[heinrichhartman]

> Is there a similar programming language that makes mathematicians feel at home?

The problem is not writing stuff down. The problem is reasoning about what you have written down. With popular languages it's really hard, to say what a line of code does. It depends on so many things (global state, scoping, local state), that you have to spell out. Google "Semantics of Programming Languages" to get an idea, what's involved with formally reasoning about code.

To have a chance to do manipulations by hand, you have to give up, at least:

- Mutable State - Side-effects (I/O)

(pure) Scheme and Haskell come into mind as contenders.