Mathematica Erased the Heuristics First

Sarah Demers, chair of physics at Yale, sits in the position where every technological displacement of intellectual labor lands first — large language models can now generate plausible derivations, solve differential equations, even propose experimental designs.

The question her department faces is not whether machines can do physics reasoning — they demonstrably can. But what happens to the human practices that built physicists when machines absorb the reasoning itself. This exact moment arrived before.

In the early 1990s, when Mathematica became standard in theoretical physics departments, the calculation didn't disappear. The software did it better. What disappeared, almost unnoticed, was the hand-heuristics, the order-of-magnitude estimates, the feel for when an answer was physically implausible because it violated some intuitive sense of scale.

The work that looked like mere drudgery. The grinding through algebra to check whether you'd set up the problem correctly. Turned out to be where physicists learned to see problems, not solve them. Departments didn't consciously choose to stop teaching this. They simply saw no reason to spend hours on skills a tool could execute in seconds. What vanished was the friction. The slow, attentional work of moving through a calculation by hand teaches something different from reading output.

When you work at that pace, you notice discontinuities and feel the shape of the mathematics. A generation of theorists emerged in the early 2000s who could manipulate symbolic systems with extraordinary fluency but couldn't estimate, couldn't sense wrongness, couldn't work at a blackboard where the tool wasn't available. The structural parallel is exact. LLMs will absorb the reasoning the way Mathematica absorbed the calculation. But there's one variable this time that might matter. An LLM's reasoning is opaque in a way that forces a choice.

You either train yourself to interrogate it, to catch the moment it's wrong, to develop the judgment to know when you can't trust it. Which requires doing the thinking yourself first, checking the work at speed, building the intuition about what's implausible. Or you don't. The departments that choose the second path will produce physicists who can access reasoning fluently but can't work without it. And in five labs where the internet fails, or ten moments where the stakes require judgment beyond pattern completion, that gap will matter more than comfort ever did.