Watching a modern AI perform can feel like witnessing a magic trick. Whether it is Gemini, ChatGPT or Claude, these models often project an aura of near-infinite wisdom, solving complex coding issues ...

One night in July, 1964, the logician Lotfi Zadeh found himself alone in his parents’ New York apartment, his dinner plans cancelled. At the time, Zadeh later wrote, he was doing “a lot of thinking ...

Many attempts to develop artificial intelligence are powered by powerful systems of mathematical logic. They tend to produce results that make logical sense to a computer program — but the result is ...

All men are mortal. Socrates is a man. Therefore, Socrates is mortal. Logical arguments like this one have been studied since antiquity. In the last few decades, however, logic research has changed ...

Earlier this month, 36 sharp-witted high school students from around the globe stepped foot on the warm and breezy campus of Stanford University. Out of more than 4,000 students from more than 2,000 ...

In ancient Greece, Euclid showed that if you agree on a small list of preliminary principles, or axioms, you can use deductive reasoning to reveal all sorts of new mathematical truths. But although ...