The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same.
But there is a growing community of mathematicians who regard the equal sign as math’s original error. They see it as a veneer that hides important complexities in the way quantities are related — complexities that could unlock solutions to an enormous number of problems. They want to reformulate mathematics in the looser language of equivalence.
“We came up with this notion of equality,” said Jonathan Campbell of Duke University. “It should have been equivalence all along.”