Episode
Grant Sanderson: 3Blue1Brown and the Beauty of Mathematics
1:03:12
Published: Tue Jan 07 2020
Description
Grant Sanderson is a math educator and creator of 3Blue1Brown, a popular YouTube channel that uses programmatically-animated visualizations to explain concepts in linear algebra, calculus, and other fields of mathematics. This conversation is part of the Artificial Intelligence podcast. If you would like to get more information about this podcast go to https://lexfridman.com/ai or connect with @lexfridman on Twitter, LinkedIn, Facebook, Medium, or YouTube where you can watch the video versions of these conversations. If you enjoy the podcast, please rate it 5 stars on Apple Podcasts, follow on Spotify, or support it on Patreon. This episode is presented by Cash App. Download it (App Store, Google Play), use code "LexPodcast". Here's the outline of the episode. On some podcast players you should be able to click the timestamp to jump to that time. 00:00 - Introduction 01:56 - What kind of math would aliens have? 03:48 - Euler's identity and the least favorite piece of notation 10:31 - Is math discovered or invented? 14:30 - Difference between physics and math 17:24 - Why is reality compressible into simple equations? 21:44 - Are we living in a simulation? 26:27 - Infinity and abstractions 35:48 - Most beautiful idea in mathematics 41:32 - Favorite video to create 45:04 - Video creation process 50:04 - Euler identity 51:47 - Mortality and meaning 55:16 - How do you know when a video is done? 56:18 - What is the best way to learn math for beginners? 59:17 - Happy moment
Chapters
The exponential function can be represented in various ways, and trying to understand it solely through repeated multiplication may not be the best approach.
00:00 - 06:05 (06:05)
Summary
The exponential function can be represented in various ways, and trying to understand it solely through repeated multiplication may not be the best approach. Choosing different modes of thought can lead to greater insights and possibilities in mathematics.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
The difficulty in reading and interpreting mathematical notation has led to wasted time and misunderstanding among scientists and students, and the awkwardness of some notations may be a result of the combination of several disciplines in a single equation.
06:05 - 10:47 (04:41)
Summary
The difficulty in reading and interpreting mathematical notation has led to wasted time and misunderstanding among scientists and students, and the awkwardness of some notations may be a result of the combination of several disciplines in a single equation. However, despite these challenges, these notations can often come together nicely and help us understand self-reinforcing growth.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
Mathematics in the 20th and 21st century physics has become increasingly detached from the physical world, but there are still examples, like chaos theory, where the two fields are heavily connected and motivated.
10:48 - 17:02 (06:13)
Summary
Mathematics in the 20th and 21st century physics has become increasingly detached from the physical world, but there are still examples, like chaos theory, where the two fields are heavily connected and motivated.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
The study of partial differential equations tries to capture the complexity of the physical world but falls short due to the impossibility of explicitly modeling reality, especially at the atomic and cosmic scales.
17:02 - 22:19 (05:17)
Summary
The study of partial differential equations tries to capture the complexity of the physical world but falls short due to the impossibility of explicitly modeling reality, especially at the atomic and cosmic scales.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
The resources necessary to simulate our universe are immense, which places limits on the number of layers that could exist beyond our own reality; despite this, people assume a uniform probability over all potential layers.
22:19 - 29:47 (07:27)
Summary
The resources necessary to simulate our universe are immense, which places limits on the number of layers that could exist beyond our own reality; despite this, people assume a uniform probability over all potential layers. Additionally, considering the potential power of computation and artificial intelligence raises questions about the number of possible word combinations that exist.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
The process of understanding starts with thinking of concrete examples that show the similarity between the quantities involved, rather than overwhelming the brain with abstract symbols that need to be populated with examples later on.
29:47 - 36:03 (06:16)
Summary
The process of understanding starts with thinking of concrete examples that show the similarity between the quantities involved, rather than overwhelming the brain with abstract symbols that need to be populated with examples later on. This allows the brain to grasp the essence of the concept more easily.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
The intricacies of analytic number theory can be daunting, but the Princeton Companion to Math offers a great introduction for those with a college-level background in math.
36:04 - 40:25 (04:21)
Summary
The intricacies of analytic number theory can be daunting, but the Princeton Companion to Math offers a great introduction for those with a college-level background in math. Explained through formulas like the convergence of infinite series, analytic number theory involves the study of primes and their positioning within number sequences.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
The beauty of mathematics lies in its various surfaces and shapes, such as torus and mobius strip, that have always intrigued minds that appreciate the intricate designs and the complexities that come with them.
40:25 - 47:00 (06:34)
Summary
The beauty of mathematics lies in its various surfaces and shapes, such as torus and mobius strip, that have always intrigued minds that appreciate the intricate designs and the complexities that come with them. Although studying the zeroes of the Riemann zeta function can be challenging, finding a way to describe them visually can help bring out the beauty of these complex shapes.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
This podcast explores the use of quaternions for robotics and graphics programming in 3D space rotations.
47:00 - 50:10 (03:10)
Summary
This podcast explores the use of quaternions for robotics and graphics programming in 3D space rotations. It is not recommended for those who are not familiar with the field or do not have a background in physics or neuroscience.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
The speaker discusses the analogy between understanding Euler's formula and having a romantic relationship, acknowledging that while the initial fascination may fade, there is still value in continued interest and appreciation.
50:11 - 54:10 (03:59)
Summary
The speaker discusses the analogy between understanding Euler's formula and having a romantic relationship, acknowledging that while the initial fascination may fade, there is still value in continued interest and appreciation.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
A neural network specialist believes that making videos can be a beautiful journey of discovery that allows individuals to connect themselves to seemingly infinite ideas and achieve a kind of immortality.
54:10 - 59:10 (05:00)
Summary
A neural network specialist believes that making videos can be a beautiful journey of discovery that allows individuals to connect themselves to seemingly infinite ideas and achieve a kind of immortality. While not always the case, creating videos can be an informative way to learn about complex subjects like neural networks.
EpisodeGrant Sanderson: 3Blue1Brown and the Beauty of Mathematics
PodcastLex Fridman Podcast
A podcast host and guest reflect on moments of true happiness found outside of relationships, specifically through music.
59:11 - 1:02:52 (03:41)
Summary
A podcast host and guest reflect on moments of true happiness found outside of relationships, specifically through music. Although music is not as present in their lives as it once was, it holds transformative power.