Proof: How it Differs in Math, Science, and Life
My favorite math professor once said, “You can’t use mathematics to provide an absolute proof of God. The existence of God boils down to the acceptance of a faith axiom based on a vast amount of evidence.” It was a big idea for a young man like myself, and it sparked a lifelong interest in integrating mathematics with religion and philosophy. It led me to ask, How does “proof” in mathematics differ from proof outside of mathematics?
Mathematicians tend not to ask this question because our discipline operates in a comfort zone. We start with a finite set of statements called axioms(assumptions). Such statements are assumed true. Using rules of logic, further true statements are proved by starting with the axioms. The proven statements as well as the axioms are referred to as theorems. In short, the process is like a game. The axioms are the pieces and the logic provides the rules, that allow a string of proven statements.
Furthermore, a property demanded of every mathematical system is that it be consistent, meaning that there is no statement “Q” such that both “Q” and “not-Q” are theorems of the same mathematical system. If such a contradiction were the case, then every statement can be proved as a theorem, and no discernible real truth prevails.
Outside the field of mathematics, however, proofs are created in a zone of less comfort. Researchers using the scientific method begin with an hypothesis, or assumption. Then they design experiments to test the hypothesis. Experiments provide evidence that is observable, empirical, measurable, and subject to reason. Just as important, experiments must be repeatable. If carried out in an unbiased manner, they should always show the same result. The scientist must then make all these findings available to others, who may question the results or want to test them once again…
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