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 ...

Lindsey Ellefson is Lifehacker’s Features Editor. She currently covers study and productivity hacks, as well as household and digital decluttering, and oversees the freelancers on the sex and ...

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.

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 ...

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 ...

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 ...