Mathematics is a broad term that describes the methods and languages that we use to reason a problem through from start to finish. The fundamental basis for mathematics is its undefined terms, axioms, definitions, and theorems. In order to understand and communicate ideas in math, we have to have a firm understanding of the basis of mathematics from which we can build arguments and proofs. Altering assumptions, such as the undefined terms, change the entire way we approach problems and describe reality.
Say we change what makes a line a line. As opposed to a continuous extent of length, straight or curved, without breadth or thickness; the trace of a moving point. Let it be a race of a moving point with a breadth and thickness. Well, now the whole concept of dimensions is altered we have no real way to describe two-dimensional space without the concept of a straight line with no breadth. The assumptions change the outcome of the entire system. Likewise, in life when we deal with absolute truths, a slight change in the context or assumptions of reality change how we describe and understand the world.
In life, we make assumptions based on our world view. After all, no one is one hundred percent certain on the issues of creation and the cosmos. This is why we as Christians have to have faith and believe that there is a triune God whose love for us led him to sacrifice his own son for our salvation. However, even a skeptic or an atheist has to have faith in their worldview. Their assumptions are alternative to Christians and this shapes the way they view life. This is similar to the example I used when we alter the assumption of what a line is, when we have faith, we make an assumption and a change in that assumption changes our worldview.
Christians view the world through the lens of scripture and the assumption that it is the word of God. This establishes our view of the world and establishes how we define terms. In other words, the bible is our rule book for our axiomatic system of reality. With such a rule book we can say that God is the absolute truth and the purpose of math, and life, is to discover and describe that absolute truth. Having a biblical outlook on life helps one see the truth in math and make sense of the world. To me it seems that there is more of an intellectual jump to have faith in the assumption that God does not exist and that reality is not based on absolute truth, rather a seeming randomness that generated this universe and maybe many more.
Since we are describing the universe as an axiomatic system and God’s word is the rulebook, let’s explain what that means. It is important that whichever worldview one chooses fulfills certain criteria. The worldview we have must be consistent – an axiomatic system is consistent if the axioms cannot be used to prove a particular proposition and its opposite, or negation. It cannot contradict itself. It must have independence – an axiomatic system is independent if you cannot get one axiom from another. All axioms are fundamental truths that do not rely on each other for their existence. They may refer to undefined terms, but they do not stem one from the other. And the worldview must be complete – whatever we attempt to test with the system will either be proven or its negative will be proven. As a ultimate being, God fulfills all criteria. Atheism does not.
To prove something in math, you must explain every step and know that each step followed the assumed rules laid out in the fundamentals of math. If there is a faulty assumption, then it will prove difficult and maybe impossible to truly prove something. This mathematical truth can be extrapolated into the discussion of absolute truth. To have a faulty assumption in your worldview, it can prove difficult or even impossible to find peace, joy, and purpose in life. This is why it is crucial to have faith in God and to establish a personal relationship based on an assumption of a loving, omnipotent, omnipresent, and omniscient father.