On the other hand a good friend of mine says that code is more like mathematics and that we should eschew (horizontal) white space where ever possible (although we agree on indentation style).

As a mathematically inclined person, I'm of the school of thought that code is often much like Mathematics too. Still I can't understand the alleged implication that "we should eschew (horizontal) white space", which is generally not the case except perhaps in some specialized areas like Universal Algebra or Formal Languages. But otherwise careful trimming of whitespace does play an important role in mathematical typesetting, which in turn is a refined art. (Made much more accessible by Dr. Knuth's work! - To whom we all owe so much!!)