In medieval European universities, students were taught not only grammar, rhetoric and logic (known as the trivium) but also the arts of arithmetic, geometry, music and astronomy (the quadrivium). The quadrivium emphasized the mathematical. In fact, in the eyes of the ancient Greeks, all four subjects — arithmetic, geometry, music and astronomy— were mathematical. The Greeks referred to arithmetic as number in itself, geometry as number in space, music as number in time and astronomy as number in space and time.
The Greeks were intrigued by the ways that numerical properties gave them insight into underlying structures. For example, they discovered a connection between number and pitch in music. For stringed instruments, the ratio of the pitch frequencies in a musical interval is related to the ratio of the length of the strings plucked. As such, music was considered to be number in time. Numbers were considered so special that it is claimed that a sect of Pythagoreans declared “all is number” and tried to base everything on number or a ratio of whole numbers. Mathematics is what brought wisdom; number was the underlying “scheme of things.”
But it is too simplistic to reduce all to number. The scheme of things is not rooted in number but in the Logos, in the God who upholds created order and sustains the world. Our world is both orderly and complex—it cannot be reduced to one aspect or fully understood through one way of knowing. Christian philosopher Herman Dooyeweerd described aspects of creation that could not be removed from a full understanding of our world. We could not fully know our world without considering aspects such as the numerical, physical, biological, aesthetic, economic and others. His philosophical framework, based on historical evidence and rooted in Reformed theology, highlights the complexity of created order.
We could use Dooyeweerd’s aspects as a template for subject areas in a holistic liberal arts education. But the aspects play a different role as well: when exploring one particular subject, such as mathematics, it is helpful to keep in mind the other aspects of creation. The Enlightenment emphasized mathematical ways of thinking, following the success of powerful new developments of calculus. After all, the new subject was able to accurately predict the path of planets. Mathematics became known as a primary, and more objective, way of knowing— at the expense of other ways of knowing. Postmodernism is in part a reaction to this overemphasis on one way of knowing.
The scheme of things is not rooted in number but in the Logos, in the God who upholds created order and sustains the world.
The Enlightenment myth is no longer the most dominant worldview in our postmodern world. While we may more fully recognize the limits of mathematics today, it remains a powerful discipline. One of the fascinating aspects of studying mathematics is seeing its abundant applications, from modelling ecosystems to developing internet search engines. It is said that we live in the Age of Big Data. This phrase captures the fact that, with the help of technology and mathematical models, there are many new opportunities to use numerical structures to gain insights into our world.
But we must take care not to reduce the complexity of the created order. Mathematical models are not neutral and are not necessarily more objective than other ways of knowing. Cathy O’Neil’s popular book Weapons of Math Destruction highlights episodes involving mathematical models, in the form of algorithms, which have damaging effects, often on vulnerable populations. O’Neil notes that these damages can occur when the mathematical model is treated as more objective than other ways of knowing. Users may also fail to take into account a model’s limitations or the assumptions built into the model.
The liberal arts tradition, armed with Reformed Christian philosophy, develops students beyond a focus on only one discipline. It emphasizes that individual subjects are part of a broader context and not all-encompassing. It is important for those who are developing mathematical models to have good communication skills, to carefully outline the assumptions of a model, to understand other ways of knowing and to recognize the potential sociological, economic or justice implications of their work. Redeemer’s Mathematics alumni are using mathematics in finance, in insurance, in the health sciences, in education and in modelling cancer dynamics and transportation networks. They are, in short, stewarding their talents, their mathematics, for reconciliation. To do this justly, it helps to be grounded with a robust worldview. Developing mathematics is a culture-making activity that brings us to awe and equips us for stewardship and reconciliation, especially if we are trained to search for these opportunities.