The recent news from mathematics (Hadamard matrices, ten advances, Navier–Stokes) matters because it is a leading indicator of how knowledge work will evolve. In math, AI increasingly takes on the search for a proof. More attention can go to choosing the question, judging the argument, and understanding what the result makes possible. The goal is unchanged: expand the frontier, and pass the knowledge along.
In knowledge work, toil is not a sign of value and complexity is not a sign of quality. Outcomes matter. I have watched effort mistaken for value in many contexts. Set aside the societal risks, which I take seriously. Much of the remaining negativity about AI mistakes effort for value in the same way: work that arrives without toil is treated as work without worth. AI slop is real: mindless, uninformed prompts followed by unvetted, uncurated output with no thought for its effects. But AI can also raise standards and accelerate outcomes.
AI makes expertise and taste more valuable. What AI changed is capability, and leveling capability does not level the landscape. The landmarks still stand. What rises is the ground people start from, and how many can start.
None of this is new in kind, only in scale and reach. Photography did not end painting; it changed what painters could explore. Recordings did not end musicianship or the concert. Typesetting, switching, and computation are more capable than ever, and the compositor, the switchboard operator, and the human computer have largely disappeared as occupations. Each time, a tool took over a task, the work grew, and a new generation did it.
My own work with AI has three aims: following my curiosity, improving how I work with these tools, and sharing results that are interesting, if not famous, and meet a basic but honest standard. I do not plan to submit it for peer review. Each note says so, and says what was checked. I welcome scrutiny, but I do not assume anyone owes it their time.
Effort is not proof of value. But working through difficulty can build judgment, and the worry about losing that is older than any of this. In the Phaedrus, King Thamus warns that writing will weaken memory, since people will trust marks instead of their own minds. He was right about the cost to memory. But that cost came with a gain: libraries, ledgers, and laws preserve more than any person can remember. Writing changed what people needed to learn and what they could build.
Producing a proof is changing too, and the world that follows will not be built on proofs found by people alone. One large problem remains open: how to develop expertise when AI takes over the tasks through which people once learned. The next generation will still have hard work to do.
We do not know what that learning will look like, and fear is an understandable response. Two responses this month seem healthy to me. Anthropic’s CEO argued that capability development should slow so that safety work can keep up with the risks I set aside earlier. The Clay Institute, responding to the announcement that Navier–Stokes had apparently been settled, said its process would be deliberately unhurried. Both make room for human judgment. People have long learned to choose questions, judge arguments, and understand results by working beside someone who could. That has not changed.