Ellenberg draws a distinction between discovering an idea and explaining it clearly. The person who first develops a mathematical concept may present it in the form in which it emerged: through specialised notation, partial insights or arguments shaped by the original problem. That account can be historically important without necessarily being the most accessible introduction.

Later mathematicians and teachers can reorganise the same idea, remove unnecessary complications and connect it with concepts that have since become familiar. Over time, a subject may acquire clearer terminology, better examples and more efficient proofs. The quotation therefore suggests that understanding is often a collective process rather than something completed at the moment of discovery. For learners, it also implies that an original source is not always the best starting point; a later explanation may communicate the underlying idea more effectively while preserving its mathematical substance.