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infinity

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Quantized Academy

How Big Is Infinity?

By Patrick Honner
September 27, 2022
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Of all the endless questions children and mathematicians have asked about infinity, one of the biggest has to do with its size.

2021 in Review

The Year in Math and Computer Science

By Bill Andrews
December 23, 2021
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Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.

An orange ball decomposing into points and rematerializing as two balls, each the same size as the first.
explainers

Banach-Tarski and the Paradox of Infinite Cloning

By Max G. Levy
August 26, 2021
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One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces.

Illustration of people along a path classifying colorful mathematical trees
set theory

Mathematicians Solve Decades-Old Classification Problem

By Steve Nadis
August 5, 2021
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A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

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.

Art for "In Quantum Games, There’s No Way to Play the Odds"
Abstractions blog

In Quantum Games, There’s No Way to Play the Odds

By Kevin Hartnett
April 1, 2019
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These games combine quantum entanglement, infinity and impossible-to-calculate winning probabilities. But if researchers can crack them, they’ll reveal deep mathematical secrets.

Art for "The Universe’s Ultimate Complexity Revealed by Simple Quantum Games"
quantum information theory

The Universe’s Ultimate Complexity Revealed by Simple Quantum Games

By Kevin Hartnett
March 5, 2019
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A two-player game can reveal whether the universe has an infinite amount of complexity.

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.

Insights puzzle

Solution: ‘Puzzles Inspired by Ramanujan’

By Pradeep Mutalik
August 8, 2016
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What can the mathematical genius Srinivasa Ramanujan teach us about number theory through mathematical structures involving infinity?


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