I think the future we'll start with unit tests/proofs and then computer will search the solution space find code passes those constraints. The code search will use heuristics.

We'll have to become good at writing those tests, but we won't implement the actual code as much anymore.

I think this the real solution to the "low-code" idea.

Another potential option is simular but the tests will be input/output demonstrations for the computer, and it will figure out the code. It won't be as correct as the first option, but might be good for software that values speed over correctness. Some bad cases may slip through.

I think we’ll start seeing a lot more formal verification or at least well tested software. Especially with the rise of drones, robotics, self driving cars etc making bugs much more harmful/deadly in a lot of places. I think for some of these cases the govt will actually step in like they have with aviation. This will make writing software a lot more bueracratic I imagine.

It won't look like formal proofs. It won't look like mathematics.

That said, there will be progress in having the compiler prove that the program doesn't contain certain errors.

'The future of Programming' by Bret Victor (https://www.youtube.com/watch?v=8pTEmbeENF4). Seems a pun about OP title but it really is related with his/her question. Take a look and you will be amazed of how good (or revolutionary by our standards) some old technologies were.

I might switch back to Vim

I think it will look like magic, literally. With mind controlling drones, virtual glasses and realities.