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foundations of mathematics
Does Time Really Flow? New Clues Come From a Century-Old Approach to Math.
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.
With Category Theory, Mathematics Escapes From Equality
Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.
Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced
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.
Mathematicians Measure Infinities and Find They’re Equal
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.