Mathematics and Science

Mathematics:

In the “mixed sciences” made famous by the medieval quadrivium (Music and Astronomy), mathematics helps to give us insight into the natures of things. Even at its most abstract (Arithmetic and Geometry), it offers knowledge of the quantitative aspects of the real physical world. Moreover, its highly logical structure and freedom from the imprecision of material being makes it ideal for elementary training in reasoning, where the beauty of mathematics both inspires wonder and makes evident the human mind’s thirst for understanding. Mathematical knowledge is more than just an object of contemplation, also serving as a direct instrument of scientific inquiry, and an indirect means of seeking after the truth. As the Book of Wisdom declares: “Thou hast ordered all things in measure, and number, and weight” (Wis 11:21).

The Mathematics curriculum begins with Euclid’s Elements, the foundational text of mathematics in Western civilization. Building on this foundation, students examine the works of Apollonius and Archimedes on conic sections. And in their final semester, they investigate number theory, various attempts to unify the study of discrete and continuous quantity, Descartes’s analytic geometry, and fundamentals of the integral and differential calculus.

Science:

For ancient and medieval thinkers, “science” denoted any area of inquiry in which true, certain, and universal knowledge was achieved, making it equally applicable to such disparate disciplines as theology, philosophy, and mathematics. The more modern sense of the word, however, is reserved for an empirically-based knowledge of the workings of nature, as discerned through the experimental observation of phenomena. Given both the dominance of this understanding of the term and the frequent neglect of natural philosophy that accompanies it, it is important for our students to understand the domains proper to each kind of “science,” as well as to recognize and appreciate their true and intimate relation.

There are three different levels of scientific inquiry: that of natural history, in which particular data are gathered and provisionally organized; that of natural science, in which hypotheses and theoretical constructs are fashioned in the attempt to correlate these data; and that of natural philosophy, in which the data are subsumed by truly causal explanations of universal validity. The direct experience of the natural world through natural history greatly augments our sense of wonder, so essential for the intellectual life. Natural science instills in the mind a sense of the order of the universe. And natural philosophy ultimately leads the mind to the recognition of the First Principle: “The heavens declare the glory of God” (Ps 19:1). While each level has its own methodology, their unification is an important goal of liberal education.

The first two levels of inquiry are treated in the first three semesters of our Science curriculum. The third is studied both in our Philosophy sequence and in the final year of the Science curriculum, where students investigate the complementarity of natural science and philosophy.