In this analogy, the narrow pre-automotive roads are the social infrastructure of mathematics: papers, journals, conferences, citations, advisor-student or mentor-mentee relationships, job postings, and the like. They are primarily designed for use by humans alone, or humans using only moderate amounts of computer assistance. The analogue of transportation here would be that of proving new results that take one from a given hypothesis to a desired conclusion.

Human mathematicians can generate such proofs, but the process is lengthy and inefficient, usually requiring one to draw upon previous work or collaboration with colleagues or students. But this laborious process also generates many beneficial secondary effects beyond the ostensible goal of getting from hypothesis to conclusion. The author(s) develop skills and expertise for future research projects. Maps of the mathematical terrain can be drawn for subsequent researchers to benefit from, for instance pointing out future directions of research or serendipitious discoveries that the author encountered or glimpsed during his or her journey. Interesting stories - such as encountering a dead end in one's mathematical exploration, and changing course to avoid it - can be told. (2/5)