1) This world is an aenigma of God. In thought of Nicholas of Cusa we can find out the idea of the aenigma. This idea has naturally its origin in the New Testament, 1 Corinthians 13, 12 : For now we see in a mirror, dimly, but then face to face. Now I know in part, but then I shall know just as I also am known. But Cusa develops a new affirmative aspect of the aenigma from its origin, namely though we cannot the truth itself in this world, we can see vaguely something of the truth, if we look at the creature carefully, because this world as a whole is an aemigma of God.
2) Cusa's interest in mathematics and geometry. In cusa's erliest work, "De concordantia catholica" there is no special interest in mathematics and geometry, but since one of his main books, "De docta ignorantia" he has a strong interest in them. In this book he says, that mathematics is very much useful to us for a apprehension of the divine. Then how is it useful? For example if we imagine an infinite straight line and
an infinite circle, then this circle has an infinite circumference, and as a result it coincides with the infinite straight line. So in geometry we must sometimes accept a ridiculous fact, that we can never experience in this world. In this point Nicholas of Cusa finds out a useful method, by which we can understand something about the infinite God, who is transcendent.
3) World and Nature. Cusa's concept of nature means the world as a whole in motion. (Cf. "De docta ignorantia" II, c. 10.) This motion comes from the 'spritus unversorum'. From this thought Nicholas elaborates the famous Idea of an infinite cosmos and an Idea of the earth in motion. The Idea of the earth in motion was very tremendous for the medieval Thinkers, because the motion at that time meant the imperfection of a being. But Nicholas could overcome the difficulty with his own concept of the famous 'coincidentia oppositorum'. Namely the maximal motion coincides with the maximal standstill.
4) Nature has a hierarchical order, which is in motion. Cusa's concept of Nature, that it has a hierarchical order, but that the order as a whole is in motion, was at that time indeed new. And he thinks that in the hierarchical order one thing, which is right in the lower order, can be right even in the higher order (Cf. "De concordantia catholica, I, c.XXi, n.192 etc.). But it is usually quite not logical. Why can he insist so? If we see the difference in the hierarchical order from an absolute viewpoint of God, then the relative difference between the orders can disappear. Then the concept of Uniformity of nature, that the modern natural science supposes, can easily come in to being from this thought. But we must note that Nicholas' own end of his study concerning nature is the arrival at the truth of God, which is behing the aenigma of the nature, not the solution of a puzzle of nature. Less