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A probably highly topical question these days: Are computational word-sense disambiguation and computational word-sense induction possible?
Here are some related to science:
We also have little understanding about how human brain works and complex decisions are made by the living beings as there are either no tools that are able to discover these nuances or the experiments raise ethical questions.
I also found there are some problems in math, particularly in topology, that no one has found the way how to solve them yet.
I am not including philosophical questions, such as those that are related to thought, personality, the universe, etc., as these are a matter of a definition.
Finally, there are many unanswered problems to explore about every individual person. Human is a very complex being and there is no free lunch way of understanding each individual the same way. So keep your best listening and analysing and try to make someone’s life better :)
Is there any prize money on extraterrestrial life question?
Fermat’s Last Theorem has been proven for decades already.
Yes, you are right. My knowledge has some holes, sorry.