The Process Is the Product: Keeping Humans at the Frontier of Mathematics
Every few weeks now there's a new headline: an AI system from OpenAI, or one of the other labs, has worked through a math problem that used to belong only to specialists. Some people read those headlines with a sinking feeling. I read them a little differently, and I want to explain why.
A compliment, not a betrayal
When a model solves a serious math problem, it isn't pulling the answer out of thin air. It learned from us. It learned from textbooks written by people who spent their careers making hard ideas teachable. It learned from proofs that were checked, argued over, and rewritten. It learned from lecture notes, problem sets, and the countless pages of scratch work that students and researchers have shared over generations.
So when one of these systems gets something right, I see it as a compliment to human research. It's evidence that the work mathematicians have done for centuries was rigorous enough, clear enough, and generous enough that a machine could learn from it. That isn't a betrayal of the people who did the work. It's a sign of how good the work was.
I understand why it can feel threatening. If you've spent years on a problem, it's hard to watch a tool move quickly through territory you mapped by hand. But the map is still yours. The tool is walking a road that people built.
Standing on the shoulders of giants
In a 1675 letter to Robert Hooke, Isaac Newton wrote that if he had seen further, it was by standing on the shoulders of giants. It's one of the most quoted lines in science, and it's quoted so often because it's true of everyone who has ever done serious work.
Think about who those giants were. Pythagoras and the idea that numbers and shapes follow laws we can prove. Aristotle and the habit of careful reasoning. Descartes, who joined algebra and geometry so we could draw an equation. Galileo, who insisted that nature is written in the language of mathematics and then went out and measured it. Newton didn't invent calculus and the laws of motion in a vacuum. He climbed up onto a structure that many people had built before him.
Now AI is standing on our shoulders. Every model that reasons about a proof is standing on Newton, and Euler, and Gauss, and Noether, and on every graduate student who posted a clean solution online. The giants didn't disappear when Newton saw further. They became part of what he saw. The same thing is happening now, and we are the giants.
What does X + Y + Z = 42 actually mean?
Here's a simple way to think about it. Suppose a system tells you that X + Y + Z = 42. That's an answer. But what does it mean?
On its own, nothing. It could be the total cost of three items. It could be the sum of three angles in a design. It could be a balance in an insurance reserve, or a step in a much longer proof, or just a coincidence. The number 42 has no purpose until a person gives it one.
That's where the human work lives. Someone had to decide that X, Y, and Z were worth measuring. Someone had to frame the question so it could be answered. Someone has to look at the result and ask: Is this right? Is it useful? What does it change? What should we ask next?
The questions, the framing, and the process are the human product. An answer is a moment. The process that produced the question, tested the answer, and connected it to everything else we know is what moves a field forward. That's why I say the process is the product.
In my own work as a mathematician and actuary, this shows up every day. A model can produce a prediction in seconds. Deciding which prediction matters, explaining it to people who have to act on it, and knowing when the model is wrong is still a deeply human job.
I've been sidelined too, and I kept publishing
I want to say something personal here, because I think it matters for anyone reading this who is early in their path.
I earned my bachelor's degree in mathematics with honors from UMass Amherst, where I also studied actuarial science. I've spent my career building predictive models, teaching, and writing about math and data. And like a lot of people, there have been stretches where I felt pushed to the side, where it seemed like the door was closing and my work wasn't going to be seen.
What I learned is that the answer is to keep going. I kept writing. I kept building. I kept putting my notes, models, and ideas out in public, on this site and anywhere else I could. Not every piece found a big audience, but every piece made the next one better, and every piece is now part of the record. Publishing is how you stay in the conversation.
To PhDs and students: keep publishing
If you're a PhD student, a postdoc, an undergraduate, or someone teaching yourself math at the kitchen table, please hear this: your work still matters, maybe more than ever.
AI systems are only as good as the human knowledge they learn from. Every clear proof you write, every well-posed open question, every careful explanation of a hard idea becomes part of the foundation that people, and now machines, build on. If humans stop publishing, the frontier stops moving. The frontier of mathematics is still a human frontier, and it needs you on it.
So here's my encouragement:
- Publish your process, not just your results. The dead ends, the reframings, and the "why I tried this" are valuable. That's the part no one else can write for you.
- Ask better questions. Tools can help with answers. Choosing what's worth answering is a skill only you can build.
- Use the tools, and stay in charge. Let AI check your algebra, search for counterexamples, or draft a first pass. You decide what it means.
- Share early and often. A blog post, a notebook, or a short note counts. Small public work adds up.
The door is open
I'm genuinely excited about where this is going. I think the best years of mathematics are ahead of us, with people and tools working side by side. But the purpose, the curiosity, and the meaning will keep coming from people.
If you're working on something, whether it's a proof, a model, a paper, or just a question you can't stop thinking about, I'd love to hear about it. Reach out, share what you're building, and keep publishing. We're all standing on each other's shoulders, and there's room up here for everyone.