Open, and small

Daily math practice that leaves a map behind

MathDaily is built around one idea: five to fifteen minutes a day should leave behind a map of what you know and how it connects — not a streak.

You can create an account and start today, so here is the size of it first. 48 of the 69 concepts on the map have material written behind them, and new fragments are capped at 1 a day — about 48 days of new material, after which a session is reviews only until more is written. The remaining 21 concepts are drawn on your tree and cannot be studied. They are not locked and nothing you could buy would open them: they are unwritten, and that is our side of it, not yours.

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Hear when more is written

The map, as it currently stands

The real prerequisite graph for single-variable calculus: 69 concepts, 152 prerequisite links, 14 layers from the shallowest to the deepest. This is the shared map, not anyone's tree, so no progress is drawn on it. 48 of these concepts have material behind them today; the rest are here because the graph is real, not because they can be studied.

Content packcalculus-single-variable@0.1.0

Why it is built this way

Three kinds of product already exist. Each is missing the same thing in a different place.

Course platforms: Progress is a percentage of video watched. That measures how much went past, not what you can do — and once you fall behind there is no way back in except the beginning.
Solvers and answer apps: They settle one question and leave nothing behind. Nothing accumulates.
Gamified apps: Enjoyable, but the structure stays invisible. Where you are, what is missing underneath, and what you could sensibly learn next are never shown to you.

The tree is the product, not the decoration

Your own graph is what a session leaves behind: lit for what holds, dim for what is slipping, outlined for what your prerequisites already allow. One object that is the progress bar, the map and the record at once, rather than three widgets that disagree.

Today: it runs on your own answers. Concepts we have not written are labelled as ours to finish — never as something you failed to reach.

Start where you actually are

Someone five years into a job who wants probability should not have to begin at what a fraction is, and should not be dropped into measure theory either. The way in is a short placement that walks the prerequisite chain by halving, and hands back a starting point rather than a score.

Today: it runs. Where a rung of the chain has no question written for it, the placement asks you directly in our own voice rather than inventing a question on the spot.

How you think is the second axis

Concepts run in one direction. Reduction, invariants, symmetry, limiting processes, construction, proof by contradiction — the moves themselves run in the other. Each fragment carries exactly one thinking tag, so getting better at mathematics becomes a second thing that can be counted instead of a feeling.

Today: 13 tags are defined, each with a written rationale and worked examples, and material you can actually reach carries 12 of them. 48 of the 69 concepts declare at least one; the rest are deliberately untagged, because a label on everything means nothing. The spread across those 12 is lopsided enough that charting it would look precise and mean nothing, so nothing charts it.

Review is the default, not a feature you remember to use

Strength decays, so the tree dims on its own. A day is one new fragment plus whatever came due, which means you never have to decide what to revise — and coming back after three weeks away costs you nothing worse than a slightly darker tree.

Today: reviews run and nothing caps them. New fragments are capped, at 1 a day, and it is the server that enforces that rather than this page. Answering wrongly dents a concept instead of resetting it, because the scheduler acts on concepts rather than flashcards.

Where this stands

The honest version. Every number below is counted from the content in this repository when the page is built.

Exists today

Accounts. Sign-up, the placement, the daily session, the hint ladder and your own tree all run against the live database — checked by signing up on it, not by reading the code.
A prerequisite graph for single-variable calculus: 69 concepts, 152 prerequisite links, 14 layers deep. Every link is a mathematical claim, and two independently written checkers agree the graph is acyclic and that depth increases across every edge.
276 misconceptions recorded alongside the concepts. They are not commentary — they become the wrong answers in the questions, so an invented one produces a worthless question.
48 fragments written: 444 minutes of reading and 96 questions behind them. Each fragment was drafted by one model and then checked by a different one, because a model asked twice mostly agrees with itself.
394 mathematical statements inside those fragments, 349 of which carry an arithmetic witness — an expression, and the value it has to produce. Every one of those was re-evaluated by an evaluator other than the one the authoring pipeline uses to assert them: the thing that claims a statement is true must not also be the thing that proves it.
48 concepts you can actually study: an approved fragment with at least one question behind it. A fragment with nothing to answer is written but not teachable, and is not counted here.
13 thinking tags, each with a rationale and worked examples of the move it names.
A scheduler that decays strength per concept, and the readiness rule that decides when a concept is open. Both are pure functions, both have tests.
All of it in this repository as versioned files. It can be diffed, reviewed and rolled back, and no language model writes to the database at runtime.

Does not exist yet

Material for the other 21 concepts. They are on the map, your tree will show them, and they cannot be studied. They are not locked and nothing you could buy would open them: nobody has written them.
More than about 48 days of new material. After that a session is reviews only, until more is written. That is the size of this thing today, and it is the reason the list at the bottom of this page exists.
Anything past the entry layer. Everything written so far sits near the bottom of the graph — limits, derivatives and integrals are mapped and not yet taught.
Anything on sale. There is no payment integration, no price and no tier. The cap of 1 new fragment a day is a line in the code, not a paywall.
Anything that answers a question you type. The hints are a ladder written in advance and reviewed before it ships; no model runs while you are studying.

Who it is for

At school

Keeping up with what is being taught this term, and quietly repairing whatever is missing underneath it.

At university

Calculus, linear algebra, probability — where working backwards usually turns up one shaky piece of secondary-school algebra holding everything else up.

Changing field

Enough probability and linear algebra to do the work, reached by naming the destination and pulling the prerequisite chain backwards from it.

For its own sake

No exam and no deadline. The thinking axis is a perfectly good way to walk through it.

If your clearest memory of mathematics is being told you were slow at it: the first fragment written for this product is about fractions, negatives and where a rule stops applying. That was not an accident.

When more is written

New material runs out at about 48 days, and after that a session is reviews until we have written more. One message when there is more — it is not a newsletter and there is nothing to read in between.