Mazur describes his lecture: "Well, I don't know the answer to the question of the title and no hedgehog will be harmed, or even mentioned again, in my lecture. The concept of area is one of the many things of interest in Euclid's Elements, and is familiar to all who have been through the Freshman program here at St. John's. There are many ways to approach it. Archimedes, for example sometimes likes to convert the problem of computing area to computing something akin to weight. I'll spend this hour considering these approaches and how they touch on broader issues in mathematical thought such as analogy, heuristic, paradox, and something I'll call characterization (a version of axiomatization). As for prior reading, absolutely none (except what you may have already read in Euclid) is needed, but I will be turning again and again to Proposition 37 of Book I of the Elements: Triangles which are on the same base and in the same parallels equal one another. So if you want to read one page in preparation, take a look at the statement and proof of that marvelous proposition."

This lecture is also part of the Steiner Lecture Series, which is made possible by a gift from the Steiner family in memory of Andrew Steiner, an alumnus of the college from 1963. The lecture series was established to bring notable speakers to campus from a variety of disciplines and endeavors, in recognition of Steiner’s intellectual versatility, and for the sake of continued learning.