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Bill Gates Interview: https://www.youtube.com/watch?v=MGiNTrj5vyI

The Anthropocene Reviewed book is here! https://www.penguinrandomhouse.com/books/672554/the-anthropocene-reviewed-by-john-green/

There are people who are probably asking why we haven't done any mathematics Crash Course videos. Well, we kinda have, we did an algebra course in partnership with Arizona State University: https://www.youtube.com/watch?v=A_QINscHY3Q

But also, it's down to a general frustration we have and a disagreement about what to do about that frustration. The frustration is that, if you teach mathematics in a way that will help students do well on tests, that is a very different course from one that focuses on the beauty and joy of math. Crash Course's goal is to always be both of those things at the same time, but we've had a hard time figuring out how to do that.

I'm not saying it's impossible, just that we've hard a really hard time figuring out how to do it.

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Good morning, John.  A couple of weeks ago, somebody mentioned me in the comments of this TikTok.  

"I was just doing my makeup for work and I just wanted to tell you guys about how I don't think math is real, and I know that, like, it's real because we all like, learn it in school or whatever, but who came up with this concept?  And you're gonna be like, Pythagoras, but how?  How did he come up with this?  How would you even figure that out?  How would you, like, start on the concept of algebra?"

I was immediately excited by this because this young woman is asking all of the right questions that not just lead to a greater understanding of math, but actually joyous understanding of math, and I get frustrated that oftentimes, the way we teach math right now ignores these questions.

How did Pythagoras, a dude who didn't have a flushable toilet, figure out an equation that we still use and is still useful today?  Thousands of years later?  A truth so true that it is more true than reality is.  Every point in our universe has some bluntness.  Every line has some wiggle, but in Pythagoras' mind, there was a perfect triangle, one that no matter how far you zoomed in, the lines were straight, the points were pointy, one in which for every right triangle, the area of the square made by the hypotenuse was exactly the same as the area of the squares made by the legs of the two triangles added together.  Exactly!  Exactly!

Now, there's the question of how he figured this out.  There's a number of thoughts about this.  We're not sure.  The one that's most discussed is that he was looking at a bunch of square tiles and he thought, if i split one of those squares diagonally, then I get a triangle and the legs of that triangle, well the squares made by them are right there.  There are those squares there, and the square made by the hypotenuse, well, it's made out of triangles if I split these other squares, but if you add those triangles we just made up, you get the two leg squares, and then he abstracted that not just to triangles made by squares, but all kinds of right triangles.

The point, though, is that he didn't need any special knowledge to figure this out.  He didn't need any special technology.  He just needed to play a game in his mind.  They say he was like, visiting a palace.  I think he was pooping.  I think, 90% chance he was pooping.

Now, the Pythagorean theorem is useful information, like, it comes in handy for people.  It doesn't come in handy for me.  That's not why it's interresting.  It's interesting because it's interesting.  The idea that we teach people the Pythagorean theorem without teaching them that mathematicians build universes in their minds that are more perfect than the one that we live in, in some ways.  That's wild.  That's wild!

Sometimes it is brought up, and sometimes the fact that Pythagoras built a cult promising secret knowledge about this stuff, and then actually delivered on that secret knowledge, that was extremely powerful and wild that you can create a universe in your mind, that also is sometimes taught, but not always.  I mean, come on!

This young woman asks, "Does math exist?"  I don't know.  I don't know!  Did Pythagoras discover his theorem or did he invent it?  Does math both exist and not exist?  Is it an artifact of our minds or of reality?  No one knows the answer to that question, but let people ask it!

The most discouraging thing is that, of course, because as discussed this is an imperfect universe, people then, like, mocked her as if she was stupid, when she's asking the question--the big questions!  Math is a game.  It's a game we play in our minds and I don't know how we ended up going from like, go play, go play, to like, uuughhh, remember this equation.  This is how we will judge you when we're deciding whether or not you get to go to college.

So bless this young woman for her questions and bless (?~3:35) the drag queen for explaining mathematics on TikTok.  So I guess this universe does have some things going for it.  

John, I'll see you on Tuesday.

Also, I interviewed Bill Gates about misinformation and internet platforms over on hankschannel if you want to check that out.  It's there.  I liked it.