Faith is one of the least accepted WoK, since it is considered by many to not bring any new knowledge to several AoK, and only really be useful in Areas such as Religious Knowledge systems. Although this is not true, since Faith can actually be used in many other AoK (such as Natural Science when doing experiments), the statement that it does not apply to all AoK may not be completely false.

Faith finds its complete opposite in Mathematics. Mathematics is based entirely on proof: the way in which we understand and explore it is through theorems, and in order to be approved theorems need proof. For example, the Pythagoras Theorem states that in a right triangle (a triangle in which to of the sides make a right angle), the square of the side opposite the right angle (hypotenuse) equals the square of the other two sides: c^{2} = a^{2} + b^{2}. It can be proven with this simple image:

(Here, c represents the hypotenuse, and a and b represent the other two sides of each triangle.)

Since Faith implies believing without proof, it seems that there is no way in which Mathematics and Faith could ever be reconciled. Though it could be argued that theorems are based on axioms, which do not require proof, this is not a very solid argument, since axioms are, by definition, “self-evidently true, and therefore do not require proof”. However, it may be fair to say that, in order to create a theorem, one must put together different axioms and have faith that they will work out the way they are supposed to.

To sum up, though Faith may have some minor uses in Mathematics, it is not used much, if at all, when gaining knowledge in this particular AoK.

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