But how does bitcoin actually work?

The math behind cryptocurrencies.
An equally valuable form of support is to simply share some of the videos.

Some people have asked if this channel accepts contributions in cryptocurrency form. As a matter of fact, it does:

Here are a few other resources I'd recommend:

(This is particularly good for understanding the details of what transactions look like, which is something this video did not cover)

Timestamps:

0:00 - Introduction
2:25 - Ledgers and digital signatures
7:21 - The ledger is the currency
10:06 - Decentralization
12:26 - Cryptographic hash functions
14:38 - Proof of work and blockchains
19:42 - Double spending
21:41 - Block times, halvenings, and transaction fees
24:40 - Thanks

Thanks to these viewers for their contributions to translations
Italian: @lcl45

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If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
Download the music on Bandcamp:

Stream the music on Spotify:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

Various social media stuffs:

[bluebrown]

If you see comments here about investing or brokers, they are scams. Videos about cryptocurrencies, evidently including ones that are just about the underlying technology/math, are hotbeds for attracting nefarious actors preying on the impressionable.

Also, hi! If you’re new to this channel, most of it is about visualizing math. I get it, you probably landed here searching for how BTC works, not to spend your afternoon getting pulled into learning about, say, prime numbers or problem-solving, but if you have a moment take a look at the rest of the channel, you may enjoy what you find.

[morenocesarp]

"I'm still confused, but on a higher level!"

[Youth-growth]

You have no idea how much I've tried to find an article or video actually explaining how cryptocurrencies work. Everyone else just goes around with analogies. They probably don't understand fully themselves. Thanks man.

[zuccca]

Literally the best explanation I have ever seen on this subject. Thank you 3B1B.

[Charlie-rhod]

When he said “I’m looking at you Charlie” I got chills

[Bayesic]

So first of all, love the vid

Just wanted to say from a purely meta kind of standpoint, I really love how this video is put together. Not even just the editing / graphics and what not, but just the way you tell the story. I'm constantly asking questions in my mind and it's like within the next minute or two you provide an answer. I'm definitely studying a lot of your videos to learn how to improve my own content because you do a masterful job at keeping your audience engaged. Fantastic work

[justinliu]

17:30 block creators
17:51 block reward
18:29 mining
19:10 decentralized consensus

[HR-qygf]

This is the clearest video I’ve ever seen, and I still don’t get it.

[bluebrown]

The basic idea is to get a feel for what 2^32 (about 4 billion) multiplied by itself 8 times feels like, building up to a comically absurd computer that would be needed to break 256-bit security.

[s]

Heisenberg, Schrodinger and Ohm are in a car
They get pulled over. Heisenberg is driving and the cop asks him "Do you know how fast you were going?"

"No, but I know exactly where I am" Heisenberg replies.

The cop says "You were doing 55 in a 35." Heisenberg throws up his hands and shouts "Great! Now I'm lost!"

The cop thinks this is suspicious and orders him to pop open the trunk. He checks it out and says "Do you know you have a dead cat back here?"

"We do now, asshole!" shouts Schrodinger.

The cop moves to arrest them. Ohm resists.

[dimethyltryptamine]

I cant wait for the english version of this video bro looks really good.

[dhoomketu]

It's an extremely information dense lecture. You have to watch portions of it again and again to grasp the underlying concepts. But once you've finished it, you feel so damn confident.

[izlebakalm]

*The future is now, you all need to start somewhere no matter how small*

[harshchikorde]

please make a video on transforms (laplace, fourier,z- transforms) as these will help many engineering students.Many people take it for granted very little is known about its physical meaning, there are subjects in engineering based on transforms like signals and systems, signal processing, control theory your vedios will surely make a difference in understanding these subjects.

[billkidney]

I like that Alice, Bob, and Charlies pk's were 01000010, and 01000011, which are just A, B, and C in ASCII. Cute.

[Hynasek]

5 years later and I still comeback to this Blockchain explanation to check if my understanding, love it

[dantraficonte]

Wow. This was incredibly well illustrated and well done

[codesymphony]

"alice sent bob $10? ok let me just run my 1000 rtx 3080s for 10 hours to verify.. yep you're good"

[jflight]

After watching this video, I have finally realized how dumb I really am.

[cristinadavies]

In 2019, people have realized there isn't going to be one crypto to rule them all. You're seeing vertical solutions where XRP is focused on payment problems, Ethereum is focused on smart contracts, and increasingly, bitcoin is a store of value. Those aren't competitive. In fact, I want bitcoin and Ethereum to be successful.