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anonymous
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The question you seem to be asking is "Can I be paid to do research, without any formal education, if I am very good?" The likely answer is no. I know many serious researchers across countless fields, and the only ones I am aware of who can make a living without any formal training are inventors who got quite lucky in terms of their ideas and their marketability. Many great artists, mathematicians, and scientists did other things to survive while doing the work they were truly passionate for, and we romanticise many very inspirational people. Research is probably much more a function of diligence and persistence, even when things are depressingly boring, than it is of intelligence or genius. I would suggest reading some of the good bits of advice many modern prodigies have given on the subject. Terence Tao in particular has several good pieces on accelerated education, working hard, and being a genius.

Yes, school can be terribly dull if you are quick. But being able to succeed in that environment is an invaluable human skill, which will prove useful in a research career when looking for funding, or when setting up research groups and similar things, as well as really showing that you have a sense of humility. We can complain about how slow and tedious bureaucracy can be, but if you really are quite good, it is worth your time to learn and understand how to survive in it. Mathematics is not simply something devoid of social interaction or human involvement. Pure and applied mathematics stem from human ideas and are inherently connected to social and cultural concepts, and these connections are often a part of what traditional formal education gives us. I would absolutely advise you to go further than what you see in a classroom, do independent and guided research as early as possible, and test out of whatever classes you can. But skipping the process entirely will handicap your ability to contribute meaningfully to mathematical research.

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