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?
A Human Invention?
Some people have claimed that mathematics is a human invention – that human beings have invented numbers and are ultimately responsible for laws and properties of mathematics. No doubt, people invented the various notation systems we use express mathematical truths. But we are not here talking about notations. Rather, we want to understand the origin of the mathematical truths themselves. Can people take credit for the existence of mathematical laws and properties?
Such a position is very difficult to reconcile with the properties of mathematical laws. Such laws are invariant – they do not change with time. But manmade laws often change with time. There was once a law setting the national speed limit in the United States to 55 miles per hour. But that law has been repealed and is therefore no longer binding. Imagine if mathematical laws were like that. Today 2+2=4, but tomorrow, we might decide that 2+2 = 27. Would that really make it so? Somehow, we know that mathematical truths are not subject to human whims.
Furthermore, manmade laws differ from country to country – each as deemed best by their respective leaders. Are laws of mathematics like that? Does 2+2=4 only in the United States, but in Europe 2+2=38? If mathematical laws had been invented by people, then we would expect different cultures to have different laws. But they don’t. Laws of mathematics are universal.
The notion that people invented mathematics is simply not true to the history of mathematical discovery. Mathematical laws are not determined by people; rather, they are discovered by people. And to be discovered, something must already exist in advance of its discovery. Hence, human beings did not create numbers nor the relationships between them.
The ancient Greeks, for example, discovered the so-called “irrational numbers.” These are numbers that cannot be expressed as the ratio of two integers (a/b). One interesting thing about this discovery is that the Greeks were not seeking it and really didn’t want it to be true. It was contrary to their expectations and made their exploration of mathematics much more difficult that they would have preferred. This refutes the notion that such numbers are a creation of mankind. Clearly, irrational numbers were not invented by humans; rather they were discovered. And hence, they already existed before the Greeks discovered them.
Another way we know that people did not create math is because numbers and the relationships between them existed before people existed. Consider Kepler’s third law of planetary motion. This law states that the period (in years) of a planet’s orbit around the sun squared is equal to its distance to the sun (in “astronomical units”) cubed. Succinctly, p2 = a3. This mathematical truth was discovered by Johannes Kepler in the early 17th century, but it was true long before that. In fact, the planets orbited perfectly well before people even existed. Clearly, mathematical truths do not depend on people since mathematical truths existed before people.
Whose Mind?
How then do we account for the existence of numbers and the relationships between them? Numbers are defined as a concept of quantity. A concept is a mental construction and as such it requires a mind in order to exist. (If there were no minds, there could be no concepts). So whose mind is responsible for numbers?
Although human begins can think in terms of numbers, we have just seen that numbers existed before people. Numbers require a mind, and yet existed before human minds. This puts the secularist in a dreadful bind. The secularist wants to believe that the universe originally had no minds, and that the human mind evolved over time. In his view, the planets orbited the sun for millions of years before minds evolved. And yet, the planets orbited according to laws of mathematics which are conceptual and thus require a mind. Hence, the secularist must both reject and accept the existence of minds before people, which is contradictory.
Conversely, the biblical position is rational because the Christian understands that there has never been a time when no minds existed. The mind of God has always existed because God is eternal. God’s mind is ultimately responsible for the existence of numbers and the relationships between them, which we refer to as mathematics. We can account for the orbits of the planets before people existed because God’s mind was in control of the universe then as it is now.
Notice that the Christian position makes sense of the laws of mathematics and their properties. We saw previously that laws of mathematics are universal – they work everywhere. This makes sense because God is omni-present and sovereign over the entire universe (Jeremiah 23:24; Psalm 139:7-10; Hebrews 1:3; Isaiah 46:10-11). Furthermore, we saw that laws of mathematics are invariant – they do not change with time. This logically follows because God does not change with time (Malachi 3:6). He is, after all, beyond time and is in fact the Creator of time. As an eternal being beyond time, God’s thinking does not change with time. We can rest assured therefore that laws of mathematics will be tomorrow and forever just as they are today.
In the Christian position, we can make sense of the fact that there are patterns in numbers, and laws that describe such patterns. God’s thinking is rational and orderly, and hence the way He thinks about numbers will be logical and orderly. We can make sense of the fact that mathematics is infinite, because the mind of God is infinite (Psalm 147:5). We can make sense of the fact that human beings can systematically discover some of the laws of mathematics. This is because we are made in the image of God (Genesis 1:26-27), and therefore have the capacity to think, at least in a finite way, after His character (Isaiah 1:18, 55:7-8). And God has revealed some of His thoughts to us. We have revelation from God and can therefore discover at least some of God’s thoughts.
In the Christian worldview, we can make sense of the fact that mathematics has application to the physical world. We expect physical reality to obey mathematical laws, because the mind of God is responsible for both. Mathematics is the study of the way God thinks about numbers, and the physical universe is controlled by the mind of God (Hebrews 1:3). Hence, the physical universe will obey mathematical laws. Yet, the secular worldview cannot account for this. Mathematics is rooted in the Christian worldview.
Notice that this argument will not work for other gods. It is the Christian God who is omni-present, sovereign, unchanging, beyond time, and who has revealed Himself to mankind. Only the characteristics of the biblical God can make sense of the existence and properties of mathematics. Any other hypothetical god would have to have exactly the same characteristics of the biblical God, and yet this other god has not revealed himself in the Bible. Without revelation, we couldn’t actually know anything about God.
How do we Know?
The secularist is unable to make sense of mathematics. He can do mathematics only because he too is made in God’s image and must rely upon biblical principles. But he cannot make sense of what he is doing based on his professed secular worldview. The secularist accepts that laws of mathematics are universal, but how could he possibly know that on his own worldview? After all, he doesn’t have universal experience. On the contrary, all human experience is limited to one tiny solar system, and most people haven’t even left the one planet. Yet astronomers assume that laws of mathematics work in the distant universe just as they work here on Earth. Why is that?
The secularist accepts that laws and properties of mathematics will work tomorrow just as they worked today. But how does he justify that assumption? It won’t do to say that they worked in the past because many things are true of the past that are not true of the future. For example, I have never died in the past; can I therefore conclude that I am immortal – that I will never die in the future? How can a secularist possibly know anything about a future that he has never experienced? And yet he banks on laws of mathematics working in the future as they have in the past. Why?
And apart from the Christian worldview, why expect the physical universe to obey mathematical laws? Every scientist does. But what is the basis for such an expectation? After all, mathematical laws are conceptual, but the universe is physical. Why do physical atoms respond to conceptual ideas? The Christian worldview expects this. The secular worldview cannot. In fact, the Nobel-prize winning physicist Eugene Wigner documented and explained the fact that his (secular) worldview could not account for the success of mathematics when applied to the physical world.[1] But why do secularists accept truths that only make sense in the biblical worldview?
The answer is found in Romans 1:18-25. The Bible teaches that God has made Himself inescapably known to all people. The Lord designed us in such a way that when we look at the world, we immediately recognize it as the creation of God. Even unbelievers cannot escape this knowledge, but they suppress it (Romans 1:18). They do not want to believe in the biblical God. They would prefer to make up another god more suitable to their preferences, or to have no god at all – effectively making themselves a god. They work very hard at this, attempting to convince others and themselves that they do not believe in the biblical God. Yet, they cannot suppress their knowledge of God completely. It is revealed in their behavior, such as their confidence in mathematics.
When it comes to biology, geology, or astronomy, secularists can delude themselves into thinking that evolution can somehow account for the patterns we see in nature. But numbers do not evolve. When it comes to mathematics, everyone must think as a biblical creationist.
[1] Wigner, E., “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Communications in Pure and Applied Mathematics, Vol 13, No 1, February, 1960.