The original version of this story appeared in Quanta Magazine. In the movie Oppenheimer, Niels Bohr challenges the physicist early in his career: Bohr: Algebra is like sheet music. The important ...

In the real world, probability is a tough thing to characterize. If I roll a die, what does it mean to say that it has a one-sixth chance of coming up 5? We say that the outcome is random because we ...

Tiny particles like pollen grains move constantly, pushed and pulled by environmental forces. To study this motion, physicists use a “random walk” model — a system in which every step is determined by ...

Random processes take place all around us. It rains one day but not the next; stocks and bonds gain and lose value; traffic jams coalesce and disappear. Because they’re governed by numerous factors ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...