Roger Bacon - Opus Majus (1267)

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If in other sciences we should arrive at certainty without doubt and truth without error, it behoves us to place the foundations of knowledge in mathematics.

Roger Bacon
For the things of this world cannot be made known without a knowledge of mathematics.

Roger Bacon
Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience.

Roger Bacon
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 the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy.

Roger Bacon
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.

Roger Bacon
I shall draw, therefore, a figure in which all these matters are made clear as far as possible on a surface, but the full demonstration would require a body like the eye in all the particulars aforesaid. The eye of a cow, pig, and other animals can be used for illustration, if anyone wishes to experiment.

Roger Bacon
The knowledge of mathematical things is almost innate in us... This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.

Roger Bacon
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.

Roger Bacon
For vacuum rightly conceived of is merely a mathematical quantity extended in the three dimensions, existing per se without heat and cold, soft and hard, rare and dense, and without any natural quality, merely occupying space, as the philosophers maintained before Aristotle, not only within the heavens, but beyond.

Roger Bacon
But we must here state that we should not see anything if there were a vacuum. But this would not be due to some nature hindering species, and resisting it, but because of the lack of a nature suitable for the multiplication of species; for species is a natural thing, and therefore needs a natural medium; but in a vacuum nature does not exist.

Roger Bacon
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.

Roger Bacon
Mathematics is absolutely necessary and useful to other sciences.

Roger Bacon