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westward comments on Research is polygamous! The importance of what you do needn't be proportional to your awesomeness - Less Wrong Discussion
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Which fields are not that competitive yet would yield useful results? What are optimal fields for bright people to enter?
A good example would be the kind of work CFAR does to learn to teach people to be more rational. It's an important topic but there isn't that much competition for practical rationality training.
GiveWell would be another example from this community. It's an important project for which there weren't real competitors when it got started.
If you want to pick a topic for yourself, I find that spaced repetition learning is an area with a lot of potential where more work is needed. I don't think the Anki algorithms is optimal. If you are strong at math you could go and take the memosync data set and develop a better algorithm for estimating the timing of cards.
When it comes to teaching people how to create good spaced repetition cards the resources that are out there are pretty limited.
It's an area where you can do genuine work that helps the world without having to be an genius.
From my perspective there are tons of interesting projects that could use more work but are outside of prestigious academic interest.
I suggest Singularity Strategies or Meta-Philosophy.
I don't know.