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Theorist

The math notebook that shows its work

Every result carries its derivation. Solve an equation and reveal the steps one at a time, each naming the rule it used and why it holds. Drag a term across the equals sign and it changes sign as it crosses — because crossing is subtracting from both sides. All mathematics is computed by an exact symbolic engine on your device — never by AI, and never in the cloud.

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Free during beta · macOS & iPadOS · In the spirit of the classic 1990s Theorist

The Quadratics tutorial notebook in Theorist: prose explanation, live sliders for a, b, and c, and a parabola that follows them.

The Quadratics tutorial: sliders drive the coefficients, the parabola follows live, and the algebra below explains what you just saw.

Learning math by doing math

Theorist doesn’t hand you answers — it hands you the moves, and lets you make them.

Every step, on demand

Simplify, expand, factor, solve, differentiate, integrate — each result becomes a new line that can reveal its working one step at a time, with the rule named and explained. The finished answer is there when that’s all you need.

Drag the algebra

Terms are things you can pick up. Carry one across the equals sign and it changes sign on the way — the gesture is the lesson. Wander down an unproductive path and nothing scolds you; the notebook records your route without judging it.

Living notebooks

Give a symbol a value on a slider and every expression, graph, and table that depends on it follows. Or set a notebook to Fixed when it should stand as a record — and if an edit breaks a conclusion, it’s marked, never silently rewritten.

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Graphs written as sentences

“Plot a·x² + b·x + c for x from −5 to 5, for each a from 1 to 3.” Ranges are real expressions that can reference your other values, and a family draws one curve per parameter so you see what a coefficient does.

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Define your own rules

Write a rewrite rule as a sentence — transform x(y + z) into xy + xz — and use it like a built-in. Every rule is checked numerically before it can ever be used; a false one is refused with a counterexample, not a shrug.

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Middle school through college

Five tutorial notebooks ship built in — from first equations to derivatives — opened as templates you can edit and save as your own. Levels change what’s suggested, never what’s allowed: a curious eighth-grader can always try calculus.

Honest practice & quizzes

Watch a problem worked, then drive a similar one yourself. Quizzes score by construction, tell you what to study, and add a little extra practice on what you missed last time — and say so when they do. No invisible steering.

Private by architecture

The symbolic engine is deterministic and runs entirely on your device. Optional Apple Intelligence features (asking questions in plain English, reading equations from images) run on-device too — and the model is never allowed to do the mathematics.

A Theorist welcome notebook: a solved equation, a symbolic quadratic, and assumption sliders.

A notebook is propositions, prose, assumptions, and graphs — every block manipulable, every result traceable.

Rotatable surfaces, reborn

The 1991 Theorist’s claim to fame, back and in colour: write z = f(x, y) as a sentence, then grab the landscape and turn it. Pinch to zoom, one tap to reset — and if the range is written in terms of a slider, the whole surface morphs live.

The saddle, grabbed and turned — and one tap puts it home.

Theorist is in beta

We’re building the modern successor to the app that taught a generation of mathematicians to manipulate, not just compute. Join the TestFlight beta, break things, and tell us — especially if you teach.

Join the TestFlight Beta

Requires TestFlight · macOS 15+ / iPadOS 18+ · Apple Intelligence features need supported hardware

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