Please welcome today’s guest writer, Sam Auyeung. Sam should have graduated in 2016 as a math major but he convinced his parents to pay another year’s tuition for him to pretend to have deep thoughts (add a philosophy major) and figure out what to do after leaving school. On a dare, he also majored in Greek. Evidently, he did not figure out what to do after leaving school because he hasn’t left; he’s in a doctorate mathematics program at Stony Brook University in New York where he thinks about geometry, topology, and scallion pancakes.
There is an episode of the podcast The Anthropocene Reviewed which has haunted me for over a year. In the episode, John Green (the YA novelist) shares a story from his days as a student chaplain at a children’s hospital. During one of his nights on call, a 3-year-old boy with severe burns was brought into the ICU. Despite his critical injuries, the boy was conscious and in brutal pain. The trauma team did what they could, but they did not think the boy would survive: “That kid’s gonna die and I know his last word. I know the last thing he’ll ever say.” Shortly after that night, Green finished the chaplaincy and immediately dropped out of divinity school. He said he could not cope with the memory of the boy and for years, he could not bring himself to discover whether the boy had survived. All he could do was pray and place his belief, “however tenuous, in mercy.” Green then quoted from All the King’s Men: “The end of man is knowledge, but there is one thing he can’t know. He can’t know whether knowledge will save him or kill him.”
The quote, tied to the boy’s story, is what has haunted me the most. I have long thought of myself as a knower and for the last three years have pursued what I once thought to be the purest form of knowledge that eternally exists in the mind of God: mathematics. If asked, I suppose I might say I am trained as a symplectic geometer who uses Floer theoretic techniques to study geometric invariants of algebraic singularities. I know what those words mean, but what good is it when most people neither know nor care to know their meaning? Do I know the ends of what I know, and will my knowledge deliver or damn me? With math, I have been delivered in two ways. When the world is chaotic, math feels like a noetic haven of stability. When the world is ugly, math exhibits elegance and beauty for those receptive to it.
But also with math, I may be damned in two ways. I may be viewed as a lofty academic who won’t admit that his field is divorced from the “layperson’s” experiences; this is sometimes self-fulfilling. I can also passionately claim mathematics to be a profoundly human activity yet be subjected to others’ remarks such as “I always hated math in school,” “Math lacks emotion,” or “What can you even do with math?” followed by a change in subject. Of course, neither of these are inevitable, and a corpus of knowledge doesn’t exclusively kill. But it can feel that way.
These meditations lead me back to Green’s story and I am embarrassed; my experiences seem slight. But there is something else. I’m reminded of Dostoevsky’s character, Ivan Karamazov, because—well, I think I am a bit like Ivan. In a famous scene, Ivan levels a challenge to his brother Alyosha, a novice at a monastery. The challenge is, unsurprisingly, a rendition of the millennia-old problem of evil but less classical. Fundamentally, Ivan’s final conclusion is not the denial that there is a God but rather a rejection of Creation in which every evil and suffering—including the 3-year old boy’s anguish—will be accounted for. Ivan believes in God, but he cannot accept a god who can justify exactly why his creation allows for horrendous evil such as infants being impaled on bayonets in front of their mothers. Ivan does not want such knowledge and for him, even knowing that such explanations exist entails ruination. Finishing his monologue, a strangely gleeful Ivan expects a defeated Alyosha to reluctantly agree.
But Alyosha does not respond with words. He simply kisses his brother.
Lately, I find myself in a situation where instead of wondering whether certain knowledge will save or kill me, I wonder whether knowledge that I bear will save or kill others. Without going into details, I’ll say this: I had believed—nay, trusted—in some evidence related to the death of a classmate (preCOVID) which gave me hope and also imparted hope to my friends at my telling. However, I then discovered that the evidence is erroneous. Do I tell my friends the truth at the cost of a loss of hope, peace, and comfort? Will the truth give life or death? Alyosha did not speak after Ivan’s tirade even though he knew even more deeply than Ivan the challenges of faith. Instead, he loves his brother. My silence could be dishonest. Or, like Alyosha, could it be love? Math brought my classmate and I together, but it cannot solve this problem. “The end of man is knowledge, but there is one thing he can’t know. He can’t know whether knowledge will save him or kill him.”
This is wonderful in an unsettling sort of way. I, too, loved math enough to major in it and I, too, identify more with Ivan Karamazov than any other literary character I’ve come across. My path has been dotted with many instances of my own arrogance and belief that I either knew everything about deeper truths or, more importantly, could learn and logic out everything I needed to know. I came to Calvin with all guns blazing to pursue a PhD in mathematics and be an “all in” knot theorist but, of course, was quickly disillusioned of my own grandeur in more ways than one. I’m still learning that math and intellectualism can’t save and fix everything, so thanks for this—it is comforting, encouraging, and humbling to know there are kindred spirits out there.
Hi Anna,
Thank you for your kind and thoughtful comment. It’s certainly taken me a lot of time to realize the limits of reason because it too, is a human activity. One of the most pleasant surprises for me in grad school has been to see world-class mathematicians bearing themselves with humility. In some sense, math is a great equalizer: everyone has math problems they cannot solve, no matter how clever they are. Math, as an activity, has lessons to offer in humility, patience, and perseverance, if one is receptive.
By the way, you probably know Prof. Sunukjian, then? He studies knots and low-dimensional topology and is the one who pointed me towards Stony Brook University where he had been a postdoc.
Prof. Sunukjian is a favourite! I did topology research with him one summer. I also did Differential Geometry/Topology with Prof. Moseley. And now I know you’re the one he used to brag about since you went to Stony Brook! (Or, rather, he would say “there was this student Sam who went to Stony Brook and, you know, Stony Brook is the best,” etc.) My own love affair with topology and knots sprang out of my middle/highschool math teacher who did his topology PhD at Bryn Mawr and gave us a knot theory crash course for a couple months.
And now that I think back, you have an excellent point about how math is an equaliser of sorts—I’ve done a lot of collaborative math, from competitions to study groups, and it has always been charming and delightful to see how everyone brings their own talents and perspectives to the table.
Oh, was the summer project with Prof. Sunukjian on the 4D lightbulb theorem? What was the project with Prof. Moseley?
And that’s awesome that you got to learn about topology and knots before college! Some of my own work considers knots and links.
Also, it’s great that you’ve done collaborative math. Math can be a very social activity.
The pursuit of knowledge is grand, wonderful even, but it is not everything. Perhaps it is that wanting to know that so trips us as humans. Because there are some things that we can’t know. Perhaps better than knowledge is belief. There are still some problems there, but belief helps cover what knowledge lacks.
Still, a wonderfully thoughtful and storied piece. Most engaging.
Thanks for sharing with the post calvin. Keep writing as your heart leads.
Hi Kyric, thanks for your comment. Yes, I agree that the pursuit of knowledge is not everything. But what I wanted to explore is when we should limit pursuit of knowledge, not because we can’t know but because knowing will not be beneficial. I’m not exploring knowledge itself but what comes after. Ivan, for example, does not want explanations for every instance of evil and suffering. In his view, to know such explanations would be for every instance of evil and suffering to have meaning. He would rather they be meaningless and lack purpose as he can’t bear believing that God has a plan involving every bit of evil. So what would come after having such knowledge is a rejection of God, his “returning the ticket.”
As for belief, my working definition for knowledge is that it is at least a proper subset of belief but has the additional properties of being true and being properly justified. In the history of epistemology, this last bit has generated a lot of debate.
You’re welcome, Sam. It’s always about what comes after, isn’t it? Do you think similarly to Ivan, then–if I may probe further?
Yes, you do call out some of the faults of belief quite well. They can make a good pairing, though, in my opinion. Belief and knowledge working in tandem brings out the best of both.
My only point there was to say that I was only considering knowledge within reach, whether it is always beneficial, and whether there might even be some virtue in ignorance. I was ignoring knowledge that we can’t know and also (without stating it), challenging an Enlightenment position that having knowledge is never bad.
Yes, like Ivan, I am unsatisfied with certain traditional theodicies.
Well, I don’t mean that belief and knowledge are paired. I mean that the conditions for knowledge are that it is belief, plus a few more conditions. cf. “all humans are mammals but not all mammals are humans.”
All right. Thanks for explaining deeper.