Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...

OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds ...

A new quantum-inspired algorithm has cracked a problem so massive that conventional supercomputers struggle to even approach it. Researchers used the method to simulate extraordinarily complex quantum ...

Liam Price just cracked a 60-year-old problem that world-class mathematicians have tried and failed to solve. He’s 23 years old and has no advanced mathematics training. What he does have is a ChatGPT ...

The original version of this story appeared in Quanta Magazine. In 1939, upon arriving late to his statistics course at UC Berkeley, George Dantzig—a first-year graduate student—copied two problems ...

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 ...

The leading approach to the simplex method, a widely used technique for balancing complex logistical constraints, can’t get any better. In 1939, upon arriving late to his statistics course at the ...

Abstract: This article studies the two-dimensional (2-D) rectangle packing area minimization problem (RPAMP), a key subproblem in floor planning for very large-scale integration (VLSI) chip design.

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 the easiest pieces first. But this kind of sorting has a cost.

Using an advanced Monte Carlo method, Caltech researchers found a way to tame the infinite complexity of Feynman diagrams and solve the long-standing polaron problem, unlocking deeper understanding of ...

Consider someone who’s perfectly content with their office chair. It’s not ergonomic, it doesn’t have lumbar support, but it works. Then, during a meeting or a visit to a friend’s office, they sit in ...

There are countless real-world uses of optimization in every area. Many technical and industrial sectors are now struggling to develop a suitable optimizer or algorithm to handle real-world challenges ...