Math Circle 2 -- Introduction
Of Stones, Summation, and Academic Sterility
The One and the Many
Calculus is usually taught as a set of formulas for solving problems, but for author and mathematician James Duane Nickel, it’s something far deeper. He sees it as a window into how we understand reality itself—how change, motion, and even infinity fit together. In this essay, Nickel traces the roots of calculus not just to mathematicians like Newton and Leibniz, but to a broader way of thinking shaped by history, philosophy, and the Christian worldview. In this conversation, we explore how ideas that may seem abstract—like “the one and the many” or the concept of limits—actually touch on some of the most basic questions about life, order, and meaning.
Before getting into this essay I’d like to briefly shine a light on a concept Nickel refers to as “the one and the many.” And specifically, its origins in the Medieval concept of the University.
EN: Your essay places the problem of the One and the Many at the center of both philosophy and calculus. For readers unfamiliar with that concept, how would you explain it in simple terms—and why do you believe it is essential not only to mathematics, but to understanding society and reality itself?
JDN: Another way to understand the phrase “the one and the many” is the phrase “unity in diversity,” words that form the basis of the words “universe” and “university.” The university was a medieval invention. It was grounded on the principle that all branches of knowledge (diversity) have an underlying theme, a governing ground (unity).
For the medieval world, the ground unity was God, i.e., for any branch of knowledge to be understood rightly, we must understand it from a grounding that is the gift of the Creator God, the gift to human beings as image bearers and the gift of creation to such beneficiaries as the venue to explore, develop, and enjoy.
The founders of these universities took seriously the Christ-centered message of Colossians 1-2.
Colossians 1:15-17, “He is the image of the invisible God, the firstborn of all creation.
For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things have been created through Him and for Him. He is before all things, and in Him all things hold together.”
Colossians 2:1-3, “For I want you to know how great a struggle I have on your behalf and for those who are at Laodicea, and for all those who have not personally seen my face, that their hearts may be encouraged, having been knit together in love, and attaining to all the wealth that comes from the full assurance of understanding, resulting in a true knowledge of God’s mystery, that is, Christ Himself, in whom are hidden all the treasures of wisdom and knowledge.”
How well these medieval institutions carried out that mandate is open to debate. There was a tendency to incorporate too much Aristotle into the mix of the knowledge they were trying to understand and inculcate, creating a synthesis known as “medieval scholasticism.”
In today’s world, the university has reneged on its original charter. We can technically name it a “multiversity” where each department carries its own weight irrespective of any serious give and take with other departments. In addition, the acknowledgement of any relationship of God to knowledge is absent. Therefore, there is no ground unity in the prospectus of today’s university. It is a hodge-podge of particulars devoid of any unifying and directive theme. I could say much more about that!
The “One and the Many” is ultimately a theological statement. It is not a philosophical statement of “abstracts” but a deep theological and concrete reality. The God the incarnate Son reveals is a unified being comprising distinct persons, persons distinct yet so related that the Gospel of John states they indwell each other (John 14-17). The early church fathers coined a word for such mutual indwelling—perichoresis, literally meaning “around dance.”
We answer the question “Who is God?” by this summary statement: “God is quintessential love in the undiminished light of the undiluted delight of the fulness of joy which is the good and blessed self-giving eternally known by the Father, Son, and Holy Spirit in their perichoretic unity of being.” There is a lot to digest in this affirmation, so take time with it. It is this God, the onto-relational Trinity, who is the Creator. We need to fill the word “God” with this type of realization. The Triune God, therefore, is the ultimate “One and the Many,” the ultimate “Unity in Diversity.” When this God creates, we can expect to see proximate “unity and diversity” all over the place, for what is made will have the maker’s imprint in it, including branches of knowledge like mathematics, the interrelatedness of human beings, indeed, the totality of reality.
The ground unity in every aspect of proximate thinking and knowledge is the reality of the Father-Son relationship in the communion of the Holy Spirit. If we seek to incorporate such a ground (the One) into all disciplines of knowledge (the many), the multiversity will convert into a university that will live up to the meaning of its name. Thus, we will see the medieval vision re-birthed and grow such richly transformational fruit that its reverberations will reach into every aspect of culture.
FOR MORE, VISIT
https://biblicalchristianworldview.net/documents/whitherMathematics.pdf
Thanks for reading Ennyman’s Territory and our Math Circles Series featuring insights from author/mathematician/educator James Duane Nickel