When I was in middle school, my mathematics teacher had a firm and loudly held opinion about calculators: they were making us lazy, atrophying our ability to compute, and producing a generation that could not think for itself. Calculators were banned from his classroom. We did everything by hand.
He was not a stupid man. His concern was genuine. And he was, I think, almost entirely wrong.
This essay is about why - and about what it means now that a far more powerful tool than the calculator has arrived, bringing with it the same fear, the same concern about atrophy, and the same fundamental misunderstanding of what tools actually do to human intelligence.
A Fear as Old as Tools Themselves
The anxiety about tools making us dumber is not new. It is one of the oldest recurring anxieties in the history of human thought. Socrates worried that writing would weaken memory - why remember something you can look up? He was right that writing changed how memory worked. He was wrong that this was a catastrophe. GPS weakened spatial navigation in people who relied on it heavily. Spell-checkers made some people worse at spelling. The concern in each case was real, and in each case, it missed the larger point.
The larger point is this: every tool that automates a cognitive function frees up cognitive capacity for something else. The question is never whether something atrophies. Something always atrophies. The question is what grows in its place - and whether the tradeoff is worth it.
My calculator teacher was focused entirely on what was lost. He never asked what was gained.
What was gained, for me, was mathematics itself. Not the mechanical layer - the arithmetic, the tedious computation - but the conceptual layer that the computation was always in service of. With a graphing calculator, I could explore functions in minutes that would have taken hours to plot by hand. I could ask "what happens when I change this parameter?" and see the answer immediately. I could develop intuition about mathematical structures - the shape of a curve, the behavior of a function near a singularity - that would have been buried under arithmetic if I had to compute everything manually.
The calculator did not make me worse at mathematics. It gave me more mathematics per unit of time - and specifically, the more interesting mathematics. The part that requires genuine thought rather than careful pencil-work.
A Tool in Service of the Deeper Skill
There is a simpler way to make this point. When a child learns to ride a bike, they can do it with or without training wheels. Without them, it is painful, slow, and discouraging. With them, the child can focus on steering, pedaling, and building confidence - while balance develops naturally underneath.
Nobody argues that children should learn to ride without training wheels in order to build character. The training wheels are not the point. The bike is the point. The tool exists in service of the deeper skill, and removing it prematurely does not produce better cyclists - it produces fewer of them.
The calculator is training wheels for mathematical intuition. It lets you focus on the conceptual layer while the mechanical layer is handled. The intuition develops faster, not slower. By the time the wheels come off - by the time you are doing serious mathematics - you have more intuition to work with, not less, because you spent your time building it rather than grinding arithmetic.
My PhD is the evidence. I was proud to tell people that the only numbers in my thesis were the page numbers. Years of advanced mathematics, and mental arithmetic never appeared once. The skill my teacher was so worried about protecting turned out to be completely irrelevant to the actual work. What mattered was intuition - the capacity to see structure, to recognize patterns, and to know which approach would work before working it through. The calculator accelerated the development of exactly that capacity.
On Hunting, Running, and Coding for Fun
Let me be honest about what the calculator teacher got right: the atrophy is real. I am worse at mental arithmetic than my parents' generation. People who rely on GPS navigate less well without it. Skills that are not exercised weaken. This is simply true.
But here is what the atrophy argument consistently misses: we do not need to exercise every skill out of necessity in order to preserve it. We can exercise it by choice, for pleasure, because the activity itself is rewarding.
Nobody hunts because they have to anymore - not in most of the world. Supermarkets exist. And yet people hunt. Not because survival depends on it, but because they enjoy it. The same is true of running - we have cars, and yet people run marathons. Of cooking - we have restaurants, and yet people spend Sunday afternoons making elaborate meals from scratch.
The worry that AI will atrophy our ability to code, to write, to reason through problems assumes that the only reason people do these things is necessity. It misses that many people do them because they love them. I code at home in my spare time. Not because I have to. Because I enjoy it. The fact that AI can now handle much of the coding at work does not touch that.
What AI does is convert necessity into choice. The skills that were obligations become hobbies, available to those who want them, no longer required of those who do not. That seems like an improvement, not a loss.
The argument for banning calculators to preserve mental arithmetic is equivalent to arguing that we should ban supermarkets to preserve hunting skills. Both positions are technically coherent. Neither is serious.
What Access to Great Teaching Has Always Required
Here is a fact about the history of human learning that we rarely state plainly: for most of history, the quality of your education was almost entirely determined by the accident of your geography and social position.
If you were born in Florence in the 1480s and your family had the right connections, you might spend time around Leonardo da Vinci. You would learn to see the world differently. You would ask questions and receive answers from a mind that spanned engineering, anatomy, painting, mathematics, and philosophy simultaneously - a mind that made connections across domains that nobody else could make, and that was endlessly patient with genuine questions.
If you were born anywhere else, to anyone else, you got whatever your local schoolmaster knew. Which was often not much, and was never Leonardo.
This is the mentorship lottery. It has determined, more than almost any other factor, who gets to develop their thinking to its full potential. Not talent - access. The most talented person in a village with a mediocre teacher is at a profound disadvantage relative to a moderately talented person in Florence with access to the right minds.
AI is dissolving this lottery. Not partially - radically. The person with a Claude account has access to something that would have seemed supernatural to any previous generation: a mind that knows everything about everything, that never gets tired, that never gets annoyed at the same question asked for the fifth time, that can shift from explaining a Pydantic class to advising on a children's book without missing a beat. That meets you exactly where you are and moves at whatever pace you need.
This is the democratization of Leonardo. Not a metaphor - a description. People would have traveled across Europe to spend an afternoon with him. Today, anyone with an account and a question has something arguably more useful: a mind with all of his breadth, available at 3am, infinitely patient, and unable to make you feel stupid for asking.
On Intuition, Exploration, and the Right Layer to Work At
The best argument against the calculator teacher is not philosophical. It is empirical. And I lived it.
The graphing calculator did not make me worse at mathematics. It changed which mathematics I could engage with. By automating the mechanical layer - the plotting, the arithmetic, the tedious computation - it freed me to operate on the conceptual layer. To explore. To develop intuition.
Intuition in mathematics is not the same as calculation. Intuition is the felt sense of why something is true, the ability to predict what a function will do before you compute it, and the capacity to recognize which technique will work on a problem you have never seen before. It is what separates mathematicians who understand from mathematicians who merely compute.
You can develop intuition by grinding through computations by hand. But it is slow, and the signal is buried in the noise of arithmetic. The graphing calculator made the signal visible. In an hour of exploration, I developed intuitions that might have taken weeks of hand-computation to build - and might have been lost entirely in the tedium.
The calculator did not lower the ceiling of what I could understand. It raised the floor of what I engaged with. The mechanical layer was automated away, and what remained was richer.
AI is doing the same thing, one level up. Not for arithmetic but for entire categories of cognitive work. The mechanical layers of writing, coding, researching, and connecting ideas are being automated away. What remains, for the people who use the tools well, is the conceptual layer. The layer that was always the interesting one.
On Breadth, Patience, and the End of the Mentorship Lottery
There is a specific kind of intelligence that has always been rare and always been disproportionately valuable: the generalist who can make connections across domains. The person who knows enough physics to understand the mathematics, enough mathematics to understand the economics, enough economics to understand the history, and enough history to understand the present.
Leonardo was the archetype. There have been others - Leibniz, von Neumann, Feynman, a handful per century. They were valuable precisely because the connections they could make were invisible to specialists. They saw the same structure appearing in different disguises across different fields and could transfer insights that specialists could not reach.
AI has this property structurally. Not because it is more intelligent than any individual human - it is not, in the deepest sense. But because it has been trained on essentially everything, it can hold the physicist's and the economist's and the historian's perspective simultaneously, and make connections between them on demand. Every conversation is a conversation with the ultimate generalist.
For the first time in history, that generalist is available to everyone. Not to the person born in the right city, with the right connections, lucky enough to cross paths with the right mind. To anyone with an account and a question.
The mentorship lottery is ending. What we do with the access we have been handed is, as always, up to us.