> Now that's a fine thing in a computer language -- and there are philosophers who say mathematical truth is no more than computation. But mathematical notation is for humans to talk about things that have meanings that humans can understand.
Then how come an unfamiliar piece of source code is easier to follow than a mathematics paper using unfamiliar notation?
You can look up the definition of each function and learn precisely what it does, without ambiguities. You can open up a debugger and trace every step of the algorithm. Source code tends to be formatted to emphasise its division into units that can be analysed separately. Even if the code uses a framework you don't recognise, you can probably understand some of the underlying logic just fine, thanks to a consistent syntax and (often) descriptive function names.
In a mathematical paper, often there's some notation that isn't defined and there isn't even any pointer where to look for definitions. Important objects are given one-letter names. Theorems are often only numbered; good luck remembering what lemma 2.17.3b was about. Proofs are written in prose (instead of something like Leslie Lamport proposed[0]). You have to fill in conceptual gaps and remind yourself of unstated assumptions. Notation and terminology is often ambiguous — what does "exponential time" mean? Is it DTIME(2^(c*n)) or DTIME(2^polynomial(n))? Does "increasing" mean "strictly increasing" or "non-decreasing"? Is zero a natural number? And so on.
A mathematical formalism that could be interpreted in a purely mechanical way would be a huge improvement.
[0] http://research.microsoft.com/en-us/um/people/lamport/pubs/p...