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Complexity Theory’s 50-Year Journey to the Limits of Knowledge
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
New results break with decades of conventional wisdom for the gradient descent algorithm.
The Cryptographer Who Ensures We Can Trust Our Computers
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
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
A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers.
The Lawlessness of Large Numbers
Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?
Computer Scientists Inch Closer to Major Algorithmic Goal
A new paper finds a faster method for determining when two mathematical groups are the same.
Neural Networks Need Data to Learn. Even If It’s Fake.
Real data can be hard to get, so researchers are turning to synthetic data to train their artificial intelligence systems.
Sparse Networks Come to the Aid of Big Physics
A novel type of neural network is helping physicists with the daunting challenge of data analysis.