I think that the answer has to do with exactly what sense of “learn” you’re using. With infinite time you could memorize every math paper, derive exact proofs of all known theorems by brute force, and octuple-check your work. It is less clear to me if you would understand it all in the way it’s original discoverers/inventors did, or that you would recognize which of the new theorems you derived were meaningful in the way we see prominent past mathematical results as meaningful.
I know there are some fields of math I have no problem following, and others where seemingly no amount of reading gets me any sense of insight into what is even being discussed. These sometimes but not always maps onto fields that others I talk to consider more complex; it’s more a matter of my mind naturally following different kinds of paths than theirs.
At this moment, I don’t think it’s feasible for any merely human mind to learn all the math in a lifetime, let alone keep up with more new discoveries as they happen. But different people will tend to have the tools to solve different arts of any given puzzle. Maybe one will have them all, maybe we’ll need a team, maybe we’ll have to have multiple projects done in series. Not even Jeffreysai thought it was necessary or optimal for one person to have all the knowledge and insights.
I think that the answer has to do with exactly what sense of “learn” you’re using. With infinite time you could memorize every math paper, derive exact proofs of all known theorems by brute force, and octuple-check your work. It is less clear to me if you would understand it all in the way it’s original discoverers/inventors did, or that you would recognize which of the new theorems you derived were meaningful in the way we see prominent past mathematical results as meaningful.
I know there are some fields of math I have no problem following, and others where seemingly no amount of reading gets me any sense of insight into what is even being discussed. These sometimes but not always maps onto fields that others I talk to consider more complex; it’s more a matter of my mind naturally following different kinds of paths than theirs.
At this moment, I don’t think it’s feasible for any merely human mind to learn all the math in a lifetime, let alone keep up with more new discoveries as they happen. But different people will tend to have the tools to solve different arts of any given puzzle. Maybe one will have them all, maybe we’ll need a team, maybe we’ll have to have multiple projects done in series. Not even Jeffreysai thought it was necessary or optimal for one person to have all the knowledge and insights.
Good points, clarified to “any” instead of “all” math.