[snowman]

Yeh, yeh, yeh, but how do you tell the difference between the boneheads and he ones that really understand what they are doing? Einstein is a one of a kind, and he made it in spite of the limits imposed on him. I kind of suspect any new Einstein would somehow do the same, so not to worry about overlooking him. For the rest of us mortals, you need some kind of standards, something to sort the wheat from the chaff.

It is necessary to have a cold, hard, mastery of arithmetic and multiplication to solve higher math problems like differential equations, where the educated guess is the rule. You can't make educated guesses without lots and lots of practice on mundane problems. Those guesses rely on learning all the "tricks" of math, especially arithmetic, which rely on lots and lots of practice doing simple, stupid multiplication and addition, subtraction problems that a calculator is useful for. It is impossible to use a calculator to solve differential equations (in general) Differential equations are math 101 in the real world, yet many of the people talking about this don't even know what a differential equation is.

Then we get to matrixes, partial diff eq, curls, vector math, spars matrixes, chaos theory and other stuff that is the meat of math and science. Much of this stuff, at this level relys on educated guesses, not systematic methods. THis is the math that makes modern car engines, nuclear reactors, bombs, electronics, cell phones, High def tv, the internet, high speed dsl connections, preditor drones, gps, and all the star wars stuff possible. Thats why calculators should not be taught until 12th grade, even in todays world. Computers are NECESSARY to actually utilize the results of this high math as the calculations would take years to do by hand, but it is NOT a chicken and egg problem, the basic math comes first, the computers, second. The computer is nothing more than a simple tool, like a power saw is to a carpenter.