Taken literally and seriously, mathematics affirms truths about numbers, functions, sets, spaces and other entities, which are as real as rocks and yet inhabit neither space-time nor our minds. There are good reasons, which I shall not consider here, for philosophers of mathematics to take mathematics seriously and literally.1 Opposing those reasons is the ensuing mystery such realism makes of mathematical knowledge. If numbers and their cousins are outside of space-time, then they cannot transmit information to our sensory detectors. If they are also neither individual nor collective mental constructions, then we are not free to imagine or stipulate or otherwise “dream up” their properties. How then can we acquire knowledge about

them? That question drives mathematical realists to despair and makes reluctant nominalists of many sensible people.