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computational complexity

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Five mountain landscapes on floating scrolls representing possible cryptographic worlds.
cryptography

Which Computational Universe Do We Live In?

By Erica Klarreich
April 18, 2022
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Cryptographers want to know which of five possible worlds we inhabit, which will reveal whether truly secure cryptography is even possible.

Illustration of a figure standing between broken orange walls and a blue unbreakable wall with a broken sledgehammer beside it
computational complexity

Researchers Identify ‘Master Problem’ Underlying All Cryptography

By Erica Klarreich
April 6, 2022
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The existence of secure cryptography depends on one of the oldest questions in computational complexity.

An illustration of a locomotive pulling train cars, with math symbols piled in the caboose.
computational complexity

Computer Scientists Eliminate Pesky Quantum Computations

By Nick Thieme
January 19, 2022
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For years, intermediate measurements made it hard to quantify the complexity of quantum algorithms. New work establishes that those measurements aren’t necessary after all.

A graphic of global air travel.
polynomials

Surprising Limits Discovered in Quest for Optimal Solutions

By Max G. Levy
November 1, 2021
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Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits.

A GIF of a fluctuating plane with a ball rolling over its peaks and valleys and then off the screen.
computational complexity

Computer Scientists Discover Limits of Major Research Algorithm

By Nick Thieme
August 17, 2021
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The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem.

Quantized Columns

What Makes Quantum Computing So Hard to Explain?

By Scott Aaronson
June 8, 2021
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To understand what quantum computers can do — and what they can’t — avoid falling for overly simple explanations.

A graphic showing improvements in the speed of matrix multiplication
algorithms

Matrix Multiplication Inches Closer to Mythic Goal

By Kevin Hartnett
March 23, 2021
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A recent paper set the fastest record for multiplying two matrices. But it also marks the end of the line for a method researchers have relied on for decades to make improvements.

Abel Prize

Pioneers Linking Math and Computer Science Win the Abel Prize

By Kevin Hartnett
March 17, 2021
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Avi Wigderson and László Lovász won for their work developing complexity theory and graph theory, respectively, and for connecting the two fields.

algorithms

New Algorithm Breaks Speed Limit for Solving Linear Equations

By Kevin Hartnett
March 8, 2021
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By harnessing randomness, a new algorithm achieves a fundamentally novel — and faster — way of performing one of the most basic computations in math and computer science.


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