I was dropped into the tech lead position at my job last year; I started in game design at art college, so having to run and gun has been fascinating. I'd be lying if I said I wasn't scared reading about much of the stuff in this comment section that really should be bread and butter.
I'm talking to my boss to see if there's some kind of training program I can pick-up on the side to help me gather what should be the basics that I've missed out on, although we're so overloaded finding the time and money is challenging. I'm lucky it's mostly CRUD, but I can't help by worry every architecture decision I'm making is going to cost us massively down the road.
A few people have made incorrect mathematical statements in this discussion, so having a math teacher might be useful when learning this stuff. My unsolicited advice: take your time and learn some mathematics you might enjoy. Trust simple mathematical definitions over long-winded "explained as easily as possible" essays.
Mathematicians congratulate each other for simple, elegant definitions (sometimes developed over decades) which make deriving results easy. If you don't understand a definition which requires only a few words, learn some of the background instead of doing 10000 Google searches for the "easiest" explanation.
Here's an example. In physics, a vector is something with a "magnitude" and "direction" and we associate feelings and intuition with this. In mathematics, a vector (in 3-dimensional space) is simply "an ordered triple of real numbers". Many people might find this definition unsatisfying, but it is simple, precise, and lots of USEFUL mathematics is created from it.
I'm talking to my boss to see if there's some kind of training program I can pick-up on the side to help me gather what should be the basics that I've missed out on, although we're so overloaded finding the time and money is challenging. I'm lucky it's mostly CRUD, but I can't help by worry every architecture decision I'm making is going to cost us massively down the road.