Alex Kontorovich: Improving math | 3b1b podcast #1

Alex Kontorovich is a research mathematician at Rutgers University, a distinguished visiting professor at the MoMath Museum, and Editor-in-Chief of Experimental Mathematics, among other things.
The tweet referenced at the end: / 1172715174786228224
Journal of experimental mathematics:
www.tandfonline.com/loi/uexm20
MoMath museum:
momath.org/
Video with Quanta:
• The Riemann Hypothesis...
Where you can find the podcast:
RSS: anchor.fm/s/636b4820/podcast/rss
Spotify: open.spotify.com/show/74ZzyhJ...
Google: www.google.com/podcasts?feed=...

[@moustholmes]

"This is the amazing thing about kids and by kids I mean PHD students they don't know what hard"

[@davidwilkie9551]

I want to call that the SiFi amorphous condensation visualisation ability. (?)

[@apm77]

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.

[@undeniablySomeGuy]

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...

[@DanielTompkinsGuitar]

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.

[@SayakKolay]

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 ?

[@DanielTompkinsGuitar]

@@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.

[@mountassaralimi8884]

Your story is similar to mine and inspirational. I had that first exposure during undergrad software engineering classes.

[@black_jack_meghav]

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.

[@DimartinoS]

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

[@wojteksocha2002]

This channel exists since 2011 and after 10 years you uploaded your first ever video. See you all in the next video in 2031!

[@atahualpaarias1840]

I'm sure it has more videos but they are unlisted or so

[@xXDarQXx]

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.

[@pvic6959]

@@xXDarQXx yup this is probably his "personal" channel

[@Garemir]

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 :)

[@black_jack_meghav]

indeed , i just want to spam a hundred thank yous in the comment section, lol.

[@Anteater23]

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!

[@mathyland4632]

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!

[@playerscience]

There is a theorem called "Abel-Ruffini" theorem, which explains it.

[@mathyland4632]

@@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.

[@spegee5332]

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)

[@mathyland4632]

@@spegee5332 :o dang. Is there a video of that talk somewhere?

[@AFastidiousCuber]

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.

[@rocketboy352]

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.

[@debanjansengupta6606]

are you from CMU?

[@mountassaralimi8884]

Whats lean ?

[@RiccardoPazzi]

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 :)

[@minimalist.6051]

This is great! You making podcasts is the thing I never knew I needed, thank you for creating such awesome content:)

[@mltghr]

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 :)

[@vanshjagyasi-iiitk4111]

I love the way how Grant addresses people as "This Human".

[@mreverbel]

Such a fantastic interview! Thank you for this, and for all the other amazing videos on your channel.

[@LordDarkhope]

As a phd student in math this is EXACTLY the content I was looking for. Ty!

[@yahav897]

So excited for this new, fresh content. Godspeed, Grant.

[@vladinosky]

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.

[@bec_Divyansh]

Thank you so much for this Sir! Would love to know more about such inspiring people from the educational domain

[@katarixy]

Finally a dedicated podcast! Thank you!!!

[@xaviermootoo3872]

This is amazing, probably the highest quality math-centric podcast I've seen so far!

[@soph.m.p4583]

Absolutely fascinating, can’t wait for next week!

[@KyleBroder]

I'm very glad to hear a discussion of computational fluency 🙏

[@black_jack_meghav]

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 .

[@m322_yt]

Thank you, I like this a lot. Looking forward to future episodes. For the ultimate math interview podcast crossover you could have Brady on ;)

[@samirhussain458]

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!

[@mountassaralimi8884]

Inspirational story dude ! Glad you found the passion for Math.

[@chess1011]

Nowadays everything has become so interesting that you can't be focused anymore 😓🙂

[@AnryGuiltar]

So true!

[@mountassaralimi8884]

It can be helpful to have a make a game plan following undergraduate syllabus and choosing textbooks. Check out Math Sorcerer on KZbin.

[@paris_mars]

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.

[@joeybee3718]

I was very happy to see you got Dr. Kontorovich to sit down for a chat. I enjoy listening to him.

[@dhruvpatel4948]

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.

[@agusottaviano9963]

I love your channel! Regards from Argentina 🇦🇷 .

[@santoshbhandari1310]

Congrats on the Copa America

[@olbluelips]

Great show! Ive wanted a nice podcast about maths for so long :)

[@Nylspider]

Woooooooo Grant podcast So excited, nice job on setting this up!

[@gayatrisavarkar8196]

"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!

[@mostlysanetrader]

Asa ahe ka...waah , 😂

[@thecrackfox99]

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

[@smrtfasizmu6161]

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.

[@kilimanjarocruz660]

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.

[@divergentmaths]

Thank you for this excellent podcast promoting maths as an exciting activity.

[@Ma_X64]

Awesome guest! So positive and expressive!

[@NoahTopper]

Hope you do lots of these!

[@akashbanerjee8554]

Thanks Grant for these podcasts.. They are really helpful for PhD student like me..Please Keep on making these kind of videos..

[@samuelabiuvaldezzavala6095]

this conversations are pure gold!

[@GunAinmNoAodann]

Fantastic podcast! Thanks for this.

[@guidoftp]

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 🇧🇷

[@franciscomackenney7664]

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:

[@linguinelabs]

Does his last name relate to contours?

[@GrantSanderson]

Underrated comment

[@green0563]

This was incredibly interesting. Thank you.

[@saifhussain3303]

Amazing! Looking forward to this

[@pavelmaksimov3850]

great talk! thank you!

[@buritosman2897]

Timestamps with conversation topics would be great for future videos

[@noonesperfect]

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.

[@RonVolkovinsky]

Really great first episode! I'd love to see figures like Edward Witten and Sean Carroll on the podcast in the future!

[@NeilDeshpande313]

My life just got better, thanks to you

[@nahblue]

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

[@30IYouTube]

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.

[@aphraxiaojun1145]

some channels that spam videos have over 100% ratio

[@30IYouTube]

@@aphraxiaojun1145 that's a youtube bug

[@yashrawat9409]

@@30IKZbin I mean he is a big creator already

[@ammyvl1]

The fallacy here is that not all subscribers watch all the videos

[@LabibaBinteWali]

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

[@RSLT]

one and only one word : Inspiring!

[@theevilmathematician]

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.

[@BoxCox]

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!

[@ronshvartsman7630]

I have had this question for so long!!

[@flatmodule839]

isn't he Kantorovich? idk if the spelling matters that much

[@BoxCox]

@@flatmodule839 Well, it might matter but the possibility is rather small I would say.

[@deepanshuchoudhary4598]

Yeah he is his son from another dimension.

[@matt.jordan]

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

[@har011]

I'm 628th subscriber. Btw 3blue 1brown is like that channel which will open your mind in different thinking skills.

[@Tifferan3112]

That intro is just stunning!

[@playerscience]

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.

[@FelixGigler]

"... and by kids I mean phd students" got me good! Great podcast!

[@TheNomadXIV]

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.

[@ARS1508]

This is perfect!!

[@nbme-answers]

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.

[@aminb9204]

Not being dumb enough to invite conspiracy theorists to your show is a low bar, lol

[@JohnWasinger]

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.

[@k.utkarsh5548]

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!❤️❤️

[@thedarkknight1865]

I'm maths student and really loved this vid 👍

[@guest_informant]

Re that last question: Veritasium uploaded on Collatz today - it featured Alex extensively.

[@uzairm3816]

yeah

[@Eljay_Kay]

Thanks for the great podcast, Grant! Can you make these episodes available on Spotify as well?

[@GrantSanderson]

open.spotify.com/episode/1Y6OUdMO6oKNbOBpIqULQZ?si=uDVc9-LPQw2yTXC6Not9Bg&dl_branch=1

[@Eljay_Kay]

Thanks for that. Should have checked the description first, I guess 😄

[@keithmahoney89]

@@GrantSanderson Looking forward to listening to this. Would it be possible to add it to Stitcher also?

[@DitDede]

A real pleasure. Thanks!

[@adr1620]

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

[@theevilmathematician]

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.

[@MarcelRobitaille]

Thank you for providing an RSS feed. So many podcasts don't these days

[@gaous]

maybe I not 40 years old yet to understand. But why do you need RSS for?

[@MarcelRobitaille]

​@@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?

[@gaous]

@@MarcelRobitaille Good to know that :)

[@RahulKumar-jo1yq]

999 subscriber Me : clicks subscribe becoming 1000th subscriber That Power is unmatched

[@chess1011]

The satisfaction LOL 😂

[@shanmukeshr1696]

Respect +++++

[@debanjansengupta6606]

Can this video be timestamped with sections like the Steven Strogatz one?

[@berryzhang7263]

kind of off topic but grant’s voice is so deep and raspy and perfect to listen to

[@ritwikpriyadarshi961]

That was very nice!

[@junaid1464]

Thank you :)

[@TimLF]

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 KZbin mashup.

[@terryyoon1856]

Im currently an undergrad studying applied mathematics and wanting to go to math phd, i would love to be in your podcast one day!!

[@mmmondegreen8074]

I would LOVE to learn more about Soviet mathematics, either the history of, Soviet mathematics pedagogy, etc. etc.

[@trivialqed]

Hope its not too late for a podcast with Tai-Danae Bradley, perfect fit for this podcast imo

[@MrKaar9012]

it will be very interesting to see if complex & Fourier analysis can be codified into Lean

[@aslpuppy1026]

What’s the experimental math journal called, and where can I find it? I want to look at it to get a better idea about what experimental mathematics is. Edit: it’s in the description

[@DrEnginerd1]

Are these on Apple podcasts yet? I couldn’t find it on there.

[@mubashir-rehman]

damn the examples are so beautiful in the talk

[@Superpellexl]

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

[@derekdreery]

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.

[@nickdick2]

So it seems that Grant got married! Congratulations!

[@droopy_911]

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😅

[@Asdfgfdmn]

What a thoughtful exchange of ideas, You are a great interviewer (reminds me of Joe Rogan curiosity and line of thinking)

[@r75shell]

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.

[@oliversc9984]

Math Podcast nice!!

[@teinili]

I clicked on this not thinking I would really be interested now I cant stop watching even though I should sleep right now :D

[@johnchessant3012]

48:47 ok this cell tower story is absolutely hilarious hahaha

[@nathanielb3510]

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.

[@Bvic3]

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?

[@yaeldillies]

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.

[@Bvic3]

@@yaeldillies Ok

[@gaous]

I thought someone called me, lol 24:55

[@idomeir9912]

Can u make a video about graph theory It's just a topic I haven't learned deeply and think it would be interesting to learn from someone like you and ur very uniquely way of teaching. I know it's not the chanel u do stuff like that but sense it's a new chanel I think I have more chances of u seeing this comment

[@aryanpatel5524]

Why no new podcast?

[@Zxv975]

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!