.png)
Guest blog by Karl-Dieter Crisman
Karl-Dieter Crisman is a professor of mathematics and computer science at Gordon College in Massachusetts. He is grateful for mentors who have inspired him to investigate connections between math and faith ever since a conference in Chicago, sponsored by InterVarsity Christian Fellowship, nearly thirty years ago. Karl-Dieter will be the 2025-26 Brabenec Lecturer of the Association of Christians in the Mathematical Sciences.
I want you to think about something that might seem unrelated to this blog. Do you remember your high school geometry class? Think about what you liked, or didn't like, about it. Yes, this question will be relevant! (If you had calculus at some point, same questions.) Take some time, the page won't reload before you think about it.
Now consider the following. Was one of your reactions that studying geometry allowed you to "glorify the Lord's name and greatness”? If you are like most of my students, the first thing you think of when it comes to mathematics is not God – that's true even if you enjoy math, and I hear that some people don't enjoy it that much.
This post is about a person whose first reaction was that geometry glorifies God, and why that should encourage us to explore creation for its own sake. But first, some background!
It turns out that there are lots of devout Christians who have contributed to the development of mathematics as we know it and were inspired by seeking God's order in the universe. Many readers of faith will have heard of the great philosophers Descartes and Pascal, who were both very good mathematicians. The founders of calculus, Newton and Leibniz, were likewise very devout (though in Newton's case not so orthodox). Leonhard Euler, easily the greatest mathematician of the 18th century, went so far as to publish a defense of the divine nature of Scripture right in the midst of Frederick the Great's Berlin, which was more interested in Voltaire's wittiness than revelation! But I think none of them compares with an obscure figure from the early 1300s, when it comes to being motivated by God in pursuing geometry.
At that time, the Castilian rabbi Abner, from the city of Burgos in what is now Spain, converted to Catholicism – without any coercion, as far as we can tell. He became known as Alfonso of Valladolid. Under that new name, he is mainly known for defending his conversion and disputing in philosophy and theology with other Jews of the time – leading him to be a controversial figure[1].
More importantly for this post, Abner/Alfonso was dedicated to geometry throughout his life. It is in his one surviving mathematical text that he says that "from [his] youth to [his] old age the one thing [he] desired from the Lord" was to "glorify [God's] name and greatness." How was he going to accomplish this? By measuring the circle!
Today, it seems like there are amazing new scientific discoveries every day. We even allow many people to dedicate most of their lives to exploring God's creation. But for most of the famous names above, and certainly for Alfonso, math was just one of many tasks on the docket. So discoveries were fewer and further between. Alfonso's goal was to reorganize geometry – that is, geometry as it had been for well over a thousand years – by learning how to measure curved shapes. In fact, he calls his mathematical text the Sefer Meyasher 'Aqov, or Straightening the Curved, in a clear allusion to the prophet Isaiah. Consider the New Living Bible version of Isaiah 40:4:
Fill in the valleys, and level the mountains and hills.
Straighten the curves, and smooth out the rough places.
I should have a spoiler alert here. Neither as the rabbi Abner, nor as the convert Alfonso, did he achieve this task. He did, however, have novel approaches to the problem – ones that seem to foreshadow approaches later taken in calculus for finding the exact length of curves. Keep in mind that even the circle wasn't really "measured" yet, because while the circle constant pi was known, mathematicians didn't know that much about it other than good approximations such as 3.14 or 22/7 – and wouldn't until nearly 1900.
Moreover, Alfonso dug deeply into the question of how parallel lines work. You might remember from that geometry class I asked you about that if you have a straight line and then some other point, you can only make one parallel line to the original through that point. But how do we know? Alfonso quoted verses such as Job 38:11 to reinforce his own (imperfect) conclusions about this, which used his ideas about infinity: “This far you may come and no farther: here is where your proud waves halt” (NIV). Alfonso says about these arguments, "From here one can (if one wishes) come near to the understanding of the existence of God."
To be sure, Abner/Alfonso wasn't trying to prove God's existence with his mathematics. Nor was he doing biblical exegesis at length to prove his mathematics. Indeed, like all of us, he had his own blinders. He was so convinced of his parallel lines that he, like all other geometers of the time, did not realize that if you lived on a curved surface, you can have more than one parallel line through a point – or none! The former case is crucial to how a GPS navigation system works using Einstein's general relativity – a theory which he based on the geometric discoveries of Bernhard Riemann, another devout mathematician.
But God doesn't ask for us to be able to comprehend his creation fully; to reference Job again, he is pretty clear that we can't, and we won't. Instead, God asks for us to understand that which we can in humility, and that we should meditate on "whatsoever things are true [or]… of good report" (Phil. 4:8 KJV). Alfonso makes it clear that geometry is one of those things, and with quotes from Deuteronomy to Ecclesiastes justifies learning for its own sake, since God created “everything for his honor and majesty” (see Psalm 96:6).
Alfonso believed that even on this topic one should “seek to find the right words to acquire a clear knowledge, emanated from the Holy Spirit.” Let's keep that in mind in an increasingly utilitarian culture – that God respects all our attempts, incomplete as they inevitably are, to comprehend the majesty of creation.
Note: All quotes from Abner/Alfonso are from the excellent translation and commentary "Alfonso’s Rectifying the curved—a fourteenth-century Hebrew geometrical-philosophical treatise" by Ruth Glasner and Avinoam Baraness. Some of these ideas were presented in a more scholarly context in a paper for the Association of Christians in the Mathematical Sciences[2].
No comments:
Post a Comment