This is a good time for mathematicians to think carefully about the purpose of their work. The development of artificial intelligence brings that question before us with unusual force. Much of the discussion concerns which tasks machines will perform and which abilities will remain distinctively human. But our response also depends on a prior question: what do we understand mathematical work to be, and what gives it its worth? If our answer has become inseparable from the production of results and the demonstration of individual ability, the present uncertainty may reveal a difficulty in our conception of the work itself.
There are broadly two perspectives on mathematics. According to one, we invent it as we construct it: we introduce concepts, choose axioms, and develop theories. According to the other, mathematics exists independently of these activities, and our task is to discover it. These perspectives need not disagree about every aspect of mathematical practice. We plainly develop formalism and arguments. The deeper question is whether the truths we come to understand owe their existence to these acts, or whether our constructions enable us to recognize something that does not depend on us.
