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Alan Turing and the Power of Negative Thinking

September 5, 2023

Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.

Q&A

Why Mathematical Proof Is a Social Compact

August 31, 2023

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

New Codes Could Make Quantum Computing 10 Times More Efficient

August 25, 2023

Quantum computing is still really, really hard. But the rise of a powerful class of error-correcting codes suggests that the task might be slightly more feasible than many feared.

The AI Tools Making Images Look Better

August 23, 2023

Researchers have discovered ways around a fundamental trade-off between accuracy and beauty in digital images.

Complexity Theory’s 50-Year Journey to the Limits of Knowledge

August 17, 2023

How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been asking questions like this for decades. A string of recent results has started to deliver answers.

Risky Giant Steps Can Solve Optimization Problems Faster

August 11, 2023

New results break with decades of conventional wisdom for the gradient descent algorithm.

Q&A

The Cryptographer Who Ensures We Can Trust Our Computers

July 27, 2023

Yael Tauman Kalai’s breakthroughs secure our digital world, from cloud computing to our quantum future.

To Move Fast, Quantum Maze Solvers Must Forget the Past

July 20, 2023

Quantum algorithms can find their way out of mazes exponentially faster than classical ones, at the cost of forgetting the path they took. A new result suggests that the trade-off may be inevitable.

How to Build a Big Prime Number

July 13, 2023

A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers.

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