Ancient Greek used geometry as a tool to understand and construct mathematics. When they did this, they used metaphysics to penetrate it. Today education does not use metaphysics any more except a case in which learners learn philosophy at universities. My question: how do you expect learners learn mathematics without knowing metaphysics if they approach Greek style of learning mathematics? In order to teach learners without using algorithm,learners must be taught some kind of tool that replaces algorithm before they approach mathematics without algorithm. In my view, metaphysics is much much harder than algorithm. It is better to keep algorithm, otherwise, most learners will fail to understand mathematics.