There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured ... Of these sciences the gate and key is mathematics ... He who is ignorant of this [mathematics] cannot know the other sciences nor the affairs of this world.

All science requires mathematics.

... mathematics is absolutely necessary and useful to the other sciences.

Mathematics is the gate and key to science.

There are four chief obstacles in grasping truth ... namely, submission to faulty and unworthy authority, influence of custom, popular prejudice, and the concealment of our own ignorance accompanied by an ostentatious display of our knowledge.

But concerning vision alone is a separate science formed among philosophers, namely, optics, and not concerning any other sense ... It is possible that some other science may be more useful, but no other science has so much sweetness and beauty of utility. Therefore it is the flower of the whole of philosophy and through it, and not without it, can the other sciences be known.

Reasoning draws a conclusion, but does not make the conclusion certain, unless the mind discovers it by the path of experience.