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Mathematics

Mathematicians can't agree what 'equals' means, and that's a problem

What does "equals" mean? For mathematicians, this simple question has more than one answer, which is causing issues when it comes to using computers to check proofs. The solution might be to tear up the foundations of maths

By Alex Wilkins

5 June 2024

More complex than it looks

Aspix/Alamy

When you see “2 + 2 = 4”, what does “=” mean? It turns out that’s a complicated question, because mathematicians can’t agree on the definition of what makes two things equal. While this argument has been quietly simmering for decades, a recent push to make mathematical proofs checkable by computer programs, called formalisation, has given the argument new significance.

“Mathematicians use equality to mean two different things, and I was fine with that,” says Kevin Buzzard at Imperial…

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