This drove me mad when I had to do introductory maths at uni. Maths as written did seem pretty sloppy and not at all like a programming language whose expressions I could parse as I expected. Obv most simple algebra looks about as you'd expect but I clearly recall feeling exactly what you describe in some cases, and commented upon it to the lecturer about it asking why it was that way during a tutorial. He humoured me, was a good guy.
But I think mathematicians probably have a point - it did evolve that way over a long time and anyone practicing it daily just knows how to do it and they're not going to do a thorough review and change now.
It's us tourists that get thrown for a loop, but so it goes. It's not meant for us.
> Maths as written did seem pretty sloppy and not at all like a programming language whose expressions I could parse as I expected.
Look at Lean's mathlib: that's what fully formal mathematics looks like. It's far too verbose to be suitable for communicating with other people; you might as well try to teach an algorithms course transistor by transistor.
But I think mathematicians probably have a point - it did evolve that way over a long time and anyone practicing it daily just knows how to do it and they're not going to do a thorough review and change now.
It's us tourists that get thrown for a loop, but so it goes. It's not meant for us.