Chemistry: We might perfect our knowledge of the fundamentals, but there's always going to be new compounds that could be invented or new biochemical reactions that could be observed in nature. And if it turns out there are other islands of stability beyond the periodic table, we'd find ourselves with a lot more to do.
Biology: Even if we manage to classify and study every living thing on planet Earth, there is no reason to believe conclusively that Earth is the only planet that has life on it. There could be planets out there with natural histories completely different from our own, and even if it turns out that life is generally pretty similar throughout the universe, there's still a practically infinite number of planets out there that could have life on them, and that life will need to be studied. And even here on Earth, just a few decades ago people were absolutely certain that nothing lived in the ocean's abyssal zone, and now deep sea research is one of the most active areas of study (because who wouldn't want to devote a lifetime of study to glow-in-the-dark Cthulhu fish?).
Physics: Don't the incompleteness theorems make a nontrivial theory of everything impossible? I mean, the equation 0=0 technically could be solved to describe anything and everything in the universe, but that doesn't make it useful. Either way, there are still several lifetimes' worth of unsolved problems, and solutions to those problems will probably create problems of their own. And the fact that we've only just now verified the existence of gravitational waves means that huge new areas of astronomy are going to start opening up.
Engineering: If engineers run out of problems, they create their own. Some of those new problems will require new science or at least new methods. For instance, think about what Oliver Heaviside did for both math and engineering, even though he didn't necessarily discover anything new, the methods and techniques he introduced enabled a great deal of later scientific and technological progress.
Sociology: A few centuries ago, the early Realists (Machiavelli, Hobbes, etc) were quite certain that they had everything figured out, but they could never have predicted how social and technological changes would shape politics and society in the future. And history never stops being written. In fact, if the "digital dark age" scenario turns out to be true, then history and archaeology could start becoming much more practical sciences.
And of course, barring radical life extension technology (see Biology, Chemistry), there's going to be an increasing need to find new ways to efficiently teach students to prepare them to work in those disciplines. 200 years ago you could effectively do science with some free time and some books. 120 years ago you would have needed a Bachelor's degree at a minimum. 50 years ago you could do with a PhD. Now, you need a PhD and several years of postdoc experience before you're considered qualified to be a scientific researcher. So the human lifespan places a certain constraint on the speed at which discoveries can be made. We can counter this by organizing into teams of specialists, but if lifespan doesn't change or increases only slowly then the number of years during which an individual person is even able to make discoveries is going to be a significant constraint.