Mathematics must take its motivation from concrete specific substance and aim again at some layer of "reality." The flight into abstraction must be something more than a mere escape; start from the ground and reentry are both indispensable, even if the same pilot cannot handle all phases of the trajectory.
A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range.
I must warn you that Gurdjieff is far more of an enigma than you can imagine. I am certain that he is deeply good, and that he is working for the good of mankind. But his methods are often incomprehensible. For example, he uses disgusting language, especially to ladies who are likely to be squeamish about such things. He has the reputation of behaving shamelessly over money matters, and with women also. At his table we have to drink spirits, often to the point of drunkenness. People have said that he is a magician, and that he uses his powers for his own ends... I do not believe that the scandalous tales told of Gurdjieff are true: but you must take into account that they may be true and act accordingly.
My thesis, paradoxically, and a little provocatively, but nonetheless genuinely, is simply this : PROBABILITY DOES NOT EXIST. The abandonment of superstitious beliefs about theexistence of Phlogiston, the Cosmic Ether, Absolute Space and Time,..., or Fairies and Witches, was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs.
Man is what he is, because a spiritual element has entered into, and taken possession of, animal consciousness. This spiritual element is not, according to Christian teaching, divine: but it is capable of entering into relations with God. It can perceive Him: in thought, it can reason as to His nature and actions: in will and feeling, it can serve and love Him, or disobey and fear Him. Such activity shows itself in what we call the working of conscience.