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continuum hypothesis

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foundations of mathematics

How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.

By Natalie Wolchover
July 15, 2021
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For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

Gödel’s incompleteness theorems.
Abstractions blog

How Gödel’s Proof Works

By Natalie Wolchover
July 14, 2020
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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

By Kevin Hartnett
September 12, 2017
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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

By Natalie Wolchover
November 26, 2013
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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.

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