Okay, human anatomy. The human body is filled with all sorts of mysterious parts, connections, etc. that we have little to no idea what is going on with them.
Take the [vomeronasal organ](Vomeronasal organ - Wikipedia organ#Humans), the thing that animals use to detect pheromones. Long known to be absent in people. Except that it turns out we do have it. Widely known not to be wired up to do anything. Except maybe it is. If the vomeronasal organ isn’t detecting our pheromones, what is?
Then there’s a gut-brain neural connection (known from fruit flies!) that it turns out also appears in humans. Note the date on the article: Sep. 20, 2018. So, really old news, right?
Studying this might lead to insights on the effects of diets, how to control obesity and in turn pare down the number of people getting Type 2 diabetes.
In any field, there are some things that are done, and some things that are not done. The things that are done are done, and if you draw a tight outline around those things and call them a “subject”, then there are subjects which are done. But there will always be other problems just outside that outline which aren’t done, and yet which are very similar to the problems inside the outline.
“Geometric optics”, for instance, is a very tight outline. But it applies to nothing in the real world, because the real world contains multiple wavelengths of light, and multiple polarizations, and materials which react in all sorts of interesting ways to different wavelengths and polarizations. To complete the field of optics, you’d have to categorize the optical properties of literally every material.
Well, as Richard Feynman put it, geometrical optics is either very simple or else it is very complicated. The basic (and approximate) rules of the simple form, which are mostly just plane trigonometry (another thoroughly-known “subject”), are indeed fully described. But if you want to know what’s really going on with the optical phenomena that the basic rules are approximating, then you get into stuff like Hamiltonian optics and Lagrangian optics, which are still active research fields.
So again, it comes down to how you define Subject X as an “academic subject”. If you’re limiting it to the particular subset of the subject that gets taught in introductory courses, then yes, there’s really nothing left to discover about those basic facts and rules. There’s a huge number of academic subjects that the claim “there is nothing left to discover” would apply to, if they’re defined in that simplistic way.
But if you’re defining “academic subject” X to include “any topics that are routinely described as forming part of Subject X”, then in pretty much every Subject X I can think of, there are still plenty of unknowns at the research level.
(ETA: see also Chronos’s answer above.)
A more interesting question might be “What are the academic subjects that still have a lot left to discover even at the basic introductory level?” That is, what subjects taught in elementary courses for non-specialists still require us to tell students “we don’t know what happened” or “we don’t know why this is so” quite a bit, even at the level of basic facts?
I would disagree and in fact came to post a clear example from mathematics, namely propositional logic. It has been proved to be a complete consistent system, that is everything that is, there are no contradictions, and every statement that is true can be proved to be true, and there is even an algorithm to do it. So there really is nowhere else to go within that axiom system.
And even if you get the big questions understood, there are millions of letters for Historians to understand. There is the home front. There is the archeology. History is so much more than “on this date these great men did this” We are learning so much about WWI from trench archaeology - WWII was so much more spread out we won’t dig it all up ever.
Adding to this, the appendix (similarly believed vestigial) recently also appears to be used as a storage for good gut microbes particularly needed after a bowel “cleansing” event. So anatomy is not solved.
The Navier-Stokes equations are just Newton’s laws applied to fluid flow, and yet we know almost nothing about them–they can be solved exactly only in a small number of limiting cases, and almost all knowledge is heuristic and empirical. They haven’t even been proven to have solutions at all, or that they don’t produce singularities (a $1M prize is at stake here). The single most important feature of fluid flow, turbulence, is poorly understood and its appearance at all (let alone behavior) can only be predicted in a very rough manner.
And of course that’s just the Newtonian version of fluid mechanics. Have fun modeling the behavior of a black hole accretion disc.
Really the only positive to come out of the whole mess is that it turns out that the fine details don’t matter too much. Computational fluid dynamics gives good answers even though you may be modeling some incredibly complicated flow with just a single volume element with a few parameters. And while no one has yet proven that the N-S equations are guaranteed to give a solution, in practice they do.
The complexity of actually proving a statement in PL is unknown. Sure, its NP-Complete, but we don’t know whether that is polynomial time or not.
In fact it’s one of the biggest, most famous, open problems in Science!!!
You solve it and you’re famous and get a bunch of money.
Another way of thinking about this is we don’t know which statements can be expressed in PL or not. So you have a complex statement with quantifiers. Can you get rid of them or not?
Again, an open problem that a lot of people would like to know how to do in general.
There’s a truckload of complete and consistent logics. So what? No one stops working on those logics and moves on. The real work starts after that.
All there is to know??? Well, you certainly don’t know all there is to know about this!
Chronos and Kimstu: And now geometric optics has been dealt with. Thanks.
Regarding Newtonian physics, as recently as 1992, Newtonian physics was shown to along existence of singularities not involving collisions, which is pretty cool for a field of study that has been intensively studied for centuries https://www.jstor.org/stable/2946572?seq=1#page_scan_tab_contents
To clarify a bit, it’s not like no progress has been made. Fluid mechanics is understood well enough to build airplanes and other stuff. It’s just that the extent of our progress is clearly minuscule compared to the scope of the problem, and huge segments of the theoretical underpinnings are completely missing. Reynolds numbers and the like just give a rough guideline to the behavior. It’s more like engineering than pure science, let alone mathematics.
My father has a friend who is an amateur historian of Navier–the friend was a physicist by trade but his passion led him to research the man as a sideline. In the course of discussing that, I was astounded to discover that turbulence was so–what’s the right phrase–imprecisely modeled? My first and last exposure to fluid dynamics led me to believe the whole thing was easily calclulable.
I don’t know about the Eneid, but the Iliad and the Odyssey are among the texts most disputed and argued about to this day. Who “wrote” them? When? How were they transmitted? What was the “original” text? What did the authors knew and understood about the (earlier) era they were describing? Why did they use the language, words, form they did? What facts or reality do they include? What does it tell us about the obscure era when they were composed and about the era they depict?