“What doesn’t transmit light, creates its own darkness.” — Marcus Aurelius
I am not particularly worried about the longevity of mathematics as an institution. Certainly, the way of life of our community is undergoing incredible turbulence. But the fact is this institution has existed as long as the written word (not coincidentally), and mathematics will remain a human endeavor as long as there are human beings around to think about it.
However, this turbulence is undoubtedly forcing us to rethink what our purpose is—or rather, what our temporary purpose has been for the last hundred or so years. This sudden and forced introspection understandably manifests as worry within a large sector of our community: the sector which is concerned mostly with solving problems. But not all of us believe that math is primarily about problem solving. And indeed, for most of its history, many adherents of mathematics understood this fact.
To me and to many others, mathematics can be called a spiritual experience. The most memorable moments of my journey through math are notably those which put me in a state of awe; in a state of amazement that the natural order of things, whether abstract or physical, is so beautiful, so perfect, and so amenable to human understanding. I will never forget the moment in which I first understood the proof of the Gauss-Bonnet Theorem—when I understood not just with my mind but in my heart that the average geometry of a surface is equal to its topology. I even remember which sweatshirt I was wearing when my teacher was explaining the Fundamental Theorem of Line Integrals—the way the world sparkled as it dawned on me for the first time what homotopy invariance was (although I did not know those words at the time). I remember looking up at the night sky one cold winter’s night when the veil was lifted—when the fact that matter tells spacetime how to bend and spacetime tells matter how to move finally became clear, after months of studying general relativity. It felt like seeing the stars for the first time.
An astounding aspect of these moments is that they can be shared. As teachers of mathematics, we carry the torch which illuminates this reality for our students. When we know an idea deeply enough, we feel an urge to spread that knowledge to our pupils, in the hope that they spread the good news further still. Math is, of course, useful in improving conditions for human beings. Systematic and logical thought coupled with imagination have taken us far as a species. But in fixating on this, we became obsessed with problem solving—with the notion that another notch in our belt will increase our glory. But ours is not the glory.
Now that machines created in our likeness are swallowing up the long lists of problems we deemed significant, the problem solvers are worried, and if they remain problem solvers alone, then perhaps they should be worried. But it is important to remember that all problems, all ideas, are already worked out. A mathematician who solves a problem demonstrates to humanity the truth value of some aspect of reality: they do not build the reality. And when they discover a truth, it becomes a shared truth—a shared truth which adds to the richness of the human experience. If humans discovered every conceivable truth on their own (I doubt it’s possible, but let’s imagine), then mathematicians would still be necessary as stewards of those truths. We will always feel the urge to explain the universe to each other, and to share in the beauty of the natural world. The beauty of all those problems, solved at the moment of creation.
Received 19 October 2026.
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