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Consider the Extent to Which Complete Certainty Might Be Achievable in Mathematics and at Least One Another Area of Knowledge.

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Mathematicians have the concept of rigorous proof, which leads to knowing something with complete certainty. Consider the extent to which complete certainty might be achievable in mathematics and at least one another area of knowledge.

When we look at it at first mathematics and history seems to be two areas of knowledge where proof leads to absolute certainity on the subject. A large proportion of people believe that in history that if there is an evidence based on a claim , whether big or small, then the claim is true. But the actual thing is if there is a proof based on a claim it gives us an idea about the claim and the rest we will have to figure out with our own perception and reasoning skills. Mathematics is comparatively free of all other ways of knowing other than reasoning. Certainty in mathematics need not always be achieved through proof. Consider the case of axioms. Consider the axiom which suggests that things that are equal to same thing are equal to one another. There is actually no formal proof which backs up this axiom or any other axiom. It is just right under your nose. Although it is said rigorous proof leads to complete certainty in mathematics, as we look more deep into the areas of knowledge the level of uncertainity increases. Proof in mathematics is completely different from proof in history. The definition of proof differs in both the contexts. In mathematics proof, refers to a multitude of theorems and definitions that you derive from a certain assumption or set of assumptions which is based on what you set out to prove or what you wanted to derive from a group of factors. And whichever method you use, it leads to the same result. The proof in mathematics for a certain topic can be found by any person depending on the dedication given to achieve the result. The proof is not something that is tangible.

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