Insight, Not Numbers

“The purpose of computing is insight, not numbers”—Richard Hamming placed this sentence on the front of his 1962 textbook Numerical Methods for Scientists and Engineers, and it was not a throwaway slogan. It was a working philosophy from a man whose entire job was producing numbers—who had produced the numbers for the atomic bomb—and who had concluded from the inside that the numbers were never the point. A calculation that does not leave you understanding something better than before is, in his view, a failure no matter how many digits it produces. Insight is not a property of outputs but a state of a mind that has come to understand: it is the experience of structure becoming visible, of grasping why a result had to come out as it did and where it would break if the conditions changed. This distinction—between producing outputs and grasping their necessity—is the sharpest available instrument for thinking about large language models that generate fluent,