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computational complexity

Art for "Mathematicians Discover the Perfect Way to Multiply"
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.

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

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 "Major Quantum Computing Advance Made Obsolete by Teenager"
quantum computing

Major Quantum Computing Advance Made Obsolete by Teenager

18-year-old Ewin Tang has proven that classical computers can solve the “recommendation problem” nearly as fast as quantum computers. The result eliminates one of the best examples of quantum speedup.

Diagram showing show the hierarchy of different classes.
Abstractions blog

A Short Guide to Hard Problems

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape.

Illustration for "Finally, A Problem That Only Quantum Computers Will Ever Be Able to Solve"
computational complexity

Finally, a Problem That Only Quantum Computers Will Ever Be Able to Solve

Computer scientists have been searching for years for a type of problem that a quantum computer can solve but that any possible future classical computer cannot. Now they’ve found one.

Lede art for "First Big Steps Toward Proving the Unique Games Conjecture"
computational complexity

First Big Steps Toward Proving the Unique Games Conjecture

The latest in a new series of proofs brings theoretical computer scientists within striking distance of one of the great conjectures of their discipline.

Abstractions blog

One-Way Salesman Finds Fast Path Home

The real-world version of the famous “traveling salesman problem” finally gets a good-enough solution.

Subhash Khot
Thinking Places

Subhash Khot, Playing Unique Games in Washington Square Park

The theoretical computer scientist behind the influential Unique Games Conjecture delights in the wonders of New York’s Washington Square Park, where he ponders the impossible.

Illustration: boxing gloves
Abstractions blog

Graph Isomorphism Vanquished — Again

Just five days after posting a retraction, László Babai announced that he had fixed the error in his landmark graph isomorphism algorithm.