Image generators are designed to mimic their training data, so where does their apparent creativity come from? A recent study ...

Scientists reconstructed 500 million years of evolutionary history to reveal which came first: colorful signals or the color ...

I n 1943, a pair of neuroscientists were trying to describe how the human nervous system works when they accidentally laid the foundation for artificial intelligence. In their mathematical framework ...

For Woodin, the dream is to build an inner model that truly approximates V and therefore includes all the large cardinals. He calls it “Ultimate L.”It might seem like a hopeless task — after all, ...

I n the fall of 2022, a Princeton University graduate student named Carolina Figueiredo stumbled onto a massive coincidence. She calculated that collisions involving three different types of subatomic ...

Second, he provided a formula for the maximum number of bits per second that can be reliably communicated in the face of noise, which he called the system’s capacity, C.This is the maximum rate at ...

Some of those who remained set to work scrutinizing decades-old assumptions. They started thinking anew about the striking features of nature that seem unnaturally fine-tuned — both the Higgs boson’s ...

The laws of physics imply that the passage of time is an illusion. To avoid this conclusion, we might have to rethink the reality of infinitely precise numbers. Strangely, although we feel as if we ...

Physicists have begun to explore the proton as if it were a subatomic planet. Cutaway maps display newfound details of the particle’s interior. The proton’s core features pressures more intense than ...

S ince the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

When 50 mathematicians spend a week in the woods, there’s no telling what will happen. And that’s the point. In February, before the COVID-19 pandemic locked down cities and closed borders, I spent ...

In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate ...