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number theory

Illustration of Fermat's Last Theorem
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Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced

Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.

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The Subtle Art of the Mathematical Conjecture

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.

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number theory

Mathematicians Discover the Perfect Way to Multiply

By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit.

Abstractions blog

Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33

A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.

Art for "Smaller Is Better: Why Finite Number Systems Pack More Punch"
Abstractions blog

Smaller Is Better: Why Finite Number Systems Pack More Punch

Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems.

number theory

How a Strange Grid Reveals Hidden Connections Between Simple Numbers

A graduate student has helped illuminate a long-suspected connection between addition and multiplication.

Illustration of lock with polynomials surrounding it
Abstractions blog

Mathematicians Seal Back Door to Breaking RSA Encryption

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

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number theory

In the Universe of Equations, Virtually All Are Prime

Equations, like numbers, cannot always be split into simpler elements.

abstractions blog

New Proof Shows Infinite Curves Come in Two Types

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.