My name is Grant Sanderson. Videos here cover a variety of topics in math, or adjacent fields like physics and CS, all with an emphasis on visualizing the core ideas. The goal is to use animation to help elucidate and motivate otherwise tricky topics, and for difficult problems to be made simple with changes in perspective. For more information, other projects, FAQs, and inquiries see the website: https://www.3blue1brown.com
This episode explores the historical methods used to determine cosmic distances, from the size of the Earth to that of the universe. Against the backdrop of renowned mathematician Terence Tao's childhood fascination with astronomy, the discussion delves into the ingenious techniques employed by ancient Greek scholars...
This episode explores the inscribed square problem, a mathematical puzzle questioning whether every closed continuous loop contains an inscribed square. Against this backdrop, the speaker delves into a simpler, solved version: proving every closed loop contains an inscribed rectangle. The solution involves a clever m...
This podcast delves into the workings of large language models (LLMs), highlighting their core mechanisms. LLMs generate text by predicting the next word in a sequence, assigning probabilities to all potential options. They develop this skill through extensive training on vast datasets, which includes both pre-training...
This podcast delves into intriguing geometric puzzles that are presented in two or three dimensions but can be creatively solved by thinking in higher dimensions. The speaker illustrates how reimagining two-dimensional tilings as projections of three-dimensional stacks of cubes, or tackling a circle's covering problem ...
In this podcast episode, listeners get an insider’s view of Manim, the custom Python library that powers the animations for 3Blue1Brown videos. Host Ben Sparks chats with creator Grant Sanderson about how Manim works, showcasing its interactive features that allow for real-time adjustments to animations right in the Py...
In this podcast episode, we dive into the fascinating science of holography and how it enables the recording and reconstruction of three-dimensional images from two-dimensional film. We start by illustrating the captivating illusions created by holograms, then explore the intricate process of hologram recording through...
This podcast episode delves deep into the intricacies of how large language models (LLMs) store knowledge, using the example of Michael Jordan to explain complex concepts like multilayer perceptrons and the transformer architecture. By breaking down the operations within MLPs, the speaker emphasizes the challenges of i...
Grant Sanderson's graduation speech questions the popular advice to "follow your dreams." He argues that while passion matters, true career success is built on the ability to add value to others. After college, he suggests the focus should shift from personal growth to making meaningful contributions to society. Sander...
This podcast episode provides an in-depth exploration of the attention mechanism in transformers, crucial for understanding how modern AI tools process language. It details the journey of word embeddings as they are refined through attention, utilizing examples to illustrate how context shapes meaning. The discussion e...
This podcast episode explores the transformative power of transformers in language models and text generation. It explains the concept of GPT and how transformers, a type of neural network, play a crucial role in the current AI boom. The episode provides insights into the process of deep learning, including attention b...
In this podcast episode, the host tackles listener questions about the index of refraction, specifically exploring why light bends when it slows down and how it's possible to have an index of refraction less than 1. He explains that this bending happens due to a change in wavelength as light enters a new medium, which ...
In this podcast episode, the discussion centers on the fascinating physics of prisms and the way light transforms into a rainbow spectrum as it passes through them. The host offers a fresh take on the typical high school explanation, diving deeper into why light slows down and how its colors are affected by different m...
This podcast celebrates the winners of the 3rd Summer of Math Exposition, a contest that promotes online math explainers. Host Grant Sanderson reviews 25 entries, pointing out their unique strengths and intended audiences. He stresses that a successful explainer is tailored to its specific audience, which makes ranking...
This podcast delves into the intriguing effect of colored diagonal stripes that emerge when linearly polarized light passes through sugar water. The speaker starts by discussing light as electromagnetic radiation produced by accelerating charges, then moves on to explain the concepts of polarization, including both lin...
In this podcast episode, we dive into the significance of the normal distribution, also known as the Gaussian distribution, in the realm of probability theory. It highlights the fascinating Central Limit Theorem, which states that when you sum multiple independent random variables, the result tends to follow a normal d...
In this podcast, the host delves into Moser's circle problem, which investigates how many regions are formed when chords connect n points on the circumference of a circle. At first glance, it seems like the number of regions follows a power of 2, but this assumption doesn’t hold. The discussion guides listeners through...
This podcast delves into convolutions, a mathematical operation that helps us understand how the sums of two independent random variables are distributed. It starts with a fun example using weighted dice, showcasing two visualization techniques: a 3D grid that lays out all possible outcomes and a sliding, flipped distr...
This podcast delves into the unexpected emergence of pi in the formula for the normal distribution. It kicks off with a fascinating story about someone's disbelief upon encountering the mathematical proof. The discussion then transitions into a classic proof that reveals this connection through an ingenious integration...
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