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When it comes to hard problems, computer scientists seem to be stuck. Consider, for example, the notorious problem of finding the shortest round-trip route that passes through every city on a map ...

Concrete sucks CO2 out of the atmosphere, but making it initially produces a lot of carbon dioxide as a byproduct. Fortunately, by rethinking the chemistry of cement altogether, we can actually use ...

A robust Neuro-Symbolic Sudoku Solver combining Graph Attention Networks (GATv2) with Dynamic Constraint Propagation. Efficiently solves NP-hard puzzles where traditional backtracking fails ...

Determining the least expensive path for a new subway line underneath a metropolis like New York City is a colossal planning challenge—involving thousands of potential routes through hundreds of city ...

Otters show how clever and playful they are. Trump Cases Land With Judge Cannon, Raising Alarms Epstein survivor breaks her silence on 'the list,' Mar-a-Lago and the fight for justice Map shows states ...

We introduce NP-ENGINE, a scalable framework that generates near-infinite and hierarchically difficult NP-hard problems within the RLVR paradigm, empowering LLMs' optimization reasoning abilities.

The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...

Researchers have successfully used a quantum algorithm to solve a complex century-old mathematical problem long considered impossible for even the most powerful conventional supercomputers. The ...

It is impossible to imagine a master chef who doesn’t know how to cook, a cabinet maker who doesn’t know anything about carpentry, or a pianist who can’t read music. All three sound like ...

Word problems are often described as “math stories” and can put complex mathematical operations into a more approachable form for students. But students often struggle when they see a combination of ...