She's built up a reputation for clarity—rare in the usually abstruse academic fields of math or philosophy. "In particular, she can make very technical material accessible to nontechnical readers," Martin says. "Her writing style is simple, clear and a pleasure to read."
Her philosophical views have changed over the years. For example, in 1990 she wrote Realism in Mathematics, which Martin calls "a very fine book, defending with great resourcefulness a realist view about mathematical objects and mathematical knowledge." (Realism is the idea that math exists independently of the human mind; we do not invent it, we discover it). But in 1997, after further contemplation of these questions, she wrote a book called Naturalism in Mathematics, which, in part, argues against the realist perspective. "She is not dogmatically attached to her views, as her switch from realism to naturalism dramatically shows," Martin says. "But she doesn't just hop around from one view to another. There's real sense in which her philosophical ideas have been steadily developing over time. Parts of earlier positions have been dropped, but much has been kept or adapted."