Verbiage Quotes (3 quotes)
A mathematician who can only generalise is like a monkey who can only climb UP a tree. ... And a mathematician who can only specialise is like a monkey who can only climb DOWN a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise. ... There is, I think, a moral for the teacher. A teacher of traditional mathematics is in danger of becoming a down monkey, and a teacher of modern mathematics an up monkey. The down teacher dishing out one routine problem after another may never get off the ground, never attain any general idea. and the up teacher dishing out one definition after the other may never climb down from his verbiage, may never get down to solid ground, to something of tangible interest for his pupils.
If it were possible for a metaphysician to be a golfer, he might perhaps occasionally notice that his ball, instead of moving forward in a vertical plane (like the generality of projectiles, such as brickbats and cricket balls), skewed away gradually to the right. If he did notice it, his methods would naturally lead him to content himself with his caddiess remark-ye heeled that yin, or Ye jist sliced it. But a scientific man is not to be put off with such flimsy verbiage as that. He must know more. What is Heeling, what is slicing, and why would either operation (if it could be thoroughly carried out) send a ball as if to cover point, thence to long slip, and finally behind back-stop? These, as Falstaff said, are questions to be asked.
The folly of mistaking a paradox for a discovery, a metaphor for a proof, a torrent of verbiage for a spring of capital truths, and oneself for an oracle, is inborn in us.