Mathematics is the gate and key of the sciences. ... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know… - Roger Bacon

Et hæc scientia certificat omnia naturalia et artificialia in particulari et in propria disciplina, per experientiam perfectam; non per argumenta, ut scientiæ pure speculativae, nec per debiles et imperfecta experientias ut scientiae operativæ. Et ideo hæc est domina omnium scientiarum præcedentium, et finis totius speculationis.

All these foregoing sciences are, properly speaking, speculative. There is indeed in every science a practical side, as Avicenna teaches in the first book of his Art of Medicine. Nevertheless, of Moral Philosophy alone can it be said that it is in the special and autonomatic sense practical, dealing as it does with human conduct with reference to virtue and vice, beatitude and misery. All other sciences are called speculative: they are not concerned with the deeds of the present or future life affecting man's salvation or damnation. All procedures of art and of nature are directed to these moral actions, and exist on account of them. They are of no account except in that they help forward right action. Thus practical and operative sciences, as experimental alchemy and the rest, are regarded as speculative in reference to the operations with which moral or political science is concerned. This science is the mistress of every department of philosophy. It employs and controls them for the advantage of states and kingdoms. It directs the choice of men who are to study in sciences and arts for the common good. It orders all members of the state or kingdom so that none shall remain without his proper work.

Prudens quaestio dimidium scientiae.