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continuum hypothesis

Gödel’s incompleteness theorems.
Abstractions blog

How Gödel’s Proof Works

July 14, 2020

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.

Measuring tapes
infinity

Mathematicians Measure Infinities and Find They’re Equal

September 12, 2017

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.

Image of spiral staircase.
Mathematics

To Settle Infinity Dispute, a New Law of Logic

November 26, 2013

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.