How Mathematics Influences Faith

Reflections from the ACMS 2011 Conference

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I attended my first ACMS conference a few weeks ago at Westmont College in Santa Barbara, CA. I had a blast. I was able to present a paper, hear some great talks, and meet/fellowship with some great mathematicians who are solid believers in their faith. Too many great moments to share them all, but here are a few thoughts/quotes from the meetings:

1. Texas needs to find a way to hijack California’s weather.

2. I have a great, beautiful, supportive, loving wife, and for this I am extremely blessed.

3. Art Benjamin is an entertaining teacher which is great to see in a mathematician. I’m sure people who have always hated the subject pay more attention when he is talking.

4. My magic square (Hint on what makes it so magic, 35):

5. He left his Father’s throne above So free, so infinite his grace! Emptied himself of all but love, And bled for Adam’s helpless race. ‘Tis mercy all, immense and free, For O my God, it found out me!

6. This earth belongs to God…

7. It is amazing to see how such different branches of mathematics can work together in ways never before thought. The example of combinatorial proofs of trigonometric identities was very cool to see.

8. Building on 6, why would we want to find different proofs for stuff we have already proved? “The proofs we have may establish truth, but they don’t necessarily establish insight.” This quote sticks with me as an educator.

9. 2, 3, 5, 8, who do we appreciate? Fibonacci!

10. Paper by Jason Wilson of Biola University: The Divine mind is impressed on the world such that the secular mind recognizes it and seeks to use it for gain. The Biblical mind not only obtains a deeper understanding of it but is even beckoned to become a partaker of it. Notice the juxtaposition of wisdom in Proverbs 8 with Jesus in John 1:1-14.

11. I was pushed to really consider for what purposes I would use a math biography in my lessons – just to present ideas, or to bring out more in the life of the mathematician/believer.

12. The more we are able to recognize our weakness, the more we are able to practice true dependence on God.

13. Great site: the Mathematics Genealogy Project

14. Glenn Van Brummelen, Quest University, has a great self-described title: Mathematical Anthropologist. Need to read The Mathematics of the Heavens and the Earth.

15. In different cultures the goal wasn’t to convince you of the proof mathematically, but rather to give you different types of understanding – there was no “naturally” correct way of doing things.

16. When missionaries entered these cultures they brought their math with them, thinking a way to convert people to Christianity was to show them the superiority and power of the math and science that Christianity produced… perhaps this is not the best way of thinking 🙂

17. Are mathematical ideas universal, as evidenced in different cultures reaching similar results independently? Or is this just evidence of our shared humanity?

18. Mike Stob of Calvin College convinced me I need to use “R” next year with my AP Stat class.

19. Talithia Williams of Harvey Mudd College gave a great (and much needed) presentation on making students aware of the misapplication of statistics in American life. A great example is in how pharmaceuticals are now peddled directly to the consumer, yet since we don’t know the actual data from the studies, it is hard to know when to take a risk on certain medication. This might make a good stats-and-society project for students.

20. “Who we are mathematically is not who we always were, or who we will always be.”

21. Often models we use in the classroom are not accurately presenting the ways the material was learned at the time of its inception.

22. Some cultures preserved their mathematical ideas and passed them down in poems and songs – I’ve found these to be effective teaching tools in the past, I need more of them.

23. Wigner – in looking at the effectiveness of mathematics, the miracle is not in the connection of math with science, but in the math itself.

24. It was great to hear Bob Brabenec of Wheaton give a talk. I’ve mentioned his work on this blog on more than one occasion. It was interesting to hear him delineate between doing philosophy of mathematics and thinking philosophically about mathematics. I myself have realized that I probably fit more in the latter category.

25. Mark Colgan of Taylor University gave a great talk on encouraging students to connect topics in Calculus with Biblical ideas by using weekly reflection papers. Though I may not follow his model exactly, I very much like the idea of introducing reflection papers into my curriculum.

26. David Stucki of Otterbeing University gave a great talk on teaching students the concept of infinity. I wish I could have focused on it more and taken more notes, but my talk was right after his. He did list some great resources which I hope to contact him about and share here.

27. Mathematics Through the Eyes of Faith is due out in August. I got an advanced copy of it and it looks great! It really addresses some of the key issues in Mathematics and the Christian Faith. Do mathematical concepts point beyond themselves to a higher reality? Can the idea of chance be reconciled with God’s sovereignty? How do we account for mathematics being so effective in describing the world? How does giving people the capacity to do mathematics fit into God’s purposes for humanity? Should be a great read. I look forward to reviewing it.

28. In trying to describe the beauty and wonder of mathematics to a broader audience it is very difficult to “describe the mathematics simply without simplifying the problem,” which is where the beauty lies.

29. There was something wonderful about being in a room full of academic colleagues and being able to all worship the Lord together.

30. I hope I don’t have to wait two more years to this again.

I'm in there, but I'm half hidden. You can try to find me, but I think I made Waldo proud.

Resources for Integrating Faith and Mathematics

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Well, it is coming down to the end of the spring semester. I am going to be quite busy over the next few weeks making sure I have all my work completed and turned in and that everything is set for graduation. So I don’t know how many posts I might get up before the middle of May. Here are a couple of articles to hold you over until then. If you read through these too quick and are left waiting for more, then check out the link on the top of page: “Resources for Integrating Faith and Mathematics.”

“The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Eugene Wigner

Wigner observes that the mathematical structure of a physics theory often points the way to further advances in that theory and even to empirical predictions. He argues that this is not just a coincidence and therefore must reflect some larger and deeper truth about both mathematics and physics.

“On Christian Scholarship,” Alvin Plantinga

How should a Christian university and how should the Christian intellectual community think about scholarship and science? Should the kind of scholarship and science that go on at a Catholic university differ from the sort that goes on elsewhere? If so, in what way? Plantinga presents one sort of view–not with the thought that this is the whole and unvarnished truth, but as a contribution to our conversation.

“Advice to Christian Philosophers,” Alvin Plantinga

In each area of serious intellectual endeavor the fundamental and often unexpressed presuppositions that govern and direct the discipline are not religiously neutral; they are often antithetic to a Christian perspective. In these areas then it is up to Christians who practice the relevant discipline to develop the right Christian alternatives. Plantinga pursues this primarily from his own discipline of philosophy, but the ideas translate into all areas of scholarship.

How is Math done Christianly?

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“For all things in heaven and on earth were created by him– all things, whether visible or invisible, whether thrones or dominions, whether principalities or powers– all things were created through him and for him.”

Colossians 1:16

The short answer to the question in the title is: I don’t know, but I have some thoughts. Those thoughts are the driving force behind the creation of this blog.

To most people mathematics seems uninfluenced by Christianity, or any religion for that matter. Math seems values-neutral. It doesn’t matter whether you are a Christian, a Jew, a Buddhist, or an Atheist, 2 + 2 will always equal 4 in a base-10 number system, the cosine of π/3 will always equal 1/2, and the Pythagorean Theorem will always be a2 + b2 = c2 . Not only do mathematical results appear to be the same regardless of creed, gender, or ethnicity, so too do the mathematical processes by which those results are obtained. There is not a Christian way of finding the zeroes of a polynomial function and a non-Christian way. The work of doing mathematics looks then to be entirely self-contained.

Even if this is true, I don’t think it serves as a valid argument that math can’t be done Christianly. Even if the results and the processes of mathematics can go unaffected by the Gospel, the presuppositions we bring to those processes and the interpretations that we make from those results are always affected by our value system. In this sense, at the very least, we can find Christian mathematics. And if we begin the doing of mathematics with presuppositions rooted in truth of the cross, death, bodily resurrection, and return of Christ, and we conclude mathematics with interpretations wholly in line with the Triune God’s redemptive plan for His creation, can it really be said that the Gospel has no influence on the process of mathematics which falls in between?

The purpose of this blog is to raise questions regarding these three stages: the presuppositions that we bring to the table of mathematics (I guess that makes it a times-table… Get it? Anyway… ), the work of doing mathematics itself, and the implications and interpretations which follow from that work.

So then, some of the things that will be discussed…

…in terms of presuppositions: First, we all have them. It is impossible to think about any subject in isolation from religious beliefs. There are many people who would disagree with that statement in general, and vehemently disagree with it when it comes to mathematics. So I plan to discuss the validity of this claim. Second, the proper presuppositions to have are Christian ones. Why? Because Christianity is true. In this regard you may find discussions here with very little, if any, math content that focus primarily on explaining and defending historically orthodox Christian faith (and all the people who grew up despising math said: Amen!).

…in terms of doing mathematics: there are some very interesting patterns and results that arise that fit very well with a theistic concept of the divine nature. We’ll discuss some examples from the history and philosophy of mathematics and push the envelope to consider how we might see these patterns and results not merely as indicative of theism, but specifically Christianity.

…in terms of implications and interpretations: I believe this is an area where it becomes very clear that mathematics is not values-neutral. The number one question I would get as a math teacher would be “when am I ever going to use this?” But that wasn’t really the question the student was asking. The question they were asking is “why should I value this?” and they expected an answer in terms of the practicality of the subject: how math would help them get ahead, make more money, solve their problems, etc. Is it right to lift up practicality as such a virtue? should mathematics only be pursued because it is useful? Or should it be pursued because it is true. Should the question driving interpretation be “what is good for me?” or should it be “what is good?” Is their justice and morality in using statistics to classify people? These are just some of the questions that arise when discussing the interpretation of mathematics, and I believe each of them has a distinctly Christian response.

Well, there it is. A lot of stuff just spilled out of my head and onto the computer for all to see. Please don’t run away. I promise it will get better from here.

Recommended Reading on This Topic: Calvin Jongsma, “Mathematics: Always Important, Never Enough. A Christian Perspective on Mathematics and Mathematics Education.”