Mathematics and Faith

Just how does an abstract discipline like mathematics find itself mixed up with a notion as difficult to pin down as that of faith. What is this thing called faith anyway? As far as I can see, I never saw faith walking around, nor was I ever able to touch it. As much as I might have wanted a heavy dose of faith as a Christmas present some years, I do not ever remember anyone telling me that they just picked me up a nice piece of faith in the local mall and got a great deal on it. In the Book of Hebrews of the New Testament of the Bible we read in Chapter 11, Verse 1: "Now faith is the substance of things hoped for, the evidence of things unseen." This has always been one of my favorite Bible verses I guess because of the profound implications of the statement. Faith has to be one of the greatest gifts with which God could have endowed man.

Yet faith--in order to grow strong-- is something that needs to be put into practice regularly, just like any other muscle in the body. Use it, or lose it, as the saying goes. Faith strengthens with use while it weakens through desuetude. Faith is simply not like some other tangible thing that you can get your finger around.

Consequently, to embrace this elusive yet noble grace, man needs some kind of driver to bring faith to the surface of existence, a precursor, so to speak, which causes faith to bubble into one's life and permits easy access to such. But what is this so-called faith driver and how do we access it so as to be able to implement faith in our lives? Moreover, how can mathematics show us that faith is something real and consequently that God the Creator, as an extension of our faith, is really out there? In short, belief is the key driver of faith. For that which we believe in no longer necessitates proof of its existence.

Yet everything we believe in has required at some time or another--in some form or another--a giant leap of faith. And here is where mathematics, faith, and God all tie in together. Let me explain. In 1931, a brilliant Austrian mathematician by the name of Kurt Gödel shocked the mathematical world with his now famous Incompleteness Theorems.

Up to this time, mathematicians were working feverishly at formalizing the mathematical disciplines and trying to show that any rigorous mathematical system was consistent within itself provided that the axioms on which such system was built were solid. Kurt Gödel rocked this world with his theorems that showed that within any mathematical system there were necessarily inconsistencies and that there were theorems within the system that could neither be proved nor disproved. His seminal work at one point during his career even produced a proof which mathematically would validate God's existence. >From the above discussion, we are starting to see--albeit superficially--some connections among mathematics, faith, and God. Gödel's work helped show that mathematics is one giant leap of faith. Yet we see evidence of this leap of faith all around us.

Just think of this the next time you go to start your car and try to ponder the interconnection between mathematics, science, and the process of igniting the engine. Yes, mathematics is all around us. Faith has crystallized into belief. For me the previous exposition is easy to accept and believe. Having studied mathematics from the basic to the advanced levels, I have firmly come to believe that God speaks to us through mathematics and that His wisdom is strewn throughout the many realms of this field.

Although for some it is impossible to conceive of an all-knowing power and creator, a dive into the myriad oceans of mathematics quickly makes one realize that it is no more difficult to conceive of such a One than to ponder the complexities and realities of this extraordinary subject. After all, what is more difficult to conceive of: an infinite number of infinities or an Almighty? When I first discovered this fact about the infinity of infinities during Set Theory class my senior year in college, I was completely mesmerized. "How could this be?" I mused. Infinity means just that--infinity. No end in sight; something that goes on forever. So how could there be more than one? Even millions.

Billions? An infinity of them? Yet strange realities such as these are what we derive from mathematics. Once these realities become validated, our faith in mathematics and in a higher being becomes more real. Faith is evidence or proof of those things we cannot see. Faith validates that even though we cannot see something, i.

e. God, that that something is still real. We see and experience applications of mathematics in the real world everyday. We have automobiles and electricity and television and the computer, the latter of which has harnessed the understanding and power of binary arithmetic. We can see these applications, touch these applications and enjoy these applications. They are real.

Yet the very foundations on which such applications are built, the axiomatic systems on which all applications ultimately derive from theorems provable based on those axioms, are, according to Kurt Gödel's work, based on a certain degree of faith. The leap from proof to truth, in the end, is always based on faith. We turn on the light switch and know without hesitation the expected result: the light goes on and the room is illuminated. We have faith in the light going on because we have seen such faith demonstrated or used time and time again. We no longer hope for the light to go on as we know it will. The light turns on because man has harnessed, via a leap of faith, the electrons that pass through the wire and generate the current necessary to illuminate the room.

The light is the evidence of things (the electrons) unseen, which through faith we have come to trust and believe exist. Thus tangible things we enjoy on a daily basis prove to us that God is no more a stretch of belief for us than the simple act of expecting the light to go on after flipping the switch. .

By: Joe Pagano


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