While American children once learned to add by reading a poster of animals and birds, they do it now by playing games on computers. Each step in between—whether it be a box of blocks or exercises ...

THE HISTORY Of computers is often told as a history of objects, from the abacus to the Babbage engine up through the code-breaking machines of World War II. In fact, it is better understood as a ...

Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source: a ...