maths in collaboration.

slowly but surely, the writing proceeds.

today was also productive in another way .. or at least it felt productive. in the afternoon i met with my younger math sibs and talked about math and about research and about open questions in gmt.

i don't know if it will become a full-fledged collaboration, but our backgrounds have a nontrivial intersection and we can understand each other well enough, mathematically.

even if it works out, the timing is difficult: both of them are applying for jobs this fall, and i'm already busy with plenty of things, like converting my thesis into a paper and working on another collaboration with another research group ..

.. which reminds me: i should get back to them.

---

i like making plans, and i prefer collaborations when there is a set plan in mind. it's not enough to have a goal in mind, or a fixed research problem: there should be a plan.

if i prove this and if you prove that,
and if our strategy works,
then done: everybody's happy.

of course, nothing is ever so neatly organised as that, and plans often have a way of going awry. in fact, answering questions is hard enough.

i don't know that many mathematicians, but often i hear this sort of dialogue:

Q: say, i have this question. do you know if ____?
pA [1]: well, if you assume this, then _____.

we don't actually answer questions in full generality, unless we are so lucky that our proof techniques fit the situation perfectly. often they don't, and we can only say what we are familiar with.

we draw pictures,
we ask questions,
we whet the problem down by reductions,
we examine the worst-case scenarios,
and we hope.

i guess i'm saying nothing important here and nothing too interesting, either. i guess i worry a lot, when in collaboration:

everyone is talking or no one is talking;

i wonder if this will really work because i've forgotten how not to doubt;

i worry if my ideas are wrong or unfruitful and that they lead me -- worse, a team of us -- down a wild goose chase, with no goose in sight.

it's one thing if i waste my own time, in the mornings, thinking to myself.

for others who make a point to show up, at my office and at this or that time and day -- how frustrating it would be, for them, if only after hours do we see that my idea is silly!

so i worry.

if it's just my idea and if it doesn't work, oh well. but if it is to become a group idea, then yikes:

now i must have a good idea, a plan;

make sure it's good,
have space in it so that others can work and contribute,

and not force them to sit down, listen to me drone on,
until i show them what might not work.

[1] that is, a partial Answer.