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The laws of physics imply that the passage of time is an illusion. To avoid this conclusion, we might have to rethink the reality of infinitely precise numbers.
Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.
Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.
Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.