GPT-5.4 Pro cracked a conjecture in number theory that had stumped generations of mathematicians, using a proof strategy that ...

In the 1930s and 1940s, for example, a group of Polish mathematicians regularly met in a café in Lwów, Poland (now Lviv, ...

Diffie-Hellman’s key-exchange method runs this kind of exponentiation protocol, with all the operations conducted in this way ...

👉 Learn how to solve two-step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two-step linear equation, we first ...

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the ...

Scientists have found a promising new way to manufacture one of industry’s toughest materials—tungsten carbide–cobalt—using advanced 3D printing. Normally, producing this ultra-hard material requires ...

Abstract: As typical structural noise, stripes commonly occur in remote sensing images captured by linear array sensors, which seriously lowers the image quality and hinders the downstream ...

Getting through a marathon can be hard work – that’s what makes it so rewarding. But the efforts are not simply physiological. Taking on 26.2 miles – and banking a whole block of training before it – ...

Abstract: We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is ...

Amateur mathematicians are using artificial intelligence chatbots to solve long-standing problems, in a move that has taken professionals by surprise. While the problems in question aren’t the most ...

Nearly 200 years ago, the physicists Claude-Louis Navier and George Gabriel Stokes put the finishing touches on a set of equations that describe how fluids swirl. And for nearly 200 years, the ...

Microscope image showing the layered structure of a new 3D-printed aluminum alloy. The wave-like patterns are “melt pools,” traces left by the laser as it melted metal powder layer by layer. The small ...