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number theory

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number theory

Landmark Math Proof Clears Hurdle in Top Erdős Conjecture

By Erica Klarreich
August 3, 2020
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Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

Visualization of the distribution of prime numbers in the shape of colorful dots in a hexagonal pattern
Abstractions blog

Mathematicians Will Never Stop Proving the Prime Number Theorem

By Susan D'Agostino
July 22, 2020
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Why do mathematicians enjoy proving the same results in different ways?

A photograph of the mathematician James Maynard outside his home in Oxford, England.
profiles

A Number Theorist Who Solves the Hardest Easy Problems

By Erica Klarreich
July 1, 2020
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In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Diagram showing a colorful visualization of the simple Lie group
Abstractions blog

The ‘Useless’ Perspective That Transformed Mathematics

By Kevin Hartnett
June 9, 2020
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Representation theory was initially dismissed. Today, it’s central to much of mathematics.

Photo of iron filings spread along magnetic field lines on a green and yellow background
number theory

Mathematician Measures the Repulsive Force Within Polynomials

By Kevin Hartnett
May 14, 2020
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Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart.

Quantized Academy

To Win This Numbers Game, Learn to Avoid Math Patterns

By Patrick Honner
May 7, 2020
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Sizing up patternless sets is hard, so mathematicians rely on simple bounds to help answer their questions.

Black and white photo of John Conway against a black background
Abstractions blog

John Conway Solved Mathematical Problems With His Bare Hands

By Kevin Hartnett
April 20, 2020
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The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

Langlands program

‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem

By Erica Klarreich
April 6, 2020
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Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.

Quantized Academy

How Rational Math Catches Slippery Irrational Numbers

By Patrick Honner
March 10, 2020
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Finding the best way to approximate the ever-elusive irrational numbers pits the infinitely large against the infinitely small.


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