I’ve noticed that mathematical papers (articles, online textbooks, etc.) are very well put together. It seems like there is a specific program that would aid in this; it’d be impossible to put a complex mathematical paper together using Word and a special font.

Is there a program to organize a mathematical paper?

AMS-LaTeX is a common program/suite of macros used to typeset math papers. However, note that the specifics of style are really set by the journals and not by the authors. I say “put a theorem declaration here” and it does so in the local style. For example:

\begin{theorem}
The square on the hypotenuse of a right triangle is equal to the sum of the squares on the remaining sides.
\end{theorem}

Later on I’ll tell it to put a proof. Note that I don’t say anything about what fonts to use or numbering schemes. That’s mostly up to the journal.

Now, the flip side of this is that a lot of these papers are really TeXed by mathematics secretaries rather than real mathematicians. Your learning curve will be steep, young padawan, but I’d highly advise learning AMS-LaTeX from the beginning rather than just plain TeX. Otherwise you’ll have to unlearn half of it.

It used to be that printing was done with one big engraved block for each page. Then people made one little block for each letter, and arranged the letters to make up the whole page. The little blocks were called “moveable type”. The process of setting them in place so the page would look nice was “type setting”, though the space was lost in a move somewhere.

Fast forward to the 1970s. Don Knuth gets the galley proofs (basically, a test print) of one of his books and thinks they look just awful. Really, a lot of books from then look basically like they were typed on a typewriter. It gives you a headache after about five pages to read. Anyhow, he sits down and comes up with TeX, which takes a bunch of “marked-up” text (similar to the M in HTML) and makes the image for each page, which can then be printed out. It electronically sets the type, which is no longer really “type”, but the end result is “a series of instructions that will tell the printing hardware what image to put on the page”.

Yes, Word has a typesetting routine in it (among other things, to make full-justified text), but TeX flies beyond it when it comes to typesetting mathematics, mainly because it was originally designed for that sort of thing and because the AMS really sponsors the hell out of it. That’s why I can say

Er, when in college (and on the rare occasion now that I produce something worthy of glossy presentation) I use Mathematica, which is cool because I can do both real work and presentation-quality typesetting in it.

TeX and LaTeX are nice, but take an awful lot of experience and time to get good results. Mathematica is WYSIWYG. But you’re paying Steven Wolfram through the nose for it. TANSTAAFL.

True. But the OP was asking what mathematicians use in their journal papers, and I’d wager that the vast, vast, vast majority of them prefer AMS-LaTeX to Mathematica for that purpose. (Same goes for physics, BTW. I understand that the use of programs like MS Word is a good deal more common in chemistry and biology.)

I could go on, but we’d be getting into GD territory.

Splanky:I’ve noticed that mathematical papers (articles, online textbooks, etc.) are very well put together.

For online presentation of mathematical text, there are various options such as jsMath (which uses source text in TeX format) and the XML-based MathML.

I would be nice to be able to input equations in some proper coded format rather than having to jury-rig them with extended Unicode characters and formatting tricks. Is there a way to get MathML to play nice with vCode? I know you can do some limited HTML/XML but I’ve never really given a try at it.

It would probably require a hack of some kind, and you know how they feel about that. On the other hand, if MathML/LaTeX can be used to generate image files (and I bet they can), it might be workable.

*I am never forget the day I first meet the great Lobachevsky.
In one word he told me secret of success in mathematics:
Plagiarize!

Plagiarize,
Let no one else’s work evade your eyes,
Remember why the good Lord made your eyes,
So don’t shade your eyes,
But plagiarize, plagiarize, plagiarize -
Only be sure always to call it please ‘research’.*

Plagiarize,
Let no one else’s work evade your eyes,
Remember why the good Lord made your eyes,
So don’t shade your eyes,
But plagiarize, plagiarize, plagiarize -
Only be sure always to call it please ‘research’.