Grant Sanderson (3Blue1Brown): Best Way to Learn Math | AI Podcast Clips

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18 Jan 202003:21

TLDRGrant Sanderson from 3Blue1Brown discusses the best method to learn math, emphasizing the importance of actively solving problems over passively watching lectures or reading. He suggests using textbooks with well-curated problem sets and recommends platforms like Khan Academy for beginners. Sanderson also highlights the benefits of programming as a motivational angle to approach math and the effectiveness of teaching or explaining concepts as a means to solidify understanding.


  • πŸ“š The best way to learn math is to focus on solving specific problems rather than just watching lectures or reading textbooks.
  • πŸ” Seek out resources with well-curated lists of problems, like textbooks with exercises at the end of each chapter.
  • πŸ‘€ Look at the questions at the end of a chapter before reading it to identify which ones you find intriguing or challenging.
  • πŸ“ Don't consider a chapter complete until you've worked through some exercises, reinforcing the concepts learned.
  • πŸŽ₯ Watching educational videos is beneficial but should be complemented with active problem-solving for a complete learning experience.
  • 🏫 Khan Academy is recommended for beginners as it provides a large set of questions to work through, especially for basic linear algebra and calculus.
  • πŸ’‘ Programming can be a motivating way to learn math, as it often requires mathematical concepts to solve problems.
  • 🌐 The Bay Area's tech culture suggests that getting into programming can lead to an interest in math for those who initially disliked it.
  • πŸŽ“ Creating educational content, like making videos, can be a powerful way to consolidate your own understanding of a subject.
  • πŸ“ˆ The principle of learning by teaching suggests that actively explaining concepts to others can greatly improve your own retention and understanding.
  • πŸ€“ The anecdotal percentages of retention (10% for reading, 20% for listening, 70% for active interaction, 90% for teaching) highlight the importance of engaging with the material.

Q & A

  • What is the best way to learn math according to Grant Sanderson?

    -The best way to learn math, according to Grant Sanderson, is to spend more time solving specific problems rather than just watching lectures or reading. He suggests focusing on problem-solving and using well-curated lists of problems from textbooks.

  • Why does Sanderson recommend looking at the problems at the end of a textbook chapter before reading the chapter?

    -Sanderson recommends this approach because it helps learners identify which problems they can solve and which ones they need to understand better. This method encourages active problem-solving and deeper understanding of the material.

  • What does Sanderson admit about his own videos in the learning process?

    -Sanderson admits that his videos are only a partial part of the learning process since they usually do not have associated exercises. He views his videos as a different part of the educational ecosystem.

  • What online resource does Sanderson recommend for beginners in math?

    -Sanderson recommends Khan Academy for beginners because it offers a large set of questions to work through and covers fundamental topics like basic linear algebra and calculus.

  • How does Sanderson suggest using programming to learn math?

    -Sanderson suggests learning to program and using the motivation from programming to push through math concepts. He notes that many people who were initially disinterested in math found a passion for it through programming.

  • What does Sanderson say about the retention rates of different learning activities?

    -Sanderson mentions a common anecdote that people remember about 10% of what they read, 20% of what they listen to, 70% of what they actively interact with, and 90% of what they teach. Although he acknowledges these numbers might not be accurate, they resonate with his experience.

  • Why does Sanderson believe teaching or explaining concepts is beneficial for learning?

    -Sanderson believes that teaching or actively explaining concepts helps in consolidating knowledge much more effectively than passive learning methods.

  • Does Sanderson think creating educational videos like his own is beneficial for learners?

    -Yes, Sanderson suggests that creating educational videos or trying to explain concepts can be a powerful way to learn, as it forces the learner to understand the material deeply enough to teach it.

  • What role does active problem-solving play in learning math according to Sanderson?

    -Active problem-solving is crucial in learning math according to Sanderson because it engages the learner more deeply with the material and helps in applying theoretical concepts practically.

  • How can someone incorporate Sanderson's advice into their math study routine?

    -Someone can incorporate Sanderson's advice by focusing more on solving problems, using resources like Khan Academy, integrating programming with math learning, and engaging in teaching or explaining concepts to others.



πŸ“š Embracing Active Learning in Mathematics

The paragraph emphasizes the importance of active learning for those beginning their journey in mathematics or even for those further along in their studies. It suggests that instead of passively watching lectures or reading, individuals should focus on solving problems. The speaker recommends seeking out textbooks with well-curated problems and engaging with them before and after reading the chapters. The advice is to not move on until exercises are attempted, highlighting the speaker's own hypocrisy for creating video content without associated exercises, suggesting that videos are only a part of the learning process. For beginners, resources like Khan Academy are recommended for their extensive question sets and basic introductions to subjects like linear algebra and calculus.

πŸ’» The Intersection of Programming and Math

This section discusses the connection between programming and math, suggesting that learning to program can motivate an understanding of mathematical concepts. The speaker shares personal observations of individuals who developed an interest in math through programming, possibly due to the practical applications and real-world problems that programming presents. The paragraph also touches on the speaker's own approach to creating educational videos, using programming to illustrate mathematical ideas, and suggests that others might benefit from a similar method of teaching or explaining concepts to solidify their understanding.

πŸ—£οΈ Teaching as a Powerful Learning Tool

The final paragraph delves into the concept that teaching is one of the most effective ways to learn, referencing a set of percentages that suggest retention rates for different types of engagement. While acknowledging the anecdotal nature of these percentages, the speaker believes in the truth behind the idea that actively teaching or explaining concepts significantly improves knowledge retention. The speaker encourages the practice of teaching as a method to consolidate learning, suggesting that it might even be more effective than reading or listening to lectures.




Mathematics, often referred to simply as 'math,' is the abstract science of number, quantity, and space, either as abstract concepts or represented by figures and diagrams. In the context of the video, it is the subject being discussed, with the focus on the best methods to learn and understand it. The script mentions that even those deep in their career might still want to explore math, indicating its ongoing relevance and depth.


Education is the process of acquiring knowledge, skills, values, beliefs, and habits. In the script, the term is used when discussing the temptation to watch lectures or read more as a method of learning math. The speaker suggests that doing problems is more effective than passive learning for educational purposes, emphasizing the importance of active engagement in the learning process.


In the context of the video, 'problems' refer to mathematical exercises or questions that learners are encouraged to solve actively. The script advises learners to spend time on these problems rather than just watching lectures or reading, as solving problems is a key part of the learning process in mathematics.


A textbook is a comprehensive guidebook used in educational institutions to present the core material for a course of study. The script mentions textbooks as a source of well-curated problems, suggesting that learners should look at the problems at the end of chapters before and after reading the material to reinforce their understanding.

πŸ’‘Khan Academy

Khan Academy is a non-profit educational organization that provides free online courses, lectures, and problem sets covering a wide range of subjects, including math. The script praises Khan Academy for its large set of questions and its effectiveness in helping beginners get comfortable with basic concepts like linear algebra and calculus.


Programming is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. The speaker in the script suggests that learning to program can be a motivating factor for understanding math, as it provides a practical application of mathematical concepts.


In the script, 'concepts' refer to the abstract ideas or principles that form the basis of mathematical understanding. The speaker mentions using programming to illuminate these concepts, indicating that practical application can help in grasping the underlying principles of math.


Exploration in the context of the video refers to the act of investigating or examining something unknown or unfamiliar in the field of mathematics. The script suggests that even those who have reached advanced levels in their mathematical journey may still wish to explore new areas of math.


The term 'ecosystem' in the script is used metaphorically to describe the various components and methods that contribute to the learning process. The speaker positions their videos as one part of this ecosystem, acknowledging that they are not the sole method for learning math.


Teaching is the process of imparting knowledge, skills, and values to others. The script mentions a common adage about retention rates, suggesting that teaching others or explaining concepts actively is one of the most effective ways to consolidate one's own understanding of math.


Retention refers to the ability to remember and recall information. The script cites an anecdote about the percentage of information retained through different methods of learning, with teaching being the most effective for retaining knowledge in mathematics.


The best way to learn math is to focus on solving specific problems rather than just watching lectures or reading.

Forcing oneself to do more problems than naturally inclined is crucial for learning math.

Seek entities with well-curated lists of problems, such as textbooks with problems at the end of chapters.

Looking at questions before reading the chapter can help identify which concepts to focus on.

Do not consider a chapter complete until working through associated exercises.

Grant Sanderson admits his videos are a part of the learning ecosystem but not the complete learning process.

Khan Academy is recommended for beginners to get comfortable with basic linear algebra and calculus.

Programming can be a motivating angle to learn math, especially for those who didn't initially like it.

Creating videos to teach concepts can be a powerful method for consolidating one's own understanding of math.

The adage that you remember 10% of what you read, 20% of what you listen to, 70% of what you interact with, and 90% of what you teach holds true in the context of learning math.

Actively teaching or explaining math concepts can significantly enhance learning outcomes.

The importance of engaging with math problems rather than passively consuming content is emphasized.

The transcript suggests that a combination of reading, problem-solving, and teaching can optimize math learning.

Using programming as a tool to explore and understand mathematical concepts can be beneficial.

The transcript highlights the value of different learning modalities in the process of mastering math.

Sanderson's approach to math education involves a blend of video content and active problem-solving.

The transcript underscores the significance of revisiting problems after reading to reinforce learning.

Engaging with math problems before and after reading related material is a recommended strategy.