Nature...does not act by means of many things when it can do so by means of a few.

One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.

In time you may discover everything that can be discovered, and still your progress will only be progress away from humanity. The distance between you and them can one day become so great that your joyous cry over some new gain could be answered by an universal shriek of horror.

Facts which at first seem improbable will, even on scant explanation, drop the cloak which has hidden them and stand forth in naked and simple beauty.

I would beg the wise and learned fathers (of the church) to consider with all diligence the difference which exists between matters of mere opinion and matters of demonstration. ... [I]t is not in the power of professors of the demonstrative sciences to alter their opinions at will, so as to be now of one way of thinking and now of another. ... [D]emonstrated conclusions about things in nature of the heavens, do not admit of being altered with the same ease as opinions to what is permissible or not, under a contract, mortgage, or bill of exchange.

I think that in the discussion of natural problems we ought to begin not with the Scriptures, but with experiments, and demonstrations.

Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.