Anon writes a symphony.

Your brain sometimes just leaves a placeholder and makes itself believe it was the real shit. Once I had a dream of a hilarious joke. I even laughed hard in my dream. I woke up, tried to remember the words immediately and it was gibberish.

It does work sometimes, but there's a good chance that you just had a dream about placeholder for one weird song, placeholder for another weird song and placeholder for mix, and the illusion just worked.

OR we're in an alternate universe where the famous composer of the millenium doesn't actually remember that visionary song, loses motivation and becomes an accountant. It's about fifty-fifty.

So, fun fact, when most people are able to recall whatever incredible idea or artistic vision they had in their dream, they soon realize that it was just their memory replaying something that already existed. An obscure song that you forgot about, a scene from an old movie that you’d think would make for a funny comic strip, etc. Now, this doesn’t mean that people aren’t creative and can’t dream of new things, it just means that your dreams just churn out a vomit of things you’ve processed before.

Source: I made it up

I was going to object, I've definitely heard songs in my dreams with fully comprehensible lyrics. I've woken up and immediately googled the lyrics and couldn't find the song at all. I found one with the same title that I had heard of but it was completely different.

The closest I've gotten to randomly coming up with music like that when awake is by singing songs in a different tune, but even then the tune was metrically the same. Came up with some bangers doing that, actually.

When I was a student I used to stay up late doing math homework

I would have these dreams where I was doing math and I’d solve really complex problems or create beautiful proofs. When I woke up I would furiously write them down before they faded, and then I would realize they were complete and utter gibberish.

Sometimes I do dream up something good, but mostly it’s junk.

One thing that dreams are definitely good for is writing ideas.

Unlike maths, it doesn't matter if a story is only half-formed or incoherent nonsense.. If there's an idea in there, you can take that and grow it in a way that actually does make sense.

I was once able to fix a bug in my dream, which actually worked out in real life - although, I needed to jump up to my laptop and hack in the solution, as the dream was fading away

Although can't really recommend dreaming of work...

Heh, for years I used to keep a notebook on my girlfriend's bedside table. I can't count the number of times I'd wake up (or finish) and have a solution to a problem pop into my head and have to write out the solution/pseudo code before it was gone forever.