Projective plane
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
Seven points, seven lines
A geometry with seven points, in which every two points lie on exactly one line and every two lines meet in exactly one point. There are no parallels, the whole thing is built out of the two-element field, and one of its lines has to be drawn as a circle.
A schedule where every pair meets once
Sort n people into groups of three so that every two of them share a group exactly once. Two divisions have to come out whole, that rules out most sizes — and at every size the divisions permit, a schedule exists.
The thirty-six officers
Six regiments send six officers each, one of every rank. Arrange all thirty-six in a square so that each row and each column holds every rank once and every regiment once. Euler could not, guessed why, and was wrong about the reason.
Named alongside it
The objects these essays reach for when they reach for this one.
Counting argumentExistence proofFano planeFinite fieldIncidenceBasisBlock designCounterexampleDivisibilityDualityLatin squareOrthogonal latin squares