By most accounts, the majority of mathematics papers and textbooks feature "informal" proofs, as opposed to "formal" proofs. Rather than work in a clearly-defined formal system where every inference step is justified by some axiom, the goal of most mathematical work is to produce human-readable arguments aimed at other mathematicians, arguments that could "in theory" be turned into formal proofs, but are not ultimately formal proofs themselves. Granted, even these "informal" proofs are more rigorous and detailed than virtually any argument seen outside of mathematics.
Furthermore, these informal proofs are written in standard, linear prose (interspersed with copious mathematical terms and symbols of course) because again the focus is on communicating the ideas, not on justifying every individual step.
They're readable for very, very simple arguments. Much like very, very simple programs are relatively readable in assembly language.
Once one moves on to more complex proofs (which, alas, usually doesn't happen until a "How To Prove It" college course, which is usually taken right after two semesters of calculus), the "two column" writing method becomes untenable.
