Tai-Danae Bradley: Where math meets language | 3b1b Podcast #5

Tai-Danae Bradley does research applying tools from physics to understanding language models, all under the broader umbrella of category theory. She is also the brilliant mind behind the blog
www.math3ma.com/
Try out the episode sponsor: brilliant.org/3b1b
Guide to Tai-Danae's thesis:
• At the Interface of Al...
Contents
0:00 - Intro
0:48 - Ad, Brilliant
2:08 - When did Tai-Danae know she wanted to study math?
13:52 - Why choose math over physics?
25:21 - What is Category Theory?
25:57 - Water Bottle Solo
40:15 - Colorless green ideas sleep furiously
46:54 - Academia vs Industry
52:06 - Blending AI with something
1:07:22 -Thesis Summary
1:27:39 - What should we be doing to ignite the math 'spark'?
Edited by Ralph Crewe
/ isntthatsomething

[@JoelRosenfeld]

It's a shame this series just stopped. I was really liking learning about other mathematicians and mathematics content creators. Will we see more in the future?

[@cogitoergosum2846]

Do one with Tao. It would be phenomenal

[@necaton]

that would be awesome

[@airronlo6818]

👌👌👌

[@Targeted_1ndividual]

It would be hard to lock down an hour and a half with him

[@wave_s6782]

25:55 didn't expect to laugh so hard during a math podcast lmao

[@iamruss74]

I actually had to take a break as I could not concetrate on what the guest was talkin about :)

[@NoriMori1992]

Lol damn, I listened on my podcast app so I totally missed that. Thanks for the timestamp!

[@TheRobation]

Oh man! That part made my lunch break a lot more enjoyable! XD

[@AlphaNumeric123]

Oh man that’s my whole life

[@jacobmohler3677]

One of my favorite things about these podcasts is seeing how the guests normally start off more reserved and how within a matter of minutes Grant has infused so much genuine interest and excitement into the conversation that they both become so engaged in what they’re talking about.

[@camposmarco27]

Another excellent choice of guest! Tai’s videos motivated me so much to continue my journey towards grad school. My only regret was not discovering PBS infinite when it was still ongoing 😔. I wish the best of luck to both of you!

[@burnere633]

I was on the same boat with regard to PBS Infinite -- in fact, when I came across it for the first time the series had just come to an end. The level of the topics covered is astounding for maths covered for a lay audience. While on the one hand I was disappointed that it -- infinite, of all things! -- had to come to an end, I'm still glad that we at least have access to the existing material.

[@williamcahoon5522]

@@burnere633 ☺️pp

[@chilljlt]

This was contagiously fun. Kept grinning through the entire episode.

[@HussainMahammadHabib]

Mee too

[@jamesjan381]

i know right :)

[@satyamraj5570]

That's same with me.

[@maymkn]

Oh, how I wish the podcast series hadn't stopped. Make them even if just one in a while.

[@pmcate2]

Glad to hear from someone else who was late starter in math. Although, depressingly, I am even more late than her. She discovered math halfway through her undergraduate studies while for me, it was during my graduate studies.

[@akinaguda]

My goodness, I love the way she talks 😅

[@DukeBG]

I know about Tai-Danae from the videos she did on PBS youtube sereies (Infinite Series), everyone should really watch those, they are amazing. Still feels like a shame that they stopped. Enjoyed listening to the interview!

[@LucasDimoveo]

I thought that my slow, line by line, sentence by sentence, way of understanding math meant that something was wrong with me. It is inspiring to hear that Dr. Bradley's learning style is just as "slow" as mine. Really cool stuff.

[@yennefer559]

me too! super refreshing to hear

[@linguamathematica2582]

15:11 "If I want to understand what's really going on, I need to understand mathematics ... I need to know or be fluent in the language that they use and that language is math" Well said! This idea recently motivated me to start this channel. (also, I miss PBS Infinite Series)

[@acinom714]

loved this episode!!! i’m very excited to binge your blog :) it looks like a nice complement for me trying to learn some category theory as a complete beginner!

[@ethanpike8209]

I just realized some of what makes your podcast so great! I felt as if I was eavesdropping on Grant and Tai-Danae’s conversation over lunch. Your questions and answers flow naturally and I can tell your listening and trying to make connections whilst satisfying your curiosity. It’s humanizing relatable and motivating. Thank you.

[@aaronebsen4057]

I love this interview. She makes grad school seams so fun. Also think some sections could use some basic visual aids.

[@citolero]

You don't get visual aids in a podcast. Despite being on KZbin, this is meant for listening to, not watching. You can find it on other podcast apps.

[@abrahanpinedo]

Totally right, even on Spotify you can post video podcast

[@DoomKaiserGliders]

@@citolero plenty of podcasts do visual aids, usually if they're posted to youtube.

[@hatimmuhammed7747]

I always enjoy your podcasts, keep going Grant

[@CurryIsNasty]

Please bring these back! I love these interviews!

[@DJmates]

SO MUCH good energy coming out of her !! A real passionate! Amazing discovery! Thanks Grant!

[@74dorset]

Absolutely love these podcasts. I don't know if you have stopped doing them indefinitely but I loved them.

[@procedupixel213]

"So that's how it works. But WHY does it work?" - I can so relate to that. Exactly my journey to math.

[@akivaprivate595]

I did not know her before the interview. I looked at her blog and it's great

[@cheyneanderson4875]

Tai did a great job of communicating the intuition for Category Theory in this video. I've been trying to get into it for a while, but have been struggling, and this helped it click :D

[@cambridgebreaths3581]

The power of just getting started. Brilliant, thank you.

[@smtsjhr]

Its so sweet getting to listen to other mathematicians talk about maths in this way. Tai-Danae Bradley is especially down-to-earth in talking about their experiences here and i think thats so wonderful : )

[@mahadlodhi]

Grant's getting more and more buffed in every successive upload. Thank you soo much grant for doing these

[@yovangrbovic536]

Clicked immediately. To me TDB is the biggest badass ever

[@mohammadal-ayoubi9786]

Thank you for uploading this on Spotify! I had eye problems for multiple times in the past year and i kept listening to this on spotify when my eyes hurt and couldn't see. Tai is amazing btw .

[@vishnupriyab1878]

Her excitement is so contagious! I am thankful for watching this particular conversation. Thanks a lot! She is the inspiration for all those who are struggling with their understanding. Her journey could let you understand the meaning of understanding.

[@karenliu529]

I was the opposite, when I was younger, I absolutely loved all the geometry proofs, especially 3D geometry. I conceptualized algebra through geometry, but at the end of high school, I remember one of my favorite teachers told me that geometry just has no future, everything is algebra when you are up in higher dimensions. I remember I was so sad.... Never quite found my passion for math for a long time until maybe when I learned a little group theory. But eventually I just kept remembering how he said geometry had no future. Now I work in an adjacent field of math but thinking back... That teacher was just such a kill joy lol

[@yennefer559]

fuck. that sucks... so much of an impact what teachers say to young people, and even the way they teach. It's depressing when they don't know how much of an impact it is. I had a similar situation with a teacher who thought I wouldn't be suited to maths despite my interest, because I was better at languages. they're both heavy on pattern recognition so idk wtf she meant. I slowly stopped engaging in maths outside of school until I had no interest in it any more.

[@adamdhalla1270]

She is SO amazing. This interview is fantastically inspiring

[@sankiago]

i completely loved it, thank you for bringing such as inspiring content

[@hysenndregjoni853]

I just have to mention that these podcasts, and the bright people invited, always manage to put a smile in my face. Their commitment to math being an accessible and exploratory pursuit first and foremost is very inspiring.

[@bernardofitzpatrick5403]

I found Bartosz Milewski ‘s utube lectures on catogory theory amazing. Excellent convo - so motivating. What a nice person she is. Going to sub to Math3ma.

[@mathaha2922]

I hadn't heard of Dr. Bradley before, but I listened intently from begin to end and enjoyed every minute. At some point, she mentioned different "learning types". I can highly recommend Veritasium's video on this subject. Thanks for this podcast! Keep them coming, please!

[@veggiet2009]

I miss Infinite Series! And I've missed her Cheery voice and abstract concepts!

[@JoelRiggs]

Oh yeah! That’s where I have seen her! What an amazing teacher - both of them!

[@kategory]

Tai-Danae Bradley, you are so motivating and inspiring! Thanks Grant for giving her the space here.

[@tinyr101]

Ooh, it’s awesome to hear that she did her PhD at the GC because I just started my biochem PhD program there! it’s such a great graduate system because you have access to ALL the universities associated with CUNY (if anyone is interested in graduate studies, I would highly recommend!)

[@JoelRosenfeld]

These are great videos. Your interviews really help me appreciate these other mathematicians and what they do. They also help me feel less alone, where it’s nice to see other faculty members and researchers take many of the same perspectives that I do. I also like how you step out of the way of the speaker. You very clearly have ideas and opinions about what the speaker is talking about, but you hold off sharing to give them the spotlight.

[@Huntracony]

It's kinda crazy by the way that the one-on-one math-focused interview podcast genre has competition.

[@Nick-kb2jc]

I feel we are slowly making progress in making Mathematics less "scary"

[@SRRS2]

What other math interview podcast do you mean?

[@Huntracony]

@@SRRS2 The Numberphile Podcast

[@TheViolaBuddy]

Also check out The Joy of X, by Steven Strogatz - which was mentioned on his 3b1b podcast episode two episodes ago.

[@silversky216]

you mean injective interviews right?

[@black_jack_meghav]

Hi Grant ! Big fan! I Highly respect , value and love your work. Truly an inspiration, your channel.

[@severoon]

Wonderful interview, Grant! Tai is supremely relatable and her early experiences with math mirror that of a lot of students now. This podcast should be cut into a highlight reel aimed at kids who feel like she did, and who think they can never do what she's doing now. Very enlightening. 1:33:30: "If math is just about thinking thoughts, I have a brain, and I can think thoughts."

[@ThinklikeTesla]

One of the best things to ever happen to me was when my mentor handed 14-year-old me the book Calculus Made Easy by Silvanus P. Thompson. The books starts off with a thesis about how the "normal" way of teaching calc seems complicated and difficult, but the subject is actually straightforward. Or at least something not to be intimidated by. TDB is the modern equivalent of this. What a time to be alive!

[@elysium8404]

you should do more of these they are so good.

[@Hz-kw3iy]

I’m soooooo thankful for this podcast! What an amazing treasure chest!

[@UsamaThakurr]

I just remembered your podcast with Sal and thought I should check it out as it was waiting on the watch later queue too long and you uploaded coincidence

[@vatitopatitopotitopolitopo4918]

Grant I love your podcasts man I hope this keeps going on for a long time EDIT: damn I jinxed it

[@tcaDNAp]

yay, Tai-Danae! After watching the thesis video, thinking about it, and now listening to this... I feel like I almost understand it! :P It's a tantalizing feeling. Consider me lured to category theory

[@tcaDNAp]

wait, there's an interview with Mithuna? 👀 Discovery journalism really does capture the vibe of my favorite channels :D

[@LiamHaleMcCarty]

1:15:10 that lightbulb animation!! 💡👏😅 Grant your attention to detail is legendary

[@shivanshgupta4448]

Just love these discussions :)

[@TechGalaxy292]

Loved this interview. Very interesting.

[@orchidejczyk]

nice interview! i've checked thesis : D so glad to see pictures done by hand :) i did same in my own thesis on statistical physics of suspensions :D also interested in ml so i think ill read the whole thesis :) thanks for inspiration!

[@terrencecooke3216]

Inspiring! I was just reminded of my destiny: math is at the core of it! Thank you from the bottom of my heart!

[@alvaroangelgarciasanchez1735]

I don't know why KZbin recommended this channel or how I started to watch this interview, but I just can say that it was great

[@a13ph0]

finally a video with Category Theory 😍

[@JoelRosenfeld]

There are applications of category theory within control theory. My engineering colleagues have asked me to look into it, but thus far I haven’t seen enough to say much about it. Mostly it looks like a sort of new dictionary, but I’m sure there is more to it. Plenty to do with operator theory there, so I’ll stick to that for now.

[@evilotis01]

aw it's good to see her again. always thought she got a pretty rough deal w the way Infinite Series was cancelled.

[@metanick1837]

Great analysis

[@mahrard]

Talking about J.Terilla’s enthusiasm reminded me of classes by D.Yetter. I can still hear him yell from excitement! So much fun.

[@leonardocastro3654]

Good!! spectacular interview, very entertaining. It helped me understand mathematics as something more everyday and simple, from the point of view of an expert. The things you can do with linear algebra, from the simplest to the most complex such as quantum mechanics. I was losing confidence with what I am studying now, little by little I am regaining it. Greetings from Argentina.

[@kamrupexpress]

Optimization is one of the most useful and fascinating branch of mathematics but is downplayed in the math world. I will be grateful if you can do a podcast with some great mind in optimization.

[@cartooncito764]

Love this

[@Josecannoli1209]

Please keep making these

[@nerdatmath]

Wow, I'm definitely reading that thesis now!

[@orchidejczyk]

also this idea of ideas learning by writing is super important and i think most of students want to deny it while it is for many of them rly important to do.

[@HussainMahammadHabib]

As a math ug I am really infected by her excitement. She is very much passionate

[@martahernandez3905]

so inspiring!!!!

[@MoxlyMakesGames]

Great episode! Would love to see Sean Carroll as a guest of this podcast.

[@Juniper-111]

This is the best

[@imtiazshakil]

He is a magician of mathematics.. 💙💙

[@quantumobject3815]

A mathemagician

[@Linoosethemooss]

I love her.

[@pancakeho0e]

Grant I love the Podcat! But can you please add timestaps?

[@airronlo6818]

more content more episodes!

[@WayTooUnderated]

Need more pods

[@reformierteapologetik5166]

This was awesome! Now, I really want to read your Phd Thesis. I found out it has the same format as Jakob Schwichtenberg's No-Nonsense books which I really enjoy. We really should aviod academic gibberish if we want students to make real progress. @Grant Sanderson Maybe you could interview Jakob Schwichtenberger and his No-Nonsense books on Physics?

[@warrenyazzie9975]

I had to think awhile to remember where I heard her name before and then it hit me, PBS Infinite Series.

[@har011]

3b1b ♥️

[@LetsGetIntoItMedia]

Awwww I miss Infinite Series! That was the start of a years-long bout of basically only watching math videos on KZbin. That was such a good channel - I hope they bring it back someday!

[@hnryjmes]

tai danae-bradley is cool af!!

[@AxiomTutor]

I like her description of category theory a lot! And I will probably use it when I describe it to other new mathematicians. But I also have another take on "why category theory". Category theory kind of gets at WHY certain things are true. In mathematics it's really hard to say what "an explanation is". In mathematics things don't have physical causes, and everything is either true or false. Where's the room for an explanation? In some sense proofs from category theory isolate the most essential and general properties with which some proof can be made. Like take the universal property of subspace topologies: The fact that the subspace and only the subspace topology has this universal property in a sense is the explanation for what the subspace topology is. The philosopher Ted Sider might say that category theory "carves at the joints" of mathematical properties, and in that way, explains what they are and why they are the way they are. When you can say "this property is needed for that result, and even a slight weakening or different property would not allow the inference" is probably as good as you get when it comes to mathematical explanation.

[@NikolajKuntner]

30:05 I suppose the language is a necessity for even posing question in higher homotopy theory or topoi.

[@putrasukardi2286]

Please continue the series. Do one with Brady from Numberphile. Hes not a mathematician but he's a character deep into mathematics in the modern times.

[@matthewglenguir7204]

Pls make more episodes

[@beta3physiaacademy-925]

Could u please explain tensors as you did in linear transformation?

[@DitDede]

I notice reflected video scenes: 3b1b of the other eye :-)

[@grahamjoss4643]

"i dont need to know what an electron is if i know what a linear operator is"

[@quindarius]

I was thinking this same thing in my nlp class. at 32:11

[@debanjansengupta6606]

Do one podcast with Terence Tao, Po Shen Loh. And please timestamp your podcasts.

[@JustJava-un8ix]

brillant !

[@adamharoon6021]

1:31:45 This is what my school's Math Club is currently working towards.

[@JohnGolden]

Re: grading discussion at 1:30. That's why we need things like Standards Based Grading or Mastery Grading, because we should measure and reward understanding.

[@NECRO1369]

I’m wondering if brilliant is just as inaccessible as other math programs like Pearson and con Academy for the blind. I’ve been having to deal with graphics and graphs that I cannot manipulate while trying to get a degree in astronomy. Yes I am blind.

[@shahriarrahman3347]

take love from bangladesh

[@mennaessam2027]

Can you please make a video about galois fields

[@determine14]

Could you make the sound a little bit louder, I'm having a hard time hearing some stuffs on the bus with my earphones :/

[@NoriMori1992]

Hi Grant! Is this podcast over, or just on a hiatus?

[@peterszilvasi752]

I have never expect that I will hear about Natural Language Processing when you are talking about category theory. It would be so nice to understand the state of the art NLP models like Transformers through category theory. 😀 Recently I heard about the Chinese room thought experiment. It goes like this: There is a native Chinese speaker, who understands the language. And there is a room, inside the room there is a man (the computer/AI/NLP models or w/e), who has a book. The book contains ALL answers for ALL questions. If the Chinese speaker put a question inside the room, then he will get back the answer from the man. He thinks that inside the room there is a native Chinese speaker, who understands the language pretty well. So the man inside the room PASSED Turing test. But the man inside the room doesn't know anything about Chinese... just following the book's instruction. In other words, Chinese room thought experiment is arguing that these AI models (weak AI) do not understand the language only "simulating" the ability to understand the language. I am really curios and excited if category theory could give us answer how these AI models work on the fundamental level. 🤔

[@W1ngSMC]

I find it weird CFGs (context free grammars) weren't mentioned.

[@abdullahamir119]

You should interview Lex Fridman

[@ucojq]

On the question of whether an ML model can generate a knowledge of syntax based purely off the statistics of a corpora: I think Chomsky would likely say no, humans only manage to do it because we're endowed with innate knowledge of the universal grammar. I wonder if there will be some nice theoretical results to bolster or refute that claim.

[@abhchow]

Surely if you've interviewed Tai-Danae that means you should interview Kelsey Houston-Edwards next