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Grant Sanderson

@3blue1brown • 461,452 subscribers

Pi creature caretaker. Contact/faq: https://t.co/brZwdQfdif

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The last IMO problem AI could not solve. For when you want to sit down for a longer problem-solving saga, here's the full video:

The last IMO problem AI could not solve. For when you want to sit down for a longer problem-solving saga, here's the full video:

Grant Sanderson

156,958 次观看 • 1 个月前

For the most recent video, I had way too much fun simulating the electric field (or rather, the component of that field responsible for radiation) and how it responds to an accelerating electric charge.

For the most recent video, I had way too much fun simulating the electric field (or rather, the component of that field responsible for radiation) and how it responds to an accelerating electric charge.

Grant Sanderson

1,251,469 次观看 • 3 年前

New video! Memorable for its delightfully absurd name, the Hairy Ball Theorem is extremely beautiful and has some surprising applications. Full video here:

New video! Memorable for its delightfully absurd name, the Hairy Ball Theorem is extremely beautiful and has some surprising applications. Full video here:

Grant Sanderson

287,634 次观看 • 9 个月前

The next chapter about transformers is up on YouTube, digging into the attention mechanism: The model works with vectors representing tokens (think words), and this is the mechanism that allows those vectors to take in meaning from context.

The next chapter about transformers is up on YouTube, digging into the attention mechanism: The model works with vectors representing tokens (think words), and this is the mechanism that allows those vectors to take in meaning from context.

Grant Sanderson

810,694 次观看 • 2 年前

On a recent trip to the UK, Matt Parker shared this delightful little probability fact with me and asked if I might animate an explanation for a video of his. It's a fun one! See his full video with shenanigans relating this to dice and more.

On a recent trip to the UK, Matt Parker shared this delightful little probability fact with me and asked if I might animate an explanation for a video of his. It's a fun one! See his full video with shenanigans relating this to dice and more.

Grant Sanderson

648,849 次观看 • 2 年前

Excerpt from a video I just posted on YouTube (about the multilayer perception layers in a transformer, and how LLMs may store facts).

Excerpt from a video I just posted on YouTube (about the multilayer perception layers in a transformer, and how LLMs may store facts).

Grant Sanderson

622,677 次观看 • 2 年前

I remember having way too much fun writing this back in 2017 when I made the Bitcoin explainer. If someone describes a cryptographic protocol as having "256-bit security", what does that really mean?

I remember having way too much fun writing this back in 2017 when I made the Bitcoin explainer. If someone describes a cryptographic protocol as having "256-bit security", what does that really mean?

Grant Sanderson

579,823 次观看 • 3 年前

New puzzle, as part of the series of monthly puzzlers with National Museum of Mathematics. As a variant: What if you start with pegs in all four corners of the square, and you want them to end up on corners of a bigger square?

New puzzle, as part of the series of monthly puzzlers with National Museum of Mathematics. As a variant: What if you start with pegs in all four corners of the square, and you want them to end up on corners of a bigger square?

Grant Sanderson

58,429 次观看 • 2 个月前

Suppose you wanted to reinvent the idea of Shannon Entropy for yourself. This puzzle is a good place to start (Full video on YouTube).

Suppose you wanted to reinvent the idea of Shannon Entropy for yourself. This puzzle is a good place to start (Full video on YouTube).

Grant Sanderson

92,408 次观看 • 5 个月前

Here's a short dynamics-based explanation of the equation e^(πi)=-1

Here's a short dynamics-based explanation of the equation e^(πi)=-1

Grant Sanderson

538,271 次观看 • 3 年前

I just put up a new video, which was a collaboration with Terence Tao about the cosmic distance ladder. You can find the full video on YouTube, and here's a bit of extra footage that didn't make it into the final.

I just put up a new video, which was a collaboration with Terence Tao about the cosmic distance ladder. You can find the full video on YouTube, and here's a bit of extra footage that didn't make it into the final.

Grant Sanderson

307,488 次观看 • 1 年前

This video was a complete joy to make. Here's a short preview, but next time you're looking to sit down for 45 minutes of math and art, take a look at the full version on YouTube.

This video was a complete joy to make. Here's a short preview, but next time you're looking to sit down for 45 minutes of math and art, take a look at the full version on YouTube.

Grant Sanderson

126,401 次观看 • 7 个月前

Well, math terminology being what it is, something like this was bound to happen eventually. (If you're curious about why these balls are so puny, the full talk is up on YouTube)

Well, math terminology being what it is, something like this was bound to happen eventually. (If you're curious about why these balls are so puny, the full talk is up on YouTube)

Grant Sanderson

131,168 次观看 • 8 个月前

I just put up a new video on the fundamentals of quantum computing, building up to a step-by-step walk-through of something known as Grover’s algorithm. Here's an excerpt of a quiz used to introduce the topic.

I just put up a new video on the fundamentals of quantum computing, building up to a step-by-step walk-through of something known as Grover’s algorithm. Here's an excerpt of a quiz used to introduce the topic.

Grant Sanderson

236,780 次观看 • 1 年前

The puzzle below is a famous cautionary tale in math. But there's more to it than just coincidence, and on the YouTube version, we dig into what's really going on. Full explanation:

The puzzle below is a famous cautionary tale in math. But there's more to it than just coincidence, and on the YouTube version, we dig into what's really going on. Full explanation:

Grant Sanderson

445,635 次观看 • 3 年前

Has anyone ever come across this way of visualizing the convolution of two functions f and g: Look at the graph of the two-variable function f(x)g(y), and consider diagonal slices over the line x + y = k. The area of those slices represents (f * g)(k).

Has anyone ever come across this way of visualizing the convolution of two functions f and g: Look at the graph of the two-variable function f(x)g(y), and consider diagonal slices over the line x + y = k. The area of those slices represents (f * g)(k).

Grant Sanderson

397,419 次观看 • 3 年前

The next video in the Laplace Transform sequence is up! Here, we dig into a concrete example, the forced oscillator. Some of you may remember that this was relevant for studying why light slows down in a medium.

The next video in the Laplace Transform sequence is up! Here, we dig into a concrete example, the forced oscillator. Some of you may remember that this was relevant for studying why light slows down in a medium.

Grant Sanderson

134,573 次观看 • 1 年前

As a preview, here's a sped-up version of one of the core scenes, though admittedly it may not make full sense without narration.

As a preview, here's a sped-up version of one of the core scenes, though admittedly it may not make full sense without narration.

Grant Sanderson

286,116 次观看 • 2 年前

New* video! If you’ve ever wondered what topology is, this problem is one of the best examples I know of to give an authentic sense of what it’s all about:

New* video! If you’ve ever wondered what topology is, this problem is one of the best examples I know of to give an authentic sense of what it’s all about:

Grant Sanderson

205,618 次观看 • 1 年前