Russ, Bypassing all the other replies, I find this question very interesting. When faced with questions like this I usually give an answer, am told it is not satisfactory, give another answer, am told it is not satisfactory, etc. Then at some point I ask the questioner to give me examples of the types of answers they would find acceptable. So.... well.... can we skip to that part? For example, would an acceptable answer be in terms of:
Something about people who do math, explaining why they make theorems? Something about the math people, explaining why theorems are necessary for those activities? Something about math itself showing theorems to be an essential part of any math? Something about the history of doing-math, showing why we now do math with theorems when we otherwise might not have? Something about the virtues of doing math different ways, showing the theorem enhanced way to be virtuous in some respect? Something about the limitations of human cognition, demonstrating why we need theorems instead of simply knowing the truth? Etc. My hunch is that some of those types of answers would be of more interest to you than others. Eric On Sun, Apr 25, 2010 12:47 AM, Russ Abbott <[email protected]> wrote: >>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/> >______________________________________ > > > ============================================================ >FRIAM Applied Complexity Group listserv >Meets Fridays 9a-11:30 at cafe at St. John's College >lectures, archives, unsubscribe, maps at http://www.friam.org > Eric Charles Professional Student and Assistant Professor of Psychology Penn State University Altoona, PA 16601
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