[constantcrying]

Archimedes really is an underappreciated figure. His ideas, specifically about calculating the area of shapes, already preempted the idea of the integral almost two millennials before Leibnitz and Newton.

When reading about ancient Greek mathematics it always is striking how little it resembles the mathematics taught in schools and how much it resembles the mathematics taught in University.

[vharuck]

IIRC, the ancient Greek mathematics we learn about today was the university-equivalent mathematics of that era. Common people did not use geometric abstractions to figure out math problems. Before Fibonacci brought algebra to Europe, everyday calculations were done on an abacus. If no abacus was nearby, people emulated one by placing stones in lines on the ground.

Pre-university schools, even today, focus on teaching practical math. Most people can get by just fine without skills in abstract math, theorizing, and proofs (though those skill would make a lot of people much better at whatever they do).

[constantcrying]

My point was that we should consider how advanced the Greeks were with their understanding of mathematics, especially their desires for proofs. And we should contrast that with how mathematics is taught today.

It's obvious that "practical math" has always been the most important and first skill to teach. But that ends at basic trigonometry.

Students are learning how to do integration in highschool (not exactly a relevant skill), long before they are confronted with the idea of proof in mathematics.

[DerekL]

*high school