I have what probably seems like a strange question: why are there theorems? A theorem is essentially a statement to the effect that some domain is structured in a particular way. If the theorem is interesting, the structure characterized by the theorem is hidden and perhaps surprising. So the question is: why do so many structures have hidden internal structures?
Take the natural numbers: 0, 1, 2, 3, 4, ... It seems so simple: just one thing following another. Yet we have number theory, which is about the structures hidden within the naturals. So the naturals aren't just one thing following another. Why not? Why should there be any hidden structure? If something as simple as the naturals has inevitable hidden structure, is there anything that doesn't? Is everything more complex than it seems on its surface? If so, why is that? If not, what's a good example of something that isn't. -- Russ Abbott ______________________________________ Professor, Computer Science California State University, Los Angeles cell: 310-621-3805 blog: http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ ______________________________________
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