Ellenberg argues that a mathematical method should be tested by approaching the same problem in more than one way. If independent calculations produce the same result, that agreement provides evidence that the method is working as intended. If they produce conflicting answers, the discrepancy signals that at least one assumption, calculation or procedure needs to be examined.

The wider point is about verification rather than mathematics alone. Reliable analysis benefits from checks that are genuinely independent, because repeating the same reasoning in the same form may simply reproduce the same mistake. Comparing different methods can expose hidden errors, weak assumptions or limits in a model. The quotation therefore presents consistency across approaches as a practical test of reliability, while recognising that disagreement is useful evidence: it identifies where further scrutiny is needed before a result should be trusted.