Computer science is a very young field. This is sort of trivially true when you compare it to, say, philosophy and mathematics, but also has consequences for my daily life. One thing it means is that seemingly-obvious questions have often not been asked. With a BS in CS you are qualified to begin answering many of them, if the question is
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proteinomics,
neuropsychology
many subfields of cognitive science
evolutionary psychology
Many of these you could ask intelligent questions with just a BA, but the equipment needed to answer them is more specialized and expensive.
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One thing I’ve learned during this job search is that many math departments want new faculty members who can propose and direct undergraduate research projects, and have some idea how they might involve undergraduates in their research program. I’ve been asked about this in pretty much every interview I’ve had so far.
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This is manifestly NOT true in math
I'm not sure I agree. One great strength of mathematics, perhaps the greatest, is that it can be very, very, very specific. By building the right vocabulary and choosing the proper abstractions, you can make it tractable to consider a question that is extremely specific. This increases the chance that it's never been asked before, without necessarly increasing the chance that you need more than a B.S. to tackle it.
Will the question and answer be interesting to more people than just you? I think that depends largely on the simplicity of the construction of the question, and the "beauty factor" of the answer.
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Combinatorics is very fertile ground for coming up with new definitions, which makes it easy to ask original (but useless) mathematically interesting questions. However, for the same reason, it is hard to be sure that your questions haven't been investigated already, using different names for the concepts.
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