Since 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 ...

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...

In blockchain development, there is a rule of thumb that only two of scalability, security, and decentralization are valid simultaneously. However, the mathematical expression of that rule was still a ...

The original version of this story appeared in Quanta Magazine. In 1974, five years before he wrote his Pulitzer Prize–winning book Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter was ...

Thomas Jefferson’s first draft of the Declaration of Independence read: “We hold these truths to be sacred and undeniable . . . ” It was supposedly Benjamin Franklin who suggested instead announcing ...