Not About Navier-Stokes

This post isn’t about OpenAI’s use of AI to solve the Navier-Stokes problem, one of the Millennium Prize problems, at least not directly. I’m not a mathematician; I have a vague understanding of the problem and certainly no understanding of the proof. But the discussion surrounding the solution crystallized some of my own thoughts about using AI in different fields. When Terence Tao writes, “I wrote recently about how the collection of good, fruitful open problems is now being mined in a nonrenewable fashion,” he’s referring to an earlier thread, and ultimately to a post by Hugo Duminil-Copin, who wrote, “When mathematicians say that the process matters more than the solution, this is not an empty statement. The richness of what emerges from repeated attempts, failures, detours, and encounters is extraordinary.” That’s a familiar statement from popular culture: The journey is more important than the destination. Hugo Bowne-Anderson, in “Beyond Navier-Stokes,” addresses the same issues: What does it mean to understand something? How do discoveries lead to new problems that are worth solving? And it relates to my own questions about AI use: AI is great at finding facts, organizing facts, and even writing about the things it finds, but what does it mean to possess that knowledge, to incorporate it into our thinking? Is it enough to have AI do the work, then read it? Here’s one way that question relates to my own work. One of my roles at O’Reilly is writing the monthly Trends piece. That piece comes from reading my RSS feed daily, which typically contains about 300 articles. I don’t read every article, but I scan titles, skim interesting pieces, read important articles, and add worthwhile items to Trends. I also use a Claude skill that performs a similar function, producing a list of a dozen or so articles daily. A similar skill runs locally on Pi/Ollama/Qwen. I admit that I occasionally think “Why am I doing all this reading? Surely Claude could read and add the top articles to Trends on its own.” But I don’t delegate the work. Claude’s taste differs from mine, for one thing (and I object to the idea that “taste” is the last human capability that AI cannot replace). Its list is useful to me for two reasons: it picks up items I missed, and it helps break ties when I cannot decide whether a development is significant. But why don’t I let Claude take over the whole process? There is some value in scanning those 300 titles, skimming the 30 articles that are possibly important, and reading the dozen that seem genuinely important. That’s how I come to “possess” the knowledge, to incorporate it into my thinking. A day, a week, a month later, someone will mention something (for example, a tool that detects whether someone is using “smart glasses”), and I’ll probably be familiar with it already. If I need to find the actual reference, Google (yes, Google with AI assistance) can locate it. (If you care, Zuckoff isn’t currently in next month’s Trends, though I might add it by the time Trends publishes.) I need a broad view of what’s happening in computing. Delegating that broad view to AI doesn’t work. Using AI to help build that broad view does. That’s one practical example of how to use AI. Tim O’Reilly’s “Writing with AI” gives another. He argues with AI, lets it lead him to research new areas. In conversation, he’s described AI as a “smart library,” a metaphor that’s appropriate and useful. We’re still learning how to use AI. How do you make knowledge your own? is the general case of the question that Tao, Duminil-Copin, Bowne-Anderson, and Tim O’Reilly are asking. It’s also the question behind the question that software developers who are incorporating AI into their processes are asking: How do we understand the code that AI is writing, especially since it can write much more code than humans? How do we incorporate that into the process of understanding software? What can we learn from AI, and how can we direct the process fruitfully? The journey to understanding is more important; that journey is what leads us to further questions and new understandings, new results. How do you make knowledge your own? is the question we need to answer if we’re not to become “stochastic parrots.”