If you don’t want to just use money, it’s not impossible by any means. It’s merely really, really hard (Edit: on average).
Steps for doing valuable research on a topic:
1) Learn enough about the topic that you know where the unsolved problems are and what attempts have already been made to solve those problems.
This can be a lot of work, but it’s necessary. Not only do you not want to duplicate work that’s already been done, but you have to know your subject quite well to know what to do without anyone telling you. Working scientists don’t just guess at which research avenues to pursue—knowing the subject well usually tells you where the subject needs to be taken farther. Be careful of fooling yourself into thinking you have a good research topic when you don’t actually know that to be the case.
2) Pick an unsolved problem and work really hard on it.
Problems in textbooks are doable because they’re presented right next to the tools you need to solve them. Research problems are hard because you have to build your own tools, or pull them out of a mountain of not-quite-right options. It’s not unusual for problems that took a year to solve to be doable by students in an hour, once they’re in a textbook. There are plenty of tips and tricks that you pick up, like doing rough calculations or special cases before the general problem, but really the only way to make a contribution is to work really hard.
If you don’t want to just use money, it’s not impossible by any means. It’s merely really, really hard (Edit: on average).
Steps for doing valuable research on a topic:
1) Learn enough about the topic that you know where the unsolved problems are and what attempts have already been made to solve those problems.
This can be a lot of work, but it’s necessary. Not only do you not want to duplicate work that’s already been done, but you have to know your subject quite well to know what to do without anyone telling you. Working scientists don’t just guess at which research avenues to pursue—knowing the subject well usually tells you where the subject needs to be taken farther. Be careful of fooling yourself into thinking you have a good research topic when you don’t actually know that to be the case.
2) Pick an unsolved problem and work really hard on it.
Problems in textbooks are doable because they’re presented right next to the tools you need to solve them. Research problems are hard because you have to build your own tools, or pull them out of a mountain of not-quite-right options. It’s not unusual for problems that took a year to solve to be doable by students in an hour, once they’re in a textbook. There are plenty of tips and tricks that you pick up, like doing rough calculations or special cases before the general problem, but really the only way to make a contribution is to work really hard.
3) Go to step 2.