I like J. Especially because it has a saner way to write it (it doesn't have to look like as if you accidentally forgot a null terminator in C strings, all the traditionally short identifiers have a long and understandable form).

I feel like it's very regrettable that the superficial aspect of J (the very hard to read syntax) is standing in the way of some very nice ideas.

To comment on mathematical notation. Before I was a programmer, I was a typographer. During my study in art academy, I invented a bunch of fonts, one of my long time projects was to make Hebrew look more like Latin fonts for example (this is a long-standing issue in Hebrew typography, with several historical attempts, but still not quite resolved). Afterwards I worked in a printing house, paginated a newspaper, typeset a bunch of books etc.

Among my coworkers (esp. in the newspaper) I was sort of known for trying to automate stuff, so, I was often suggested as a candidate for "difficult" typographical tasks, like setting sports tables, chess diagrams, music sheets and the most damned and hated kind of typographical work: math formulas.

I've helped publish a course book on linear algebra for a university. It was a multi-year project which I joined in the middle. I have never seen so much pain, struggle and reluctance as I've encountered while working on this thing. People tasked with proofreading demanded extra pay for proof-reading this stuff, and still wouldn't do it. Just put it away and later explain that they had other things to do. The lady who had to translate the mostly hand-written, or sometimes typed on a typewriter manuscript would just skip work on the days she was supposed to input the manuscript into our digital system.

Everyone passionately wanted this project to burn in hell. And the reason for this was the mathematical notation. Typical proofreading techniques don't work on math formulas. The text is impenetrable to anyone, often even to the people who wrote it, including both the author and the editor. Parenthesis are a curse, because in the manuscript they are one of the elements that is most commonly forgotten or misplaced. Single-letter variables are the other one. Overloading the same symbols with different meaning is yet another one. It gets worse when the same symbol is used in its normal size, subscript and superscript.

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When I talked about my experiences to people with degrees in math, they way they tend to respond to this is by saying that "math is overall so hard, that mathematicians don't typically notice the extra struggle they incur on themselves by the bad language choices, it pales in comparison to the difficulty of the main problem they need to solve".

And, I kind of can see it... on the other hand, I see no reason _the students_ have to endure the same torture. They aren't solving any novel mathematical problems. Their task is usually reading-comprehension combined with memorization.

And then I saw Sussman book where he uses Scheme to write math formulas (I think it was about physics, but it still used a lot of math). Dear lord, it was so immeasurably better than the traditional mathematical notation. I really wish more people joined this movement of ditching the mathematical notation in favor of something more regular and typography-friendly as Scheme...