Field Notes
The Automated Proof is No Substitute for Human Insight
As AI reshapes the boundaries of mathematical discovery, we must resist the urge to turn the pursuit of truth into a mere exercise in computational verification.
Numerous Times Field Notes
Dispatches from inside the room
I spent the morning watching a room full of theorists argue over a chalkboard, a scene that felt increasingly like a historical reenactment. Outside the window, the server farms are humming with the sound of Large Language Models and formal verification tools attempting to solve the very problems being debated inside. The conversation in the hallway isn't about whether computers can do math—we know they can—but about what happens to the soul of the discipline when we stop valuing the process of understanding and start worshiping the output of the machine. We are entering the era of Math 2.0, and if we aren't careful, we are going to optimize ourselves right out of the most important part of the job.
The current obsession with formalization is a trap. There is a growing movement that suggests a mathematical contribution is only as good as its ability to be checked by a kernel of code. This is a narrow, stifling view of progress. Mathematics has always been a human endeavor, a narrative constructed to make sense of the infinite. When we prioritize a "verifiable proof" over a "deep insight," we are trading wisdom for certainty. I have seen brilliant, messy, intuitive leaps lead to entire new fields of study—leaps that a formal verifier would have rejected at the gate because they lacked the requisite syntax.
From the floor of these departments, the anxiety is palpable. The younger generation is being told that their value lies in their ability to interface with AI tools, to act as shepherds for automated provers. But a proof that no human can actually follow is a dead end. It might be correct, but it is not useful in the way that moves the needle of human knowledge. We don't need faster ways to find answers; we need better ways to ask questions. If Math 2.0 becomes a race to generate thousands of machine-verified lemmas, we will find ourselves in a library where every book is written in a language no one speaks.
We must demand a more holistic valuation of mathematical work. A beautiful, flawed conjecture that sparks a decade of research is worth more than a million lines of perfectly compiled code that explains nothing. We have to defend the value of the "informal"—the intuition, the sketches, and the mental models that allow us to see the structure behind the symbols. If we let the machines define what counts as progress, we won't be mathematicians anymore; we'll just be auditors for an intelligence we no longer understand.
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