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Grant Sanderson (@3blue1brown) — Past, present, & future of mathematics

Grant Sanderson (@3blue1brown) — Past, present, & future of mathematics

48 segments available

I had a lot of fun chatting with Grant Sanderson (who runs the excellent 3Blue1Brown YouTube channel) about: * Whether advanced math requires AGI * What careers should mathematically talented students pursue * Why Grant plans on doing a stint as a high school teacher * Tips for self teaching * Does Godel’s incompleteness theorem actually matter * Why are good explanations so hard to find? * And much more 𝐄𝐏𝐈𝐒𝐎𝐃𝐄 𝐋𝐈𝐍𝐊𝐒 * Apple Podcasts: https://podcasts.apple.com/us/podcast/grant-sanderson-3blue1brown-past-present-future-of/id1516093381?i=1000631087010 * Spotify: https://open.spotify.com/episode/0u05TKwP8pozY4ojY4e0fH?si=SfRvmI-8R4q-jBPogrpMBw * Transcript: https://www.dwarkeshpatel.com/p/grant-sanderson 3Blue1Brown: https://www.youtube.com/@3blue1brown 𝐓𝐈𝐌𝐄𝐒𝐓𝐀𝐌𝐏𝐒 00:00:00 - Does winning math competitions require AGI? 00:08:24 - Where to allocate mathematical talent? 00:17:34 - Grant’s miracle year 00:26:44 - Prehistoric humans and math 00:33:33 - Why is a lot of math so new? 00:44:44 - Future of education 00:56:28 - Math helped me realize I wasn’t that smart 00:59:25 - Does Godel’s incompleteness theorem matter? 01:05:12 - How Grant makes videos 01:10:13 - Grant’s math exposition competition 01:20:44 - Self teaching

Segments Timeline

1
0:54 - 2:46
1:52 duration378 words

AGI and Math Competitions

Grant Sanderson discusses the implications of artificial general intelligence (AGI) in relation to math competitions like the International Math Olympiad (IMO). He explores the nuances of what AGI means, the continuous nature of intelligence in AI, and how achieving gold in the IMO could signify a significant milestone in AI development. This segment delves into the creativity involved in solving complex math problems and the potential impact of AI on various professions.

"By the time that an AI model can get gold in the  International Math Olympiad, is that just AGI?   Given the amount of creative problem solving  and chain of thought required to do that. To be honest,..."

2
2:46 - 5:01
2:14 duration468 words

The Creativity of Math Problem Solving

In this segment, Grant elaborates on the creativity required in mathematics, comparing it to games like chess and Go. He emphasizes that solving IMO-level problems involves a unique level of abstraction and lateral thinking, which distinguishes it from traditional AI capabilities. Grant reflects on the future of AI in mathematics and how it might evolve to tackle complex problems creatively, while also addressing the limitations that currently exist.

"if it's getting gold in IMO, having seen  some of those problems from your channel,   I'm thinking “Wow, that's really coming  after podcasters and video animators.” I don't know. That feels orthogona..."

3
5:01 - 6:50
1:48 duration343 words

The Distinction Between Math and Other Fields

Grant Sanderson discusses the differences between mathematical problem-solving and other fields, such as chess. He argues that the creativity and abstraction required in mathematics are distinct from the strategies used in games. This segment highlights the unique challenges faced by AI in replicating human-like creativity in mathematics and the implications for future job markets.

"Tell me why I should be less amazed by  it or maybe put it in a different context   but the reason I would be very impressed  is… With chess, obviously this is not all   the chess programs are doing, ..."

4
6:50 - 9:07
2:16 duration455 words

Where Should Mathematicians Go?

In this thought-provoking segment, Grant reflects on the societal roles of mathematicians and where their talents can be best utilized. He questions the traditional paths that many mathematicians take, such as academia and finance, and suggests that there may be untapped potential in other sectors like logistics and manufacturing. Grant emphasizes the importance of inspiring students to think critically about their career choices and the impact they can make.

"I'm surprised you wouldn't be more compelled. I am compelled. Or you just don't think that skill  of — this problem is isomorphic to   this completely different way of thinking  about what's happening..."

5
9:07 - 12:59
3:52 duration770 words

The Value of Diverse Applications of Math

Grant discusses the importance of applying mathematical skills in various fields beyond academia. He shares insights on how mathematicians can contribute to different industries and the potential benefits of interdisciplinary collaboration. This segment encourages a broader perspective on the value of mathematics in society and the need for mathematicians to explore diverse career paths.

"Because I think this thing happens when you fall  in love with math or some sort of technical field,   by default in school, you study that. And when  you're studying that, effectively you're going   ..."

6
12:59 - 15:03
2:03 duration410 words

Critical Thinking in Career Choices

In this segment, Grant emphasizes the importance of critical thinking when it comes to career choices for math students. He encourages young mathematicians to consider their unique skills and how they can apply them to make a meaningful impact in the world. Grant shares anecdotes and examples of individuals who have successfully transitioned from traditional math fields to innovative roles, inspiring others to think outside the box.

"But I don't know. I don't know what  more effectively looks like because   at the end of the day I'm like I'm  a Math YouTuber. I'm not someone who   has a career in logistics or manufacturing or  all..."

7
15:03 - 17:03
1:59 duration414 words

The Future of Mathematical Tools

Grant discusses the evolution of mathematical tools and how they shape our understanding of the world. He reflects on the significance of programming and notation in enhancing mathematical fluency and problem-solving capabilities. This segment explores the potential for future advancements in mathematical tools that could further revolutionize the way we approach and solve problems.

"We were talking about this before the interview  started but we have a much better grasp on   reality based on our mathematical tools.  I'm not talking about anything advanced.   Literally being able ..."

8
17:03 - 19:20
2:17 duration452 words

Miracle Years in Mathematics

In this insightful segment, Grant explores the concept of 'miracle years' in the careers of mathematicians and scientists. He discusses how significant breakthroughs often stem from years of preparation and thought, culminating in a single year of prolific output. Grant reflects on his own experiences and the potential for future mathematicians to experience similar moments of clarity and creativity.

"I think there's something to be said for the fact  that there's still so much more value in paper.   if you and I were going to go into some math  topic right now. Let’s say you ask me something   tha..."

9
19:14 - 20:07
0:52 duration192 words

The Role of Youth in Creativity

This segment discusses the unique advantages of youth in fostering creativity and innovation. Grant suggests that young individuals often have fewer obligations, allowing them to explore ideas freely, which can lead to significant contributions in their fields.

"If I try to reflect on my own history with what  I'm doing now I think I didn't appreciate early   on how much potential energy I had simply from  being a student in college where there's just a   bun..."

10
20:07 - 21:03
0:55 duration202 words

Navigating Success and Creativity

Grant reflects on the challenges that come with success in academia, discussing how obligations can stifle creativity. He shares anecdotes about maintaining focus on scientific pursuits amidst the distractions that success can bring.

"I don't know if this is all also the case  for the people who have had genuine miracle   years where they were like letting  out all of this stuff and then it   takes a decade to build up that  same l..."

11
21:03 - 22:10
1:06 duration228 words

The Origins of 3Blue1Brown

In this segment, Grant recounts the beginnings of his YouTube channel, 3Blue1Brown, and how it started as a personal project during his senior year at Stanford. He discusses the unexpected journey from a programming project to becoming a math educator on YouTube.

"things that eat into their mind share  and time and all of that such that even   if it's just 20 hours a week, that  really interrupts a creative flow. Were you a student when you started the channel?..."

12
22:10 - 23:20
1:10 duration246 words

The Inefficiency of DIY Math Tools

Grant discusses the challenges and inefficiencies of creating custom tools for math visualization. He reflects on the creative freedom that comes with building one's own tools while acknowledging the potential drawbacks of such an approach.

"If the goal was to make Math YouTube videos it  would have been a wild thing to do it by making   [Manim](https://github.com/3b1b/manim)  as the method for it because   it's so strikingly inefficient ..."

13
23:20 - 24:25
1:05 duration222 words

The Value of Ownership in Creativity

This segment highlights the importance of ownership in creative projects. Grant explains how having control over one's tools can enhance creativity and lead to unique contributions in the field of mathematics.

"Then again there's a lot of other people  who make their own tools for math GIFs and   little illustrations and things which  on the one hand feels very inefficient   If people come across a math GIF ..."

14
24:25 - 25:31
1:05 duration251 words

The Low-Stakes Start of 3Blue1Brown

Grant shares insights into the low-stakes nature of starting his YouTube channel, emphasizing how not aiming for immediate success allowed for deeper exploration and authenticity in his content creation.

"This is personally interesting to me because  I also started the podcast in college and it   was just off track of anything I was planning on  doing otherwise. And this is many, many orders   of magni..."

15
25:31 - 26:28
0:57 duration206 words

Niche Content and Audience Engagement

In this segment, Grant discusses the benefits of creating niche content. He argues that focusing on specific topics can lead to more meaningful engagement with audiences and allows creators to produce high-quality material tailored to their viewers.

"ways maybe that's helpful because I see a lot  of people who jump in with the goal of being a   Youtuber. I think it's the most common at desired  job among the youth is to be like a tiktoker or a   Y..."

16
26:28 - 27:01
0:32 duration111 words

The Surprising Absence of Early Numeracy

Grant reflects on the surprising lack of basic arithmetic and numeracy among prehistoric humans. He discusses how this absence challenges modern assumptions about the universality of mathematical concepts.

"The beauty of the internet is that there's  an incentive to do that and I don't know if   this is the case with your podcast when you're  starting out, but not thinking about how can   I make this as ..."

17
27:01 - 28:41
1:40 duration295 words

Cultural Perspectives on Counting

This segment explores how different cultures perceive and utilize numbers. Grant shares examples of tribes with limited numeracy and discusses the implications for understanding human cognition and mathematical intuition.

"doesn't come about naturally in the course of  interacting with the world. Is that surprising? You're right that it's so in our bones that  it's hard to empathize with not having numeracy.   If you th..."

18
28:41 - 29:12
0:30 duration107 words

The Abstract Concept of Numbers

Grant and his host discuss the significance of abstract numerical concepts in daily life. They ponder the importance of understanding numbers beyond their practical applications, considering how abstraction shapes thought processes.

"some senses we've also like lost some numeracy or  lost some intuition in others, where now if you   ask middle school teachers what's a difficult  topic to teacher for students to understand   they'r..."

19
29:12 - 30:34
1:22 duration242 words

Mental Constraints in Mathematics

In this segment, Grant addresses the mental constraints faced by mathematicians. He speculates on the importance of analogies and exposure to diverse fields as key factors in overcoming challenges in mathematical problem-solving.

"Yeah, I have seen the thing from [Joseph   Henrich](https://heb.fas.harvard.edu/people/joseph-henrich)   where there's still existing tribes where  they're in this kind of situation. They   can do num..."

20
30:34 - 31:36
1:02 duration163 words

Collaboration in Mathematics

Grant discusses the collaborative nature of modern mathematics, highlighting how teamwork and communication among mathematicians enhance the field. He reflects on the increasing number of authors in mathematical papers and the importance of conferences for collaboration.

"the obvious stuff like the commerce examples  you mentioned where you go to a restaurant   and you're figuring out what to pay or what to  tip but that seems a very particular example. Do I really use..."

21
31:36 - 32:36
1:00 duration192 words

The Newness of Mathematics

In this segment, Grant explores the relatively recent developments in mathematics, particularly at the high school level. He discusses the historical context of mathematical advancements and the factors contributing to the emergence of new mathematical concepts.

"you've had to disparate fields such that you  could maybe see that a problem-solving approach   that was used here might be useful here.  Sometimes that's literally codified in the   forms of connecti..."

22
32:36 - 33:36
1:00 duration213 words

The Role of Population in Mathematical Development

Grant examines how the growth of population and the economic freedom to pursue academia have influenced the development of mathematics. He discusses the shift towards pure mathematics and the implications for contemporary mathematical research.

"kid and was in this math circles event and someone  was asking this person, "What surprised you about   your job?” The first thing he said was how much  travel was involved. He wasn't expecting that. ..."

23
34:06 - 35:36
1:30 duration287 words

The Evolution of Pure Mathematics

In this segment, Grant explains how the concept of pure mathematics has evolved over time. He highlights that historically, mathematicians often worked alongside other disciplines, and it wasn't until more recently that pure mathematicians emerged. He attributes this shift to population growth and increased economic freedom for academic pursuits.

"I wouldn't have thought of math as being  new in that way, especially at the high   school level. I remember there's always  a sensation that it's frustrating that   all of the things are actually way..."

24
35:36 - 36:57
1:20 duration276 words

The Role of Technology in Mathematical Discovery

Grant discusses how advancements in technology have influenced the development of new mathematical theories. He uses examples like information theory and chaos theory to illustrate how the need for practical applications and computational tools has driven mathematical innovation.

"Maybe it's pretty reasonable that most of it is  much, much more recent. That would be my guess. Some of these things seem actually pretty modern  like information theory. It is less than 100 years   ..."

25
36:57 - 38:00
1:03 duration182 words

The Intersection of Mathematics and Quantum Physics

In this thought-provoking segment, Grant reflects on how mathematical concepts could have been discovered prior to the advent of quantum physics. He emphasizes the importance of asking the right questions and how the right tools can lead to significant breakthroughs in understanding complex phenomena.

"A lot of original concepts in chaos theory came  from basically running simulations or doing things   that required a massive amount of computation  that simply wouldn't be done by hand. Someone   cou..."

26
38:00 - 39:12
1:11 duration239 words

The Importance of Motivating Problems in Mathematics

Grant highlights the necessity of motivating problems in pure mathematics. He argues that textbooks often lack context for why certain axioms are chosen, which can hinder students' understanding and engagement. He emphasizes the need for educators to present mathematics as a tool for solving real-world problems.

"probabilities but we're only allowed  to use unitaries.” They could have   just discovered quantum mechanics  or quantum information from there. The thing about math, especially if you're  talking abo..."

27
39:12 - 40:28
1:15 duration252 words

Knot Theory and Its Unexpected Origins

In this segment, Grant delves into the origins of knot theory, explaining how it emerged from a flawed theory about atomic structures proposed by Lord Kelvin. He discusses how seemingly arbitrary questions can lead to significant mathematical developments and the importance of curiosity in the field.

"Knot theory is something that emerged because  Lord Kelvin had a theory that all of the   elements on the periodic table had structures  which were related to a knot. A knot being if   you have a clos..."

28
40:28 - 41:29
1:00 duration146 words

The Role of Educators in Shaping Mathematical Careers

Grant shares anecdotes about the profound impact educators can have on students' mathematical journeys. He recounts stories of teachers who inspired students to pursue mathematics, illustrating how small gestures can lead to monumental changes in a student's trajectory.

"So really, you want to ask what are the  things that prompt people to ask what   turns out to be a mathematical question given  that the space of what would be mathematical   questions is so unfathoma..."

29
41:29 - 42:43
1:14 duration220 words

The Challenge of Educational Video Games

In this segment, Grant discusses the difficulties of creating educational video games that are both fun and pedagogically effective. He reflects on the success of games like 'The Witness' and how they can evoke the same feelings of problem-solving as mathematics, while also addressing the challenges of game development.

"I don't play enough games so I can't really  speak to it in the way that well-versed game   designers can but one thing to understand is that  games are very hard to make. It takes a lot of   resource..."

30
42:43 - 44:38
1:54 duration371 words

Innovations in Textual Explanations

Grant explores advancements in textual explanations for mathematics, highlighting platforms like Mathigon that offer interactive learning experiences. He argues that while video content has gained popularity, there are significant innovations happening in written educational materials that deserve recognition.

"the fundamental mechanics that become relevant  to much much harder ones such that if you do it   with the right sequence you have the feeling of  epiphany in ways that are very self-satisfying. You c..."

31
44:38 - 46:30
1:52 duration382 words

The Value of In-Person Teaching

In this segment, Grant emphasizes the importance of in-person teaching for educators, arguing that it helps maintain empathy and connection with students. He discusses the balance between online content creation and traditional classroom teaching, advocating for educators to remain engaged with their students.

"in terms of more and more thought put towards  empathy to the learner and things like that. Should the top 0.1% of educators  exclusively be on the internet   because it seems like a waste if you were..."

32
46:30 - 48:00
1:30 duration297 words

Educators as Motivators and Mentors

Grant reflects on the multifaceted role of educators, suggesting they act as motivators and mentors rather than just content deliverers. He discusses the importance of personal connections and tailored guidance in fostering students' interests and potential in mathematics.

"disagree with the idea of taking them out  of their existing circumstances. Maybe   for a year or two so they don't lose that  sharpness but then put them right back in   because it makes them better ..."

33
48:00 - 49:34
1:33 duration322 words

The Ripple Effect of Encouragement

In this poignant segment, Grant shares stories of how a single moment of encouragement from a teacher can profoundly influence a student's life. He illustrates the long-lasting impact educators can have on their students' futures through simple acts of recognition and support.

"Then should we think of educators  more as motivational speakers? As   in the actual job of getting the content  in your head is maybe for the textbooks   or for Youtube but why we have college  class..."

34
49:34 - 53:06
3:32 duration726 words

The Dangers of Negative Feedback

Grant recounts a personal experience from his school days where a substitute teacher's negative comment about his abilities in math could have derailed his confidence. He emphasizes the importance of positive reinforcement in education and how detrimental comments can have lasting effects on students.

"Two examples of this come to mind. One  is this woman who was saying she had this   moment when she got pulled aside by the teacher  and he just said, “Hey, I think you're really   good at math. You s..."

35
52:51 - 54:29
1:37 duration323 words

Online Education vs. Personal Connection

Grant critiques the notion that online education can replace the personal connections formed in traditional classrooms. He argues that while online resources can be valuable, they often lack the nuanced understanding of individual student needs that a teacher provides. This segment emphasizes the importance of interpersonal dynamics in learning and the limitations of online explanations.

"I was in the best possible circumstance  to not let that hit hard because one,   I had the moral high ground of “Hey, I've just  been helping all these people. I understand it   and I've been doing yo..."

36
54:29 - 56:21
1:52 duration377 words

Accidental Discoveries in Mathematics

Grant shares an intriguing anecdote about a mathematician who unknowingly solved two unsolved problems after mistaking them for homework. This story illustrates the serendipitous nature of mathematical discovery and how unexpected opportunities can shape a researcher's career path. It underscores the idea that initial conditions and random encounters can lead to significant breakthroughs.

"I had [Tyler Cowen on the   podcast](https://www.dwarkeshpatel.com/p/tyler-cowen-2)  and he obviously has Marginal Revolution and   these youtube videos where he explains economics  and he had a simil..."

37
56:21 - 57:06
0:45 duration160 words

Understanding the Dunning-Kruger Effect

In this segment, Grant discusses the Dunning-Kruger effect and the importance of recognizing one's own limitations in knowledge. He reflects on his experiences in college, realizing the vast differences in expertise among peers, and how this awareness can be beneficial for personal growth and understanding one's place in the field of mathematics.

"It's the thing where if you  know a crossword is solvable,   you just keep going at it until you solve it. Or the four-minute mile, right? Exactly. That's a great example. Another valuable experience,..."

38
57:06 - 59:20
2:13 duration385 words

The Relevance of Godel’s Incompleteness Theorem

Grant addresses the practical implications of Godel’s incompleteness theorem, explaining that while it is a fundamental concept in mathematics, it rarely impacts day-to-day mathematical practice. He compares it to the halting problem in computer science, emphasizing that most mathematicians do not actively worry about these theoretical issues in their work.

"Do you think it's fair to have a mental model that  has a static g-factor type quality here such that   your two standard deviations below and that is  forever the state of things? Or do you think   t..."

39
59:20 - 1:01:45
2:24 duration453 words

The Challenge of Good Explanations

In this segment, Grant explores why good explanations are often hard to find. He discusses the difference between knowing something and being able to explain it effectively, emphasizing the need for explanations to be tailored to individual learners. This highlights the complexities involved in teaching and the challenges educators face in making concepts accessible to diverse audiences.

"that there are people like that. Von Neuman’s  another example of one of these, right? How much does Godel’s Incompleteness theorem  practically matter? Is it something that comes up   a lot or is it ..."

40
1:01:45 - 1:03:11
1:26 duration245 words

The Economics of Explanation

Grant delves into the economic factors that contribute to the scarcity of quality explanations in education. He argues that many explanations are created for specific audiences, which limits their general applicability. This segment emphasizes the need for more universally accessible educational resources that can cater to a wider range of learners.

"That's really interesting that something  from the outside and in popularizations   seems to be a very fundamental thing where  people have definitely heard about this. A good analogy here is the halt..."

41
1:03:11 - 1:05:11
2:00 duration381 words

The Role of Personal Experience in Learning

Grant reflects on his own experiences in creating educational content and how personal insights shape his approach to teaching. He discusses the importance of understanding the learner's perspective and how this influences the effectiveness of explanations. This segment highlights the value of personal experience in the educational process.

"like what's it like to not even know numbers?  How would you start to explain what numbers are?   Maybe you should go from a bunch of concrete  examples. But like the way that you think about   number..."

42
1:05:11 - 1:06:44
1:32 duration318 words

The Creative Process Behind Video Production

In this segment, Grant shares insights into his video production process, emphasizing the importance of personal involvement in the creative details. He discusses the challenges of delegating tasks and how the mundane aspects of production are integral to his thought process. This highlights the unique approach he takes in creating educational videos.

"Is the process of making your  videos, is that mostly you? Yes. Given the scale you're reaching,  it seems that if it was possible,   a small increase in productivity  would be worth an entire product..."

43
1:06:44 - 1:09:11
2:27 duration484 words

The Limitations of AI in Creative Work

Grant discusses the limitations of AI tools in the context of his creative work, particularly in animation and video production. He reflects on the challenges of using AI for tasks that require a deep understanding of visual output and personal expression. This segment emphasizes the ongoing need for human creativity in educational content creation.

"It's similar for why I maybe find it quite  hard to use Co-pilot and some of these   LLM tools for the animation code. It can be  super great if you're learning some new library   and it knows about t..."

44
1:09:59 - 1:12:12
2:13 duration427 words

Peer Review and Quality in Math Content Creation

Grant elaborates on the peer review system implemented for the Summer of Math Exposition, explaining how it helps identify high-quality content among numerous submissions. He discusses the importance of community engagement and the role of co-watching in promoting videos, suggesting that the quality of content can thrive when creators are motivated and supported by their peers.

"the output. This is the comment describing  it in English. But even then that wouldn't   hit the problem. I would have to articulate  what the thing I want is in the first place.   And the program lan..."

45
1:12:12 - 1:14:43
2:31 duration494 words

The Role of Motivation in Learning

In this insightful segment, Grant reflects on the importance of motivation in self-teaching, particularly in mathematics and related fields. He discusses how personal projects and supportive social circles can significantly enhance learning experiences, arguing that access to quality explanations is secondary to having the drive to learn. This perspective challenges traditional views on education and emphasizes the need for intrinsic motivation.

"application I mentioned that during the summer,  in addition to the main task I wanted them to do,   I'd give them freedom to do something relevant  to math exposition online that was their own   thin..."

46
1:14:43 - 1:26:31
11:47 duration2193 words

Disrupting Education: The Social Factors at Play

Grant discusses the limitations of educational technology in disrupting traditional learning systems. He highlights how these tools often benefit motivated learners while leaving others behind. The conversation emphasizes the significance of social factors, such as peer influence and personal goals, in fostering a successful learning environment, suggesting that motivation is the key driver for effective self-education.

"I misphrased if I said production quality, I  just meant the whole composition as a whole. Yeah, well there's a selection filter too,  right? In that first year, there were 1200   submissions and I fe..."

47
1:26:31 - 1:28:43
2:12 duration400 words

Social Dynamics in Learning

In this segment, Grant explores the importance of social dynamics in education, suggesting that peer influence and personal projects significantly enhance motivation to learn. He humorously proposes a hypothetical scenario where social engineering could optimize learning environments, highlighting the need for engaging interactions over mere access to information.

"And I don't know the best way to get more people  into things. I have had a thought and this is   the kind of thing that could never be done in  practice but instead it's something you would   like wr..."

48
1:28:43 - 1:30:51
2:07 duration431 words

Grant's Teaching Aspirations

Grant shares his aspirations to become a high school teacher, emphasizing the importance of staying connected to the student experience. He advocates for more STEM-savvy individuals to engage in teaching, arguing that it is a high-leverage way to inspire future generations in mathematics and science, and reflects on the need for a more structured approach to integrating teaching into careers.

"Final question. This is something I  should have followed up on earlier,   but your plans to become a high  school teacher for some amount of   years. When are you planning on doing that  and what do ..."