In describing the characteristics of a scientific investigator, Liebig once pointed out that certain disciplines, like mathematics, are merely an indispensable instrument for the attainment of scientific ends. He remarked that it is not the mere instrument which plans and executes the work, but the human intellect. It is obvious that without the power of observation, without sagacity, all mathematical knowledge is useless. We may imagine a man who, favored by a good memory, has rendered himself intimately acquainted with every theorem of mathematics and has obtained an eminent degree of skilfulness in handling this instrument, but is altogether unable to invent a problem for solution. If we propose to him a problem, and thus give him the conditions for its solution, he will succeed in obtaining an answer by performing the current operations with which he is familiar, and express it in a formula consisting of certain symbols, the meaning of which, however, is perfectly unintelligible to him, because he is deficient in other attainments essential for judging of its truth. Such a man is a mere calculating machine. But as soon as he possesses the capacity and the talent of proposing a question to himself and testing the truth of his calculations by experiment, he becomes qualified to investigate nature. For whence should he derive his problems, if not from nature or from life?
Scientific Inquisitiveness—An Anecdote. JAMA. 2016;316(11):1219. doi:10.1001/jama.2015.17102