An essay in this week’s issue of Science magazine by Andrew Hodges, the dean of Wadham College at Oxford University and the author of Alan Turing: The Enigma argues that, great as these achievements are, Turing’s greatest contribution was defining the limits of what computers can “know”—that is, what is computable. By formalizing the computability question in 1936, Turing illuminated the deeper issue of what humans could know: Is our knowledge limited in the same way as computers? Or do we have some sort of mental “intuition” (Turing’s word) that supersedes the power of mere machinery?

Turing wasn’t sure (though he suspected that the strange rules of quantum mechanics may give our brains some non-deterministic wiggle room). Three quarters of a century later, we’re not much closer to an answer. Even in this age of “big data,” where computers churn through gobs of information to come up with cannily human-like responses (consider IBM’s Jeopardy-beating Watson computer, named, incidentally, after the CEO with poor computer-demand forecasting skills), humans are far better at everyday tasks like making sense of a scene. Artificial intelligence remains a dream.

Turing’s work on computability led to an even deeper question, according to Hodges: “Does computation with discrete symbols give a complete account of the physical world?” In other words, is the world computable? Can a machine, in principle, rise not just to the intellectual capabilities of human beings, but supersede those capabilities? Can a computer know everything?