The Answer is . . . Yes
Is mathematics subjective or objective? This is a big question yet we can answer this in one word: Yes. Now wait, how can math be both subjective and objective? Isn’t that a contradiction? Indeed it would be a contradiction unless we clarify what is meant in the initial question. If we are asking about math in its entirety, then absolutely this would be a contradiction; if we are asking about individual elements of math, then this is actually not a contradiction. One word will obviously not suffice, so let’s take a closer look.
Before we look at the well-known example of 1 + 1 = 2, let’s first note a few things. Firstly, math is abstract. It’s not tangible yet we know that it exists. Similarly, emotions and feelings are abstract yet they obviously exist as well. We take note of this because these subjects can be become fairly complicated the further we go; however, just because we might not understand something fully or just because something isn’t tangible, or isn’t able to be seen with our eyes, doesn’t mean it doesn’t exist or it is entirely subjective.
Secondly, symbols and methods in math are subjective. When we look at cultures throughout history such as Ancient Egypt, Mesopotamia, or Greece, we see that each had their own symbols that stood for numbers. In Mesopotamian culture, a symbol that represented “1” stood for what we know as the number 60. Similarly, finding the volume of a prism for example was majorly different in those cultures than our modern math today. However, the crucially important thing to understand is that though the methods and symbols used to get to the answer differed, the answer that they came to was the same.
What does this mean? Well it directly tells us that the symbols and methods used are subjective. If you look in a math textbook, you might see something to the effect of “There are multiple ways to reach the same answer.” The example also tells us that an explicit answer is reached. Note that it says “answer” and not “answers”. We do recognize that there are limitations to calculations. Some tools might give a minutely different answer as compared to another, but we know that the difference is not based on thesubjectivity of the foundation of math but with the limited capabilities of technology and human ability.
The Fine Example of Gasoline, Cars, and Emotions
Let’s now look at 1 + 1 = 2. We understand that each symbol we see in the proposition is subjective. In our culture, we have assigned values to each of these symbols, however, that does not mean what the symbols stand for rely on the symbols themselves. So then, is the core of 1 + 1 = 2 subjective? That is, what the symbols stand for? The answer is no. Why? Well, we know that emotions are objective. The way we might describe them or understand them are subjective, but at their core, they’re objective. The name we assign to anger, for example, does not matter, and we can describe it as best as we can, but we know the basic emotiondoesn’t change. The feeling of anger is anger and it is universal. Math is math; the core of it doesn’t change and we can’t bend it to mean something else other than what it is, that would be simply absurd! Next time you go to the gas station, try filling up your 14-gallon fuel tank with 16 gallons of fuel…I’m guessing it wouldn’t go too well. We can use any measuring system, change any symbol name, or use any symbol we like, the inherent truth of that fuel-tank though is that it can only hold a finite amount of space. An objective amount of space.
Ultimately and most importantly, math is objective and holds together because it is a reflection of a creator and designer who is God. Let’s take a look at some scripture passages:
The Basis For True Mathematics
“In the beginning God created the heavens and the earth. Then God saw that everything that He had made, and indeed it was very good. So the evening and the morning were the sixth day.” ~ Genesis 1:1,31
For by Him all things were created that are in heaven and on earth, visible and invisible, whether thrones or dominions or principalities or powers. All things were created through Him and for Him. And He is before all things, and in Him all things exist. ~ Colossians 1:16-17
You are worthy, O Lord, to receive glory and honor and power; for You created all things, and by Your will they exist and were created. ~ Revelation 4:11
Truth shall spring out of the earth, and righteousness shall look down from heaven. ~ Psalm 85:11
Not only do we see that God has created all things, but through Him they exist. Math was ultimately created by God and through Him, it exists and holds together. Now, how does it reflect Him?
“I am the Alpha and the Omega, the Beginning and the End,” says the Lord, “who is and who was and who is to come, the Almighty.” ~ Revelation 1:8
We learned from an early age that numbers go on for infinity. What is the largest number? Well there isn’t one; they go on for infinity. Math reflects God because God is infinite. Many places in Scripture tells us of God being eternal and that His attributes are eternal and infinite. Revelation 1:8 is just one passage that highlights this truth. The only plausible way for a concept that is infinite to exist is by an infinite creator.
Where do we go from here? We recognize that math is abstract and can be difficult to understand, and it has subjective elements that rely on the direction of humans and cultures (names of signs, methods, etc.); however, those elements rely on the objectivity of the core of math which ultimately owes its existence and continuity to and through the infinite Creator, God.
Next time you go fill your vehicle with fuel, ask yourself why the fuel-tank can only hold 14-gallons of fuel.
Beck Crandall is a current undergraduate student at Thomas Edison State University majoring in a degree in Mathematics. He serves in playing music and operating sound at his Church body in New York and works part-time for a small business. He enjoys spending time with friends and family, creating music, hiking, and enjoying God’s creation. Ultimately, he is a sinner saved by God’s grace.