By Kenneth Nehrbass
Is God a mathematician? asks astrophysicist Mario Livio (2009). To evangelicals, the question may sound like Livio is interested in how the laws of the universe point to a God who created such an orderly universe, with purpose and brilliance. However, while the field of faith integration has helped Christians to make such connections between creation and God’s character (Poythress, 2015), Christendom has not always been quick to embrace the notion that the laws of nature are God’s “other book” (ie., His handiwork on display for us to marvel at His beauty). Livio’s question can be answered by exploring four related questions:
1. If math is supreme, what room is there for God?
Actually, the nuances of Livio’s question demonstrate that many people (whether Christian or not) believe that mathematics subverts the faith. Livio’s question may be more accurately posed, “Can all that we used to ascribe to God really be explained by mathematicians?” For example, if we can use math to discover the probability of a hurricane hitting the coast of Florida this year, or the likelihood of a man in Zambia living to the age of 76, what room is there to describe natural disasters as “acts of God” or death as an event that comes in “God’s timing?” Or if mathematicians can calculate the probability (not the “chance”) of any number turning up through the roll of a pair of dice, how does God figure into the equation? On a grander scale, despite formulating the law of gravity, Newton could only conceive that it was God’s hand which held the planets eternally in orbit. However, once physicists used mathematics to calculate the rate that the universe has been expanding (only to collapse at some point), how then should we conceive of God’s role in holding the universe together?
2. Where do the laws of math come from?
God’s role in all of this has to do with the origin of the laws of math. As early as Plato, thinkers have tried to understand what put these mathematical “laws” into place. Are they human, divine, or simply “there?” Math seems to be perfect, its laws are unbreakable, and it is true for all times and places—these are characteristics we usually reserve only for God. Are mathematical truths eternally true, because they are located in God’s very nature? Or are they contingent truths, created by Him, but nonetheless perfect and eternal? Or are the laws of math and physics merely human inventions?
Christians have tended to be empiricists, believing that natural laws were established by an omnipresent, omnipotent and eternal God, yet can be discovered through rational thought and empirical study. However, if mathematical laws are true apart from human existence (ie., they are not social constructs), and in fact are true regardless of whether matter ever existed, then they must belong to the realm of “ideas” rather than the realm of matter. If that’s the case, why does the universe – made up of physical matter – obey something from the world of ideas? This points to the mystery of the relationship between the eternal and the created.
3. What is the relationship between the eternal and the material world?
Livio explains that what finally helped scientists find the connection between the physical world and the world of ideas was an innovation from Rene Descartes. Note that Livio is not referring to Descartes’ famous effort to prove his own existence (and God’s)- in fact, the success of Cartesian philosophy is questionable, because as soon as Descartes published it, French philosophers pointed out, “Your entire argument relies on human reason, but you have not shown that human reason is reliable.” That’s why Descartes went on to argue the ramifications of Anselm’s (more enigmatic) ontological argument for God.
Actually, Livio points out, it was Descartes’ discovery of the relationship between algebra and geometry—something that plagued mathematicians for 2000 years – that had a more lasting impact. (He discovered that any line, circle, wave, etc., on a graph can be expressed in algebra, and vice versa). Before Descartes, algebra belonged to the world of ideas—it was believed to be true eternally, whereas Euclidean geometry belonged to the physical world—because it describes spatial relationships. Descartes’ discovery of the connection between algebra and spatial planes allowed for mathematicians to BEGIN looking for connections between the physical world and the world of mathematical laws/ideas
Because of this realization that the physical universe obeys laws which can be written algebraically, Livio explains, Newton was able to develop calculus. The real breakthrough was not as much that Newton found an algebraic equation for gravity—though this was remarkable, and has been shown to be accurate to the distance of 1/56,000 of a mm (p. 218). The real advance was Newton’s theory that the laws of gravity on earth are true everywhere in the cosmos. Math could explain the universe.
If the physical world (geometry) could be explained with the world of ideas (math), what else could math do? Could it explain the orbits? (Livio explains that earlier scientists presumed that the orbits would be elliptical, but it was not until Kepler that we knew the equation for them). Could mathematical laws be used to test the logic of philosophy? (Boole showed how this was possible, in the 19th century). Livio traces mathematicians’ efforts since Descartes to explain just about everything, including behaviors that we find in human-made institutions. Some examples include:
- Many principles in economics and sociology rely on the “normal distribution” curve
- Knot theory helps explain the shape of DNA
- The Global Positioning System takes into account equations from the theory of relativity
Stepping back a few centuries, it was this trajectory (explaining the universe with science) that worried the church in Galileo’s day. D’Souza (2008) has downplayed the Church’s role in suppressing Galileo and other scientists. However there is no need to sugarcoat the fact that Christendom has had a branch that has been wary of “worldly knowledge”, from the magisterium, to the Reformation principle of sola scriptura, to the anti-intellectualism of 20th century Fundamentalism. Yet Christianity has also always had its Anselms, and Galileos and Keplers and Newtons. And it has also had its more ordinary faith integrationists (like myself) who see no problem with math’s ability to explain so much of the universe. In fact, this only further pushes the question, Why? What set the universal laws in motion? Mathematicians have been unable to agree on this answer, because, as Livio points out, it is not a question that math can answer.
4. Why does math work?
There have only been a handful of answers to the question, “Why does math work.” And Christian historians of science often say that it was Christianity’s ability to locate the laws of math in the handiwork of God which allowed for such great advances in science in the 16th and 17th centuries. The historical record, however, shows it is an overstatement to say that advances in math were only possible because of the Christian worldview. Apologists tend to only look at the advances during the Protestant Reformation to bolster this thesis. In reality, the various competing worldviews have all engendered some contributions to mathematics, regardless of whether they found a foundation for why math works. Note, however, that only Christianity has a satisfying answer for the question “Why does math work?”
Answers to the question “Why does math work?” (that is, why is it apprehensible, and universally applicable?) – summarized from Nickel (1990).
|Answer||Worldview foundation||Discoveries as this worldview was prominent|
|It doesn’t. There is no guiding order to the universe; no consistency or meaning||Polytheistic, animistic||Some concepts in trigonometry and some concepts in algebra from India|
|It doesn’t. Math is purely theoretical; applications to the real word are not well-regarded – the material world is not a true “copy” of the theoretical “ideals”||Greek philosophy: Mechanistic- the dualism of ideas and forms||Euclidean geometry|
|It doesn’t. Accumulation of knowledge about the physical world is not highly valued or trusted||Early Christian: Monotheistic- but influenced by Greek philosophy||Advances in indeterminate equations (Diophantus) and trigonometry (Menelaus)|
|Because God authored it. The universe has a God who speaks, and who is the foundation of the mathematical laws. It is our act of worship to discover those laws and to harness them for the betterment of humankind. The laws we discover on earth are true throughout the universe because God is Lord of all (Kepler)||Protestant Reformation||Newton’s laws of motion and his calculus, logarithms (Napier), Heliocentrism widely accepted (Galileo) and further explained with Kepler’s laws of planetary motion, Euler’s equation.|
|We don’t know why. And it doesn’t matter (Lagrange), or it is a mystery we have to accept (Einstein) or we need to invent a meta-mathematics (Hilbert) to explain why, and then we will need to invent super-mathematics to explain meta-mathematics.||Modernism: Purely naturalistic view of the world||Probability, calculus notation|
|It doesn’t. Even math is uncertain (Russell)- we can know nothing (Hume). We cannot trust our senses (Berkeley). All descriptions of knowledge are relative. This is just one of many universes, this is the current one. It has no meaning. We are just the “collision of atoms” (Russell) or the product of a selfish gene (Dawkins).||Secular nihilist, postmodernist.||Set theory; theory of relativity, quantum physics|
Psalm 19 indicates that the study of natural laws can help us to further understand God’s handiwork. And Kepler noted that mathematicians agree with Psalm 111:2: “Great are the works of the Lord; they are pondered by all who delight in them” (NIV).
Is God a mathematician? Of course!
D’Souza, D. (2008). What’s so great about Christianity. Tyndale.
Livio, M. (2009). Is God a mathematician. Simon & Schuster.
Nickel, J. (1990). Mathematics: Is God silent? Ross House.
How do you integrate faith with the hard sciences?