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IlyaShpitser comments on Open thread, Oct. 12 - Oct. 18, 2015 - Less Wrong Discussion
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Why isn't there a good way of doing symbolic math on a computer?
I want to brush up on my probability theory. I hate using a pen and paper, I lose them, they get damaged, and my handwriting is slow and messy.
In my mind I can envisage a simple symbolic math editor with keyboard shortcuts for common symbols, that would allow you to edit nice, neat latex style equations, as easily as I can edit text. Markdown would be acceptable as long as I can see the equation in it's pretty form next to it. This doesn't seem to exist. Python based symbolic math systems, like 'sagemath', are hopelessly clunky. Mathematica, although I can't afford it, doesn't seem to be what I want either. I want to be able to write math fast, to aid my thinking while proving theorems and doing problems from a textbook, not have the computer do the thinking for me. Latex equation editors I've seen are all similarly unwieldy - waiting 10 seconds for it to build the pdf document is totally disruptive to my thought process.
Why isn't this a solved problem? Is it just that nobody does this kind of thing on a computer? Do I have to overcome my hatred of dead tree media and buy a pencil sharpener?
What would be really nice is tablet software that can translate handwritten math into latex, and compile that into pdf.
By the way, what I think you want is not "doing symbolic math on a computer," but "having a good input method for equations."
edit: Also can someone please write a good modern programming language for typesetting? With all due respect to Dr. Knuth, tex is awful.
TeX as a language is awful, but what it can do is wonderful. And of course everyone uses LaTeX (TeX made usable by Lamport), or at least I do, so I see little of the TeX language itself. There was nothing like it when Knuth created it, and almost forty years on, there is still nothing like it. As far as I know, the only other typesetting language that has gained even a niche is the hideous SGML, in comparison to which TeX is a thing of superlative elegance and beauty. TeX has a specialised sublanguage for mathematics, both usable for input (so far as linear text can be) and generating high-quality output, so it became the standard for document preparation in the mathematically based sciences. It's still inferior to human typesetting, but that's only available for final printer's copy. What you had to do back then, well, trip down memory lane omitted for brevity.
To do better than TeX, at this point, needs a lot more than coming up with a better language to think about typesetting with. It will have to replicate the TeX ecosystem, provide two-way conversion between it and TeX, and have a visual interface. Visual interfaces for programming languages are really hard, and they generally don't get developed beyond demos that wow audiences and then go nowhere.
And it has to be done by one person, because a committee will just create a bloated, Turing-complete mess.
Which is why it hasn't happened. It needs someone with an expert passion for programming, technical typesetting, design, and languages considered as a medium of thought. Knuth, Jony Ive, and Dijkstra all in one. But anyone like that would have bigger things to do with their talents.
Yes, I understand all that. It is hard to move away from shitty languages once they gained market share.
But latex, while improving on many things compared to base tex is hobbled by tex as well (for example, why do I need to recompile to resolve references, haven't we invented multipass compilation like half a century ago?) I am happy to double down on "(La)tex is a shitty language." It's very useful of course, but the state of typesetting today is sort of like if everyone programmed in Cobol for some reason.
That depends on what you consider to be big. It's not big by the standards of academia. But it might be big by the standards of real world impact.