To my mind there are several explanations for this phenomenon. Firstly, writing in mathematics is generally more graphic than programming, which is linear, alth

To my mind there are several explanations for this phenomenon. Firstly, writing in mathematics is generally more graphic than programming, which is linear, although of course, mathematical writing can be expressed linearly (in TeX!). Secondly, of course, most mathematical is relatively informal. The large proportion of strange symbols should not overly impress us: even in the best journals, mathematical proofs are not given as step-by-step logical deductions from the axioms. This is for the obviously sensible reason that such (excessively) formal proofs would be vastly longer and essentially incomprehensible to even the most gifted mathematician. [1] Thirdly, programs have a constructive flavour to them: we work with finite objects (floating-point numbers rather than real numbers, for example) and any object or inference made by the computer is something we can understand in a finitistic way, even if it might take us a very long time to do so. In understanding the operation of the computer (even if only through a high-level programming language, rather than machine code) we see how each step of a computation is to be carried out. The algorithmic character of computation appeals to our intuition: if we wished to sit there and perform each step in a construction then we would get the expected result. Of course, this last reason is much of the motivation behind Brouwer's intuitionism, and there is presumably a reason that so many computer scientists take a constructivist line of one sort or another. [1] See, for example the calculations in this Math Overflow answer: http://mathoverflow.net/questions/14356/bourbakis-epsilon-calculus-notation/31778#31778 http://mathoverflow.net/questions/14356/bourbakis-epsilon-ca...