Die Mathematiker sind eine Art Franzosen. Spricht man zu ihnen, so übersetzen sie alles in ihre eigene Sprache, und so wird es alsobald etwas ganz anderes.
Mathematicians are a kind of Frenchmen. Whenever you say anything or talk to them, they translate it into their own language, and right away it is something completely different.

Most classifications, whether of inanimate objects or of organisms, are hierarchical. There are 'higher' and 'lower' categories, there are higher and lower ranks. What is usually overlooked is that the use of the term 'hierarchy' is ambiguous, and that two fundamentally different kinds of arrangements have been designated as hierarchical. A hierarchy can be either exclusive or inclusive. Military ranks from private, corporal, sergeant, lieutenant, captain, up to general are a typical example of an exclusive hierarchy. A lower rank is not a subdivision of a higher rank; thus, lieutenants are not a subdivision of captains. The scala naturae, which so strongly dominated thinking from the sixteenth to the eighteenth century, is another good illustration of an exclusive hierarchy. Each level of perfection was considered an advance (or degradation) from the next lower (or higher) level in the hierarchy, but did not include it.

Statistics: The only science that enables different experts using the same figures to draw different conclusions.

That is the way of the scientist. He will spend thirty years in building up a mountain range of facts with the intent to prove a certain theory; then he is so happy with his achievement that as a rule he overlooks the main chief fact of all—that all his accumulation proves an entirely different thing.

The truth us that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space.