If they were taught this kind of thing from an extremely young age in school every year these interviews would be trivial, Just like speaking your native language is trivial.

We don't quite reach a very high degree of practical math literacy even though everyone is taught from a young age. Calculus considered as "incredibly difficult" being an example.

I know a lot of students who would not understand the idea behind calculus concepts, even though they knew the formulae. They simply could not grasp a very simple thing like "area under the curve" or "Slope of a curve". This was at a large private school with a selective admissions process. I know for a fact that my college educated parents (50+) would not know how to solve a calculus problem. So yeah, Calculus is a pretty bad example because it IS incredibly difficult for the general population.

I don't know if this is like a smarts thing or just a poor math education thing.

As someone who does math for a living, I’m always frustrated because I truly believe it’s a poor math education thing. But then people just respond, “oh MYNAME, you just think that because you’re good at it/you’re a math person.” As if that made the point less valid rather than more valid.

Leonardo da Vinci was likely one of the most intelligent humans ever to have lived, and didn't understand calculus. It wasn't for lack of interest, either! He was fascinated with parachutes, timing falling objects and trying to understand the rates of change. But despite nibbling at the edges of calculus, he never got there.

In contrast, it's now completely ordinary for a teenager to not only get to the core ideas but solve complex calculations with them in timed tests!

This is an odd comparison.

I think DaVinci was way before Newton.

High school students aren't asked to invent calculus just to understand it.

I didn't invent djikstras graph traversal algorithm but I can read and understand it.

I think there's a difference between original invention and understanding 'n usage.

We all stand on the shoulders of giants and have increasingly powerful complimentary cognitive artifacts that let us easily do things that used to be very difficult.

In a more extreme version, consider that ancient Greek and Roman mathematicians struggled with long division problems that many of us can do in our heads now!

Why? Arabic numerals are far more effective than Roman numerals for the task and after having learned them, we have a permanently increased ability to do certain kinds of calculation.

That's very fascinating.

I look at quicksort and that was revolutionary at the time.

Do we have ways to better conceptualize the world around us? Or are our brains evolving outside of some normal evolutionary process?

Fascinating to me.

I think both are true but mostly the first. Human evolution has sped up dramatically in the past 15,000 years, but it's still very slow.

Arabic numerals, literacy, maps, bayesian reasoning, etc are unnatural, but better ways to conceptualize the world around us and these tools and others have steadily become more prevalent throughout the population.

Maybe quicksort hasn't permated through much of society, but binary search has! People born 100 years ago became comfortable flipping through phone books and quickly finding a name, whereas that would have taken a conceptual leap for most born 200 years ago.

I completely agree with you.

I think it's a failure of the school system from a very early age because math is heavily dependent on foundations of previous classes.

And I think it's more than just sharing the information we have to also make rational thinking fields as fun and cool as the emotional expression fields of study like English or Music and not the domain of 'nerds'.

I think our whole culture would be way better off if people had better critical thinking logic and math skills.

> because math is heavily dependent on foundations of previous classes.

This is a point I hadn't thought enough about before. Great insight.

It makes me think that maybe we just suck at education in general, and it only shows up in the subjects where continuation is dependent on previous courses.

If you completely fail to understand american history, you can lie to yourself about being good at it, and continue to believe that when you get to european history. If you completely fail to understand the lessons from Fahrenheit 451, you can believe you're good at English (the subject, not the language) while you move on to Shakespeare.

The only (pre-college) subjects I can think of that really require you to actually understand the prereq's material are math and language. And they share that people say "I'm just not a math person" or "I'm just no good at languages."

I'd never thought about it with that lens before, but now I'm feeling kinda pessimistic. Like, if this hypothesis is true, it's not about bringing math education up to the bar of other subjects, it's about overhauling the entire system.

You use your native language all the day, all the time. It's nowhere near the same.