[Originally published as part one of Evolutionist Math]
You have probably heard of evolutionary biologists—those who study biology from the perspective of Darwinism. And you have probably heard of evolutionary geologists, or evolutionary astronomers—those who study their respective disciplines from secular assumptions of origins. But have you ever heard of evolutionary mathematics? No doubt there are some mathematicians who believe in neo-Darwinian evolution, but can math itself have an evolutionary origin? What would that even mean?
We can consider, at least as a hypothetical scenario, the idea of particles-to-people evolution in the field of biology because we know that organisms change over time. We know that descendants are not exactly the same as their ancestors. And therefore, it is natural to ask what kinds of changes are possible. The evolutionist believes that organisms like fish can eventually give rise to organisms like people.
The creationist argues that organisms diversify but remain the same basic kind. Contrary to the straw-man arguments asserted by some evolutionists, creationists do believe that animals change over time—but that there are natural limits to such change. The fact that organisms change means that we can intellectually consider (for the sake of argument) either creation or evolution as a possible scenario to explain the patterns we find in living organisms today.
Likewise, the Earth changes over time. Canyons deepen a bit each year, and continents erode a bit with time. We can attempt to explain Earth’s features either in light of the history provided in Scripture (such as supernatural creation and the global flood), or under the assumption of uniformitarianism—that slow and gradual processes are responsible for most of Earth’s features. Hence, we can look at geology from either a creation or evolutionary perspective.
And since things change in outer space, the same reasoning applies to astronomy.
Granted, we would argue that the evolutionary interpretations of biology, geology, and astronomy are riddled with difficulties, and ultimately self-refuting since science is based on the principles of biblical creation. Nonetheless, the fact that things change allows evolutionists to imagine an evolutionary scenario to account for the patterns we observe in the physical world.
But what about the world of mathematics?
How can we account for the patterns we observe in numbers? Since numbers do not change, there can be no such thing as “evolutionary math.” Hence, the patterns in mathematics can only be explained from a creationist perspective. As such, the existence of mathematical truths is a confirmation of creation and a refutation of any secular position on origins.
What is Mathematics?
Mathematics is the study of the relationships between numbers. When we discover a pattern such as “a positive number multiplied by a negative number always yields a negative number,” we are doing mathematics.
Over the course of history, mathematicians have discovered many patterns between numbers which we call “laws” or “properties.” There is the commutative property of multiplication, for example, which tells us that the order of terms in a finite product does not matter; that is a × b = b × a. This is a property because it is universal—it works for all numbers. It doesn’t matter what number you pick for a or what number you pick for b. It will always be the case that a × b = b × a. Laws/properties of mathematics are universal.
Furthermore, laws and properties of mathematics are invariant—meaning they do not change over time. The commutative law of multiplication has always been exactly what it is today. It has always been true and will always be true. This is the case with all laws and properties of mathematics.
Consider the simple equation 1 + 1 = 2. Was there ever a time when this was not so? Clearly not. We trust that 1 + 1 = 2 everywhere in the universe and at all times.
Given that laws of mathematics are universal and invariant, it follows that they did not evolve. It is not as though in the distant past 1+1 equaled 1, and then gradually over millions of years, 1+1 equaled 1.3, then 1.5, and so on until it eventually equaled 2 as it does today. We cannot account for the properties of mathematics by supposing that they changed over time because mathematics does not change with time. Hence, the properties and laws that express the relationships between numbers are only compatible with a creationist worldview—not an evolutionist one.
To be clear, I am not discussing notations or definitions. Notations are the way human beings have chosen to express or represent numbers and the relationships between them. Notations can change over time as human beings decide to experiment with different systems.
Even today, several different notation systems exist. We can write the number six as a word “six” or as an Arabic numeral “6” or as a Roman numeral “VI.” But these all mean the same thing; they express the same mathematical concept.
Furthermore, human beings get to define what mathematical operators mean; hence we have decided that the “+” operator means addition. But once the definitions are in place, the mathematical truths that follow are not determined by people, and do not change over time.
What are Numbers?
We use them every day, but few people have stopped to contemplate the question, “what exactly are numbers?” Numbers are defined as a concept of quantity. As a concept, numbers exist in the mind. They are abstract, not physical. You can think a number, but you cannot touch a number because it is not made of atoms.
The representations we use to express numbers may well be physical. We can write the numeral “3” on a piece of paper, and the ink will be made of atoms. The numeral is tangible, but not the concept it represents. After all, we could then burn the paper, destroying the numeral “3” and yet the concept of “3” would remain.
Numbers conceptualize a quantity. Often such a quantity may be of tangible items, such as apples. You can touch three apples, or three bananas, but the concept of “three-ness” cannot be touched because it exists in the mind.
One of the amazing things about mathematics, and this partially accounts for its usefulness in the physical world, is that numbers can be abstracted from the objects they quantify. In elementary school, students learn that if you have three apples, and two are removed, you will have one left. But this rule also applies to bananas, oranges, rocks, houses, molecules, aardvarks, quasars, and anything else you can dream up. It is a universal principle that 3-2=1.
We are tempted to ask, “three of what, minus two of what, equals one of what?” Amazingly, the answer is, “It doesn’t matter.” Laws and properties of mathematics work regardless of the physical objects (if any) to which they are applied. How then can we make sense of the patterns we observe between numbers?