I’m on a streak of fairly vivid dreams, leaving me not especially well-rested but boy what a ride it’s been.
According to my dream last night, the most fundamental unit of time is known as an IAI.
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I’m not sure this is what you are looking for, but many years ago I went to bed mystified by (mathematical) integration; dreamed about it; and woke up the next morning understanding it. Which was weird (but good).
j
Years ago, I had an erotic dream about someone that I had never consciously thought of in that way. But, after waking up from the dream, and thinking about it, I realized that, yeah, I was attracted to her. (No, I never did anything about it, as I knew her only professionally, nor did I ever tell anyone about it. 
)
A series of dreams almost had me convinced that I was a child actor on Gilligan’s Island. I even got a mention in the song.
I applied for a job at a company once, company XYZ. bombed the interviews and never heard back. Then one night I had a dream I was walking on the campus of the same company as an employee, then when I woke up I said to myself ‘I guess I’ll be working at XYZ’.
A few days later I got a call, the person they picked instead of me for the job declined the offer, so they picked me as their backup.
I dont think I’d ever seen the campus either, but when I saw a photo online after all this it looked like the campus I was walking on. I’m guessing I saw a photo once, consciously forgot it and had the memory in my subconscious.
I don’t remember dreams much at all. But I had one really good dream once. I was nearing the end of two years of therapy, where I had worked through a lot of stuff and cleared it out of the way. The dream (which I think might be a fairly common sort of dream in this situation) was me in the house that I grew up in, only it was larger, and mostly empty, and all the windows and doors were open and a very nice, sweet breeze was wafting through every room. The metaphor was obvious, even to me. What I learned from this is that, hey, therapy can work!
Interesting? Yes. Useful? No.
Rose Wilder Lane (the daughter of Laura Ingalls) wrote about this experience. She said she was fatigued and couldn’t understand something about a math problem, so she took a nap. In her dreams, she came to understand the math perfectly, and woke up and wrote out the math stepwork and yes, she had mastered it in her sleep
I dream often of a lady pointing at an open book.
It’s always when I’m pondering a question that I cannot fathom an answer.
I wake up with an answer in my head. I’m not saying all answers have been right. Just that I felt, at the time, I was making a concrete decision.
There’s still this ridiculous dream I had as a kid where some weird crooks kidnapped me, but before leaving they put me in a bath. When awake I realized that they wanted to make a clean getaway.
In the realm of things that are actually useful, I’ve also dreamed some bits of music, usually some sort of accompaniment. This is usually after spending a long time finally getting to play a piano.
I’ve had dreams about eating unusual (new to me) combinations of food, which I then tried out. Some were quite good - others just weird. Bacon and sliced strawberries in a sandwich was one of them - I didn’t enjoy it the first time, but it grew on me.
Irrelevant to topic, but have you changed anything about your diet or before-bed routine that may be credited with this streak of vivid dreams?
Maybe you should give the King’s Hand a try.
Back in my 20s I was given a pocket watch that had belonged to my grandfather. It wasn’t very valuable aside from the sentimental value but it was old and very worn and looked very cool. I didn’t carry it and put it away somewhere. After a couple years I thought about it one day and went looking for it. Couldn’t find it anywhere. This caused me some anxiety as it made feel as if I had been a poor steward of a family heirloom. I looked for it every so often over the course of a year or more. One Saturday morning as I was sleeping late, I had a vivid dream of finding the watch in an old foot locker full of odds and ends that I was pretty sure I had checked more than once. Got up, went to the footlocker, rummaged around a bit and there it was.
My wife is constantly losing her watch. Every time she asks me if I’ve seen it, I say, “Have you looked in Christopher Walken’s ass?”
Funny!
I can not actually fly. 
OMG, the King’s Hand Twitter thread is hilarious. (And adorable, if bizarre.)
I had a dream once where I found the manuscripts of a bunch of Shakespeare’s tragedies, and it turned out that all of them originally had a character named … Severus Snape. Of course he had to be edited out. He kept making antidotes and saving people when they got poisoned, and giving all the other characters rude and snarky but generally excellent advice, so nobody died at the end.
I rarely remembers my dreams, but quite a few years ago, an image from a dream of mine became one of my most successful short stories.
I’ve gained insight into myself, anyway.
About two decades ago when I was dating my now-husband, I had a lot of anxiety, much of which was keeping me from trusting the relationship. One night I had a lucid dream that I was in a haunted house, and there was a ghoul whose face was terrifying to look upon. The whole place was filled with ghosts too scary to look at. Sr. Weasel was standing in the doorway, oblivious, and then he wandered away. And that fucking ghoul gave me a nasty look and then followed him! I picked up an umbrella, ran after them and beat the living tar out of that thing. I took on every single one of those bastards.
Another, sadder one, when I let my estranged mother back into my life I didn’t really know how to feel about it. I’d dealt with my issues with her so much in therapy I didn’t really feel attached in any way. I had a dream I was standing by a window. I looked over at a friend and said, “Have you ever made a decision that you think is important, but in reality changes nothing at all?”
Kinda maudlin, but I think it’s funny how my brain works things out in my dreams.