Questions about research in mathematics

[flamengo]

A person told me that doing math research independently (alone) is very difficult, because the findings of someone who is not interacting with the experts in a given field of study will most likely not be "novel", that is, they would have already been published before. Is that true ? Can the problem that an independent researcher is working on quickly become obsolete(except for the very famous)? If so, why? Even if research in literature and everything else is well done, is it impossible to do research in mathematics alone?

 

[fresh_42]

A person told me that doing math research independently (alone) is very difficult, because the findings of someone who is not interacting with the experts in a given field of study will most likely not be "novel", that is, they would have already been published before. Is that true ?

Either that or it is not of interest. It could as well just be wrong.

Can the problem that an independent researcher is working on quickly become obsolete(except for the very famous)?

Obsolete is a validation and as such depends on how you measure this. I have no idea what you mean by this. There is always a chance, that a result becomes part of a larger theory and as such will be downgraded to a Lemma or Corollary. But this is true for every new result, independent of who found it.

If so, why?

Why what?

Even if research in literature and everything else is well done...

This is quite a big, big IF.

... is it impossible to do research in mathematics alone?

No. It is not impossible. It might be impossible to publish your results in a way that others will recognize it, but the research itself is possible. Of course it depends heavily on your background. Wiles basically worked completely on his own for many years. However, he already knew what he was doing and had an excellent education and basis to start with. For a layman it is practically impossible. But in mathematics there are many areas in which not many people do research, e.g. on certain algebras. So a result there has good chances to be new. However, there is usually a reason nobody investigates them: it's either too difficult or too uninteresting.

Those general statements as your friend apparently told you are risky, because they don't cover all circumstances. And neither did your question, so it's hard to tell. Maybe you're a genius like Perelman, I can't know. And as said above, it also depends on the specific field. I wouldn't tackle analysis or number theory, but there might be promising questions e.g. where mathematics meets biology.

 

[mathwonk]

ask yourself how likely it is that someone practicing say basketball alone would afterwards be able to walk on to an nba team. of course there are a few examples: lebron james jumped from high school to nba and ramanujan was a mathematical genius working alone, but it is unusual to say the least. even beethoven studied with haydn.

 

[Dr. Courtney]

Applied math is probably more accessible than pure math. As an experimental physicist, I've mentored a several successful projects in applied math, but I wouldn't know where to begin helping a student with a project in pure math.