One of the first things you learn in a programming 101 course is to write readable code, and to name your variables properly. This notion has seemingly never translated into mathematics. Everywhere you look, there are one letter constants, variables and functions, and an abundance of hard to remember symbols for operators, crammed together into tight, linearly laid out expressions. Characters are often borrowed from Greek, being short of Latin ones.


As soon as you get into college-level mathematics, any non-trivial mathematical expression starts to look like signal noise that programmers would instantly [ridicule](https://en.wikipedia.org/wiki/Write-only_language) if it were a programming language.


Was there ever a movement to make mathematics more readable? Is being so succinct really worth it? Does it get better with enough experience? Would using memorable names for mathematical symbols and operators have any downside aside from length? Would a neatly indented, airier layout/syntax for expressions?


I'm not trying to stir up an argument, I'm genuinely curious, having been frustrated by this for a long time, and I'd be keen to hear what actual mathematicians think about this.



Why did mathematical notation stay so hard to read?
Mathematics uses very few variable names in any proof compared to the number of variable names occuring in typical programming languages. Variable names survive only for short passages, except for a small (less than a dozen) *global* variables. The names are subject to a host of conventions (for example, $\varepsilon$ is a *small number*, $N$ is a *large number*) which are not found in programming languages. More distinct symbols are available, as we are not constrained to use ASCII. Try to rewrite a serious piece of mathematics in the style of a programming language, and you will quickly see that it is unreadable.


