For decades, the search for extraterrestrial life has been confined largely to faint radio signals and conjecture. Now, the ...

Everyone has looked up at the clouds and seen faces, animals, objects. Human brains are hardwired for this kind of whimsy.

Roblox sees weak reactions to fee and capex guidance, with costs limiting growth and value only near lower support levels.

For over a decade, mathematicians have failed to agree whether a 500-page proof is actually correct. Now, translating the ...

Mathematician Grigori Perelman solved the Poincaré conjecture, and then rejected the $1 million prize that came with it.

The COLA method can help identify whether you're operating on speculation, belief, evidence, or principle—and respond ...

Our survival system evolved to respond to shadows before confirming threats. Adaptive in nature, exhausting in modern life.

When Hannah Cairo was 17 years old, she disproved the Mizohata-Takeuchi conjecture, a long-standing guess in the field of harmonic analysis about how waves behave on curved surfaces. The conjecture ...

Hannah Cairo found herself stuck on a problem that wouldn’t leave her mind. It wasn’t a regular homework assignment—it was a decades-old mathematical puzzle believed to be true by leading experts in ...

Mathematicians have finally solved a geometry problem that has puzzled the field for decades. By wiggling a needle around while spinning it, you can minimize the amount of space it moves through, ...

The original version of this story appeared in Quanta Magazine. Sometime in the fall of 2021, Andrew Krapivin, an undergraduate at Rutgers University, encountered a paper that would change his life.