I'm interested in both your list and the reasons why. Submitting your list before reading other's contributions would be preferred.
Optionally: who is (or isn't) successfully addressing them. Individuals, organizations, companies, governments, other. How and/or why not?
I've submitted this question previously to HN (most recently over three years ago), and ask it periodically on several forums for seven years now.
I've written fairly extensively on my own views, reasonably findable if you wish, but my interest here is in gaining fresh input, resetting my own biases, and not colouring the discussion overly myself.
1. "exercise theory" in STEM subjects like math. Just because you learned all there's to learn from your book, your teacher, your circle of experts doesn't mean you will immediately be able to tackle some random (appropriate to your level of development) problems in some randomly chosen textbooks, papers, journals etc. The only people who work on similar problems are those who work on tangentially related fields like, say, general problems of edjumacation or writing tips and tricks books for taking tests s.a. SAT, GMAT or PhD prelims whose main message is just "practice till you're blue in the face". Most any master or expert knows just practice alone (however many years you do it) is not enough. Sometimes, a person might have a sudden weird insight that can make all subsequent practice (in a narrow subject, field or a chapter in a book) unnecessary. But all(?) inquiry into such phenomena are easily shut down simply by labeling them some amorphous concept like "talent".
2. no resources for learning how to read humongous code like you would a novel. The current situation is that everyone is a writer of code, but not a reader. Everybody is a Shakespeare, but no one can read :) I trawled Amazon back to front and sideways and looked through hundreds of books and found only one related to the subject: [0]. I don't know how good a book this one is, though
3. solutions for nasal problems. The existing solutions, be they cosmetic or more serious are stuck in medieval times. For example, post-nasal drip is an annoying and non-life-threatening problem that causes some slightly embarrassing problems like bad breath, but there's no effective solution to this problem
4. speaking of bad breath, believe it or not, there's currently no solution for people suffering from chronic halitosis; if you're a microbiologist and/or chemist who knows their way around germs, you could probably devise a solution and sell it to companies (those that are still stuck in the early 20th century) like J&J and become a billionaire :)
5. "root cause of health problems" theory. Say, a person suffers from bad complexion. Nothing helps. One day while at the gym, they injure their lower back trying to set a new personal deadlift record. While recovering they realize, their lower back hurts if they drive it forward while standing or walking. From there they discover they have natural anterior tilt which is aggravated by their way of exercising. They opt for other exercises like hack squats. The next thing they know their complexion is cleared up and as a bonus, the persistent feeling of butterflies in the stomach is gone (which they might have attributed to their generally anxious personality). Basically, as it turns out, the problem was: aggressive anterior tilt that is a problem on a good day -> the tilt is aggravated by the style of exercise -> general chronic inflammation -> anxiety and bad complexion. But development of such a "theory" might be a brutally difficult problem for historical, cultural and logistical reasons
... but forget about these problems, there are very many lower hanging apples out there like, say, effective alternative to free weights for people who cannot train with them for any reason (disabled, frail, unique body constitution etc). The current "alternatives" like Smith machines are inadequate. Also, wouldn't it be awesome if dogs could walk themselves? How about a "smart collar" that can make it happen? Yeah, I know your nhd probably doesn't allow unaccompanied dogs roam around free :)
There are many, many, many,...,many persistent and nagging problems that are waiting for solutions. A lot of these can't be dealt with just by writing another app.