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continuum hypothesis
foundations of mathematics
How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.
For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.
Abstractions blog
How Gödel’s Proof Works
His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.
infinity
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.
Mathematics
To Settle Infinity Dispute, a New Law of Logic
To determine the nature of infinity, mathematicians face a choice between two new logical axioms. What they decide could help shape the future of mathematical truth.