Foundations

Learn Reading Mathematics

How to read a definition, a theorem and a proof. The skill general reading does not give you, taught before the two thousand pages that assume it.

Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

20 lessons in Reading Mathematics

A definition decidesSaying the symbols out loudUnpacking a definitionExamples and non-examplesReading “for all”One counterexample settles itReading “there exists”The order of the quantifiersSet-builder notationSubscripts, sums and familiesNegating a statementReading “if P then Q”Converse, inverse, contrapositiveReading “if and only if”Hypotheses and conclusionWhat each hypothesis is doingWhat a proof isWhy is this step allowed?Reading a proof line by lineWhat to do when you are stuck
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Reading Mathematics exactly where it's useful.

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