British Mathematician Quotes
In our daily walks we tread with heedless step upon the apparently uninteresting objects of which it [geology] treats; but could we rightly interrogate the rounded pebble in our path, it would tell us of the convulsions by which it was wrenched from its parent rock, and of the floods by which it was abraded and placed beneath our feet.
Particulars are frequently fallible, but universals never. Occult philosophy lays bare Nature in her complete nakedness, and alone contemplates the wisdom of universals by the eyes of intelligence. Accustomed to partake of the rivers which flow from the Fountain of Life, it is unacquainted with grossness and with clouded waters.
One thing at least they have not forgotten, that geometry is nothing if it be not rigorous, and that the whole educational value of the study is lost, if strictness of demonstration be trifled with. The methods of Euclid are, by almost universal consent, unexceptionable in point of rigor. Opening Address by the President, Section A
That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea. But mathematical texts generally begin the story somewhere in the middle, leaving the reader to pick up the thread as best he can.
To [the scientific man] the discovery of a new law of nature, or even of a new experimental fact, or the invention of a novel mathematical method, no matter who has been the first to reach it, is an event of an order altogether different from, and higher than, those which are so profusely chronicled in the newspapers.
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.
I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalize in different directions - they are not just repetitions of each other.