> I came across this article by V.I. Arnold Interesting article! It argues that when mathematics became dissociated from both physics and geometry, it became t

> I came across this article by V.I. Arnold Interesting article! It argues that when mathematics became dissociated from both physics and geometry, it became this horrible abstract algebraic kabbala that's at once disgusting and pointless. The article talks a lot about France; I think in France the problem is a problem of selection / elitism: how to rate lots of students in a reproducible way in order to keep only a few. This process doesn't leave much room to rêverie or the joy of learning. It's a disease that modern proponents of "le mérite" don't understand. ("Mérite" is hard to translate; maybe "self worth"; it's a vast debate in France). More generally, the problem of teaching is that it tries to put results in the heads of students. Some results took years or centuries to discover, and it would be impractical or impossible to tell the story of that discovery. But our minds are story machines; stories are the only thing we understand and crave for. A list of facts is the most boring thing imaginable and the hardest to remember. Yet it's not clear if there's any other way, esp. because there are so many facts to learn, and so little time. Yet that doesn't excuse everything. It should always be possible to connect theory to real world applications. Here's a little observation about geometry for example. My kids are currently learning about the Pythagorean theorem, where in a square triangle, the length of the "hypotenuse" is the square root of the sum of the square of each opposite side. But what does "hypotenuse" mean? In math books (as well as on every website that I could find, see https://www.google.com/search?tbm=isch&q=pythagorean+theorem https://www.google.com/search?tbm=isch&q=pythagorean+theorem) the square triangle is always shown with the square angle at the bottom, usually to the left, and the long side (the hypotenuse) is a slope going from north-west to south-east on the page. It turns out, hypo-tenuse means "that which supports". Obviously if the square triangle sits on its square angle, the hypotenuse doesn't support anything. But if the hypotenuse is instead horizontal and the square angle at the top, then we begin to see the front of a temple. The Pythagorean theorem helps solve a myriad of problems, but one of them is extremely practical: how to build a temple with a square top at the front. That's more interesting than a²+b²=c².