## Sunday, April 24, 2011

### american english vs. "mathematιcal english"

there are some bits of mathematical english that i find myself using more and more, in everyday conversation, like:

"to this end .."
"it follows that .."
"note that .."
"consider the following ____" [1]

sometimes i wonder if others .. say, my students .. understand that i'm using these words in a slightly different sense than usual:
"Now consider the following linear transformatiοn," said the professor, who, upon walking to the left corner of the chalkboard, began to write at twice the speed as before.

The student paused, and considered the possibility of keeping his notes thorough and complete.

After a moment, he set his pen down and closed his notebook. "Nah," he said to himself.
i wonder how often that happens .. (-:

as for the word "indeed" -- how i use it, anyway -- it appears right after stating a claim, thereby signaling the start of a sub-proof .. but only when the claim is not stated separately like a Lεmma or Sublεmma. as an example:
"without loss, $f_k$ also converges pointwise a.e. to $f$. indeed, the sequence {fk} is norm-bounded in $L^p(X)$ with $p > 1$, so a standard functiοnal analysιs argument, using the Baηach-Alaοglu theοrem and Mazμr's Lemma, implies that .."
to be honest, i don't know how i developed that habit .. maybe from the advisor? i probably picked up a lot of habits from him.

on a barely related note, i quite like old-fashioned words.

at some point i had wanted to give a lecture in which i'd state a claim and start its proof with the words "verily, we note that .." but i never got around to it, though. (-:

[1] after a while, reading maths papers feels a little formulaic. there are only so many instances of "such that" which i can bear. on the other hand, perhaps the formulaic jargon we have is good ..

.. because it means that non-native english speakers can present their ideas just as well, for everyone to read. it makes my life easier, at any rate: my french is rudimentary, my german essentially non-existent. then again, i wonder if i can read de giοrgi in his original italian ..?