The English of Mathematics

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# The English of Mathematics

I recently gave a talk on the english of mathematics, and it included some fun topics which (since I wasted so much time coming up with them...), I thought I'd share with my friends at PlanetMath.

My talk slides and all the fun stuff generated is here:

http://math.arizona.edu/~mcleman/MiscFun.html

The first fun thing is a list of "randomly generated" non-words which somehow SOUND mathematical in nature.

The second is using N-gram models of english to generate random mathematical sentences.

Finally, motivated by Rooter, I modified their code to produce abstracts and first pages of randomly generated mathematical papers. I have a sample on the page, which I think is pretty fun to read through.

I had a lot of fun working on this stuff, so I hope you at least get a kick out of reading it. Feel free to respond with any comments.

Cam

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## Re: The English of Mathematics

We're interested in *parsing mathematical texts* (move from natural language to a formal, universal language) and

in *generating mathematical texts* (move the opposite direction). The stuff you've been working on could give you a head-start on working out a more general discussion of of the "linguistics of mathematics".

Which in turn would be part of an "anthropology of mathematics" (which is one way to characterize what Ray and I are working on).

(This random text generation stuff is often compared to Burroughs's "cut up"

method. My work on the "scholium system" has something in common with

that method too; e.g. here's a quote:

Because scholia-based documents are made up of little pieces whose

semantic content has been exposed through an ongoing process of

annotation, they can be readily refactored; and new, meaningful,

derivative works produced from their atomic components. The process

of annotation also opens the way to increasingly powerful

computer-based inference about the system's contents.

So, you can imagine here doing something like what you've done with words

again, but with paragraphs. I'm trying to make things

make sense, rather than make them look like they make sense...

but the principle is somewhat similar.)

If you want to learn more about the stuff we're working on,

stop by http://planetx.cc.vt.edu/AsteroidMeta/HDM

and poke around some. Feel free to add comments or questions.

## Re: The English of Mathematics

Silly as it may sound at first sight, this could actually have serious uses. One of the things Joe and I are interested in is the linguistics of mathematics with an eye on applications to artificial intelligence. Hence, I could see how your n-gram models could prove useful in trying to come up with a grammar of mathematicianese.

## Re: The English of Mathematics

Yeah, the N-grams model seem to be one of the most applicable methods in linguistics...I've run across quite a few while doing research on the topic: cheat detection, spam filtering, and someone even used them to decide whether or not some ancienct works were actually written by Plato. I'd be interested in learning more about any applications you're researching.

Cam

## Re: The English of Mathematics

> I know so little about computer science that the randomly generated

> papers sound to me exactly like the real ones...

Along those line's there's the infamous Sokal incident in which a physicist wrote a fake postmodern article and had it pass review and be published in the journal "Social Text".

## Re: The English of Mathematics

> Cameron,

>

> This is awesome! Your "math paper" is so amusing to read! Is

> you math paper generator somewhere online?

I hope to make it so evetually, but it's got a bunch of bugs in it right now, so that I have to manually edit the paper to make it compile right each time. I'd like to eventually have it runnable from within the broswer like the original program does, but I need to fix a few things first...maybe over winter break...

In any case, I'm glad you enjoyed it.

Cam

p.s. Ray, have you read the Sokal paper? It's a really good time.

## Re: The English of Mathematics

Whoops.

http://math.arizona.edu/~mcleman/MathEnglish.html

## Re: The English of Mathematics

Cameron,

This is awesome! Your "math paper" is so amusing to read! Is you math paper generator somewhere online? I would love to give it a try. The computer science paper generator is a blast too. Unfortunately, I know so little about computer science that the randomly generated papers sound to me exactly like the real ones...

Alvaro

## Re: The English of Mathematics

A related link is

http://www.elsewhere.org/pomo

which is an "post-modern nonsense generator". The result seems to

be licensed for non-comersial use :-) Somewhat more serious is

http://www.physics.nyu.edu/faculty/sokal/transgress_v2/transgress_v2_sin...

which is the famous nonsense paper by Alan Sokal. Amazingly, this

paper was actually published in a scientific journal. The hoax

is described here:

http://www.physics.nyu.edu/faculty/sokal/lingua_franca_v4/lingua_franca_...

Sokal's homepage is here:

http://www.physics.nyu.edu/faculty/sokal/

## Re: The English of Mathematics

Oh no, I follow the link and there is a HTTP 404 error