He had collected observations of the stars and used all his mathematical knowledge to explain them.

他曾经收集过观察星球的数据，并且利用他的全部数学知识来解释这些数据。

Without kings, without bureaucracies, without standing armies, these early farming populations fostered the development of mathematical knowledge, advanced metallurgy.

没有国王，没有官僚机构，没有常备军，这些早期的农业人口促进了数学知识和先进冶金技术的发展。

Physicists appear to be unconscious of the gulf, while psychologists, who are conscious of it, have not the mathematical knowledge required for spanning it.

物理学家似乎没有意识到鸿沟， 而意识到它的心理学家却没有跨越它所需的数学知识。