*Every branch of mathematics has key results that are so*

important that they are dubbed **fundamental theorems.**

The customary view of mathematical research is that of establishing the truth of propositions or theorems by rigorous deduction from axioms and definitions. Mathematics is founded upon axioms, basic assumptions that are taken as true. Logical reasoning is then used to deduce the consequences of those axioms with each major result designated as a theorem.

As each new theorem is proved, it provides a basis for the establishment of further results. The most important and fruitful theorem in each area of maths is often named as the *fundamental theorem* of that area. Thus, we have the fundamental theorems of arithmetic, algebra and so on. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus.

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