The prospect of actually "finishing" physics could be a nightmare for those working in it.
I had a friend who was a brilliant pure mathematician, his teachers and friends agreed he fully deserved to do a PhD in complex analysis - but complex analysis was essentially done in the 19th century, there's just not a lot of research opportunities there.
I have a friend who is a professor with a PhD in complex analysis. Multivariable complex analysis (along with the theories of complex manifolds and analytic spaces) is very far from over.
Heck, one of the Millennium Problems (the Hodge conjecture) is in complex geometry (granted, in the more algebraically flavoured part of it).
I can't really believe that this is the case, although I'm nowhere near being a mathematician. The very nature of knowledge is that every new understanding or discovery raises even more questions.
So complex analysis is pretty much done? Well, could the methods of complex analysis suggest analogical methods in other analytic fields? What work could be done at the intersection of complex analysis and X, when X is any other mathematical field? Also, I hear it is frequently useful in the solution of physical problems. There are many unsolved physical problems that could benefit from being reviewed from a complex analysis perspective.
> There's just not a lot of research opportunities
Maybe this is the crux of the matter; it is not that there is any lack f work still to be done in complex analysis, but there are few research areas in the field that can or are able to attract funding.
True but you’d hate to be the physicist that spent their career going down the wrong path only to see tomorrows physicists discover the big breakthroughs and the realization that your contribution will be sent to the dustbin of history.
Yah. Well, for most of us, the prospect of making a significant contribution to the sum of human knowledge is a faint prospect.
They say all political careers end in failure. Very few politicians die in the saddle, or simply retire. Most of them are destroyed. My guess is that most careers in science research end similarly; lots of career-length research projects fail to achieve their goals, and very few scientists get Nobels for world-changing discoveries.
> for most of us, the prospect of making a significant contribution to the sum of human knowledge is a faint prospect
Physicists are bright people with other options. They forewent those other options to have an increased chance at contributing to human understanding. I can empathize with the greater tragedy of their failure than that of e.g. a millionaire adtech founder.
