Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics. Computer proof assistants have been an intriguing subplot ...

Proof is a measure of the alcohol content of a beverage. In the U.S., policymakers define proof as twice the percentage of alcohol by volume (ABV). For example, a drink with 40% ABV is 80 proof.

The amount of alcohol in a distilled spirit — for instance, vodka or whiskey — is known as the ”proof.” Different countries have different standards for an alcoholic beverage’s proof. In the United ...