I think the clear answer is that you want both -- maths notation, and at least one implementation in a non-specialized programming language with clear functiona

I think the clear answer is that you want both -- maths notation, and at least one implementation in a non-specialized programming language with clear functional/procedural semantics. If you understand one or the other, you then you can also learn the mapping between the two. This is also important to remove ambiguities in notation, makes errors in each more obvious, and aids in reproducible results. Of course, applicable input and output data also needs to be supplied for verification. If the code is too long to publish in a paper (usually there is at least some core idea that can be expressed) then it should be in GitHub or elsewhere at a stable URI -- papers often refer to academic sites that 404 soon after. As a non-mathematician who has been recently been looking at papers in journal back-issues from about 1970 to 2010, I certainly would have benefited from this. On a related note, another issue is that that maths must be implicitly ordered in the context of the prose of the paper, while programs have actual entry-points and (without nitpicking) explicit ordering. (It's possible that ordering can be relaxed, but correctness preferred over runtime cost.) I think "maths-as-data" is more important here -- use a parsable common notation with enough meta-data that I can view it any way I want -- as math-with-greeks, math-with-friendly-names('en-us'), as APL, as plain Python, Python with numpy, etc.