MSC2191: Markup for mathematical messages

proposals/2191-maths.md

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+# Markup for mathematical messages
+
+Some people write using an odd language that has strange symbols.  No, I'm not
+talking about computer programmers; I'm talking about mathematicians.  In order
+to aid these people in communicating, Matrix should define a standard way of
+including mathematical notation in messages.
+
+This proposal presents a format using LaTeX, in contrast with a [previous
+proposal](https://github.com/matrix-org/matrix-doc/pull/1722/) that used
+MathML.
+
+See also:
+
+- https://github.com/vector-im/riot-web/issues/1945
+
+
+## Proposal
+
+A new attribute `data-mx-maths` will be added for use in `<span>` or `<div>`
+elements.  Its value will be mathematical notation in LaTeX format.  `<span>`
+is used for inline math, and `<div>` for display math.  The contents of the
+`<span>` or `<div>` will be a fallback representation or the desired notation
+for clients that do no support mathematical display, or that are unable to
+render the entire `data-mx-maths` attribute.  The fallback representation is
+left up to the sending client and could be, for example, an image, or an HTML
+approximation, or the raw LaTeX source.  When using an image as a fallback, the
+sending client should be aware of issues that may arise from the receiving
+client using a different background colours.
+
+Example (with line breaks and indentation added to `formatted_body` for clarity):
+
+```json
+{
+  "content": {
+    "body": "This is an equation: sin(x)=a/b",
+    "format": "org.matrix.custom.html",
+    "formatted_body": "This is an equation:
+      <span data-mx-maths=\"\\sin(x)=\\frac{a}{b}\">
+        sin(<i>x</i>)=<sup><i>a</i></sup>/<sub><i>b</i></sub>
+      </span>",
+    "msgtype": "m.text"
+  },
+  "event_id": "$eventid:example.com",
+  "origin_server_ts": 1234567890,
+  "sender": "@alice:example.com",
+  "type": "m.room.message",
+  "room_id": "!soomeroom:example.com"
+}
+```
+
+
+## Other solutions
+
+[MSC1722](https://github.com/matrix-org/matrix-doc/pull/1722/) proposes using
+MathML as the format of transporting mathematical notation.  It also summarizes
+some other solutions in its "Other Solutions" section.
+
+In comparison with MathML, LaTeX has several advantages and disadvantages.
+
+The first advantage, which is quite obvious, is that LaTeX is much less verbose
+and more readable than MathML.  In many cases, the LaTeX code is a suitable
+fallback for the rendered notation.
+
+LaTeX is a suitable input method for many people, and so converting from a
+user's input to the message format would be a no-op.
+
+However, balanced against these advantages, LaTeX has several disadvantages as
+a message format.  Some of these are covered in the "Potential issues" and
+"Security considerations".
+
+
+## Potential issues
+
+### "LaTeX" as a format is poorly defined
+
+There are several extensions to LaTeX that are commonly used, such as
+AMS-LaTeX.  It is unclear which extensions should be supported, and which
+should not be supported.  Different LaTeX-rendering libraries support different
+sets of commands.
+
+This proposal suggests that the receiving client should render the LaTeX
+version if possible, but if it contains unsupported commands, then it should
+display the fallback.  Thus, it is up to the receiving client to decide what
+commands it will support, rather than dictating what commands must be
+supported.  This comes at a cost of possible inconsistency between clients, but
+is somewhat mitigated by the use of a fallback.
+
+### Lack of libraries for displaying mathematics
+
+see the corresponding section in [MSC1722](https://github.com/matrix-org/matrix-doc/pull/1722/)
+
+
+## Security considerations
+
+LaTeX is a [Turing complete programming
+language](https://web.archive.org/web/20160110102145/http://en.literateprograms.org/Turing_machine_simulator_%28LaTeX%29);
+it is possible to write a LaTeX document that contains an infinite loop, or
+that will require large amounts of memory.  While it may be fun to write a
+[LaTeX file that can control a Mars
+Rover](https://wiki.haskell.org/wikiupload/8/85/TMR-Issue13.pdf#chapter.2), it
+is not desireable for a mathematical formula embedded in a Matrix message to
+control a Mars Rover.  Clients should take precautions when rendering LaTeX.
+Clients that use a rendering library should only use one that can process the
+LaTeX safely.
+
+Clients should not render mathematics by calling the `latex` executable without
+proper sandboxing, as `latex` was not written to handle untrusted input.  (see,
+for example, https://hovav.net/ucsd/dist/texhack.pdf,
+https://0day.work/hacking-with-latex/, and
+https://hovav.net/ucsd/dist/tex-login.pdf .)
+
+Certain commands such as `\newcommand` are potentially dangerous; clients
+should either decline to process those commands, or should take care to ensure
+that they are handled in safe ways.  In general, LaTeX commands should be
+filtered using a whitelist rather than blacklist.
+
+In general, LaTeX places a heavy burden on client authors to ensure that it is
+processed safely.
+
+
+## Conclusion
+
+Math(s) is hard, but LaTeX makes it easier to write mathematical notation.
+However, using LaTeX as a format for including mathematics in Matrix messages
+has some serious downsides.  Nevertheless, if clients handle the LaTeX
+carefully, or rely on the fallback representation, the concerns can be
+addressed.