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."
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4 Comments
Add CommentInteresting!
Reply | Report Abuse | Link to thisVery cool to find out where all those Westinghouse/Intel winners end up. I've heard a fair percentage do not pursue math/science/engineering disciplines, those are the interesting ones.
Reply | Report Abuse | Link to thisGood article!
The idea of infinity having various sizes sound ridicules. If normal numbers
Reply | Report Abuse | Link to this1 2 3 ad infinitum are used, it has no end. If you use each number with a decimal place going ad infinitum it sound like it would be bigger, but both have no end, infinity. As for philosophy that's just how we live and perceive our surroundings. Everyone is a philosopher. What they teach is how other people viewed life.
I recall trying some experiments in geometry on a computer. When I made certain constructions I was surprised that a completely new theorem jumped out. I had the strong feeling that I discovered it rather than inventing it. Nothing new here - lots of mathematicians get that feeling. I think that somehow the realist / naturalist disagreement will never be settled satisfactorily because each has intractable problems.
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