It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak.
Gottlob FregeThe aim of scientific work is truth. While we internally recognise something as true, we judge, and while we utter judgements, we assert.
Gottlob FregeI compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.
Gottlob FregeThere is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height.
Gottlob FregeIt is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak.
Gottlob Frege