all. It took years later and rediscovering parameterisation and stuff like that before I could even make sense of a contour integral because I was just bombarded with theory and no rote learning. Vector calculus was the same. Green's theorem this, divergence theorem that. I just wanted to *do* the integrals, god dammit!
Im currently an undergrad studying applied mathematics and wanting to go to math phd, i would love to be in your podcast one day!!
can't believe I spent one hour watching this (watching it at 1.5x speed). don't regret it a bit! love you guys (well, i don't mean it that way :P, old guy here, working in a math-related field, graduated in a former communist country too). edit: "the second second tower" - the drama of my life... people are hard to change. Kudos!
I thought someone called me, lol 24:55
One thing about Lean and Coq - how do you proof that there is no mistake in checker itself? Like, for example, Rust programming language were claiming that it is memory safe if you don't use "unsafe" blocks. But then, counter example appeared, without unsafe blocks but leaking memory.
What a thoughtful exchange of ideas, You are a great interviewer (reminds me of Joe Rogan curiosity and line of thinking)
1:05:00 I know nothing of the progress of automated proofs. Are we to the level where we will build a database of all papers with formalised proofs and use those very simply to guide complex demonstrations? Or is it just a basic software with only a standard library of common theorems?
Well I can speak for mathlib in Lean at least. Some areas of mathematics are well into formalization (number theory, category theory...) and others aren't (analysis (it's very advanced, but the low level stuff is hardly usable because everything is so general. We are still lacking specific theories, like real and complex analyses), combinatorics...). A good indicator we keep track of is whether we can give a standard paper to a Lean-trained undergrad and have them formalize it without needing to formalize even more basic theory. We also sometimes formalize IMO problems, but of course the maths involved are pretty limited.
But really mathlib is a big monolith of mathematics that everyone expands in a different direction. People push for improvement in diverse areas of maths and if something hasn't been formalized yet it's most likely that nobody has yet been interested in it enough.
@@yaeldillies Ok
Not only math, I am learning speaking skills here.
Woooooooo Grant podcast
So excited, nice job on setting this up!
As a chessplayer (IM and pretty close to GM at some point in time ) I find pretty normal that chess programs learn more from their own playing than from a human chess database. Humans apply general rules and principles while computers go straight by shear computing power. A computer will always play the best move but humans will generally play the safest move. As Kasparov described Karpov once , he plays " a pretty good move". For a computer there's no point in studying strategy separated from tactics (as humans do) cause there is no any difference on how computer operates.
This is perfect!!
I once heard a lecture on number theory, it was how some GPS problem was solved with Chinese remainder theorem, it was far beyond my level, I was in calc 1, as a result I really don’t remember it.
If you’re looking for an insight of abstract , mostly theoretical seeming mathematics can have practical real applications.
damn the examples are so beautiful in the talk
Thanks for the great podcast, Grant! Can you make these episodes available on Spotify as well?
open.spotify.com/episode/1Y6OUdMO6oKNbOBpIqULQZ?si=uDVc9-LPQw2yTXC6Not9Bg&dl_branch=1
Thanks for that. Should have checked the description first, I guess 😄
@@GrantSanderson Looking forward to listening to this. Would it be possible to add it to Stitcher also?