Vanilla 1.1.9 is a product of Lussumo. More Information: Documentation, Community Support.
1 to 34 of 34
This is coming from this recent thread and a few other things that are going on in the background of MO these days.
We often hear good things about how MO is useful in a mathematician's daily work. "MathOverflow is like the colleague down the hall" is something I hear very often. Our founder Anton once said: "I want(ed) MathOverflow to be useful for me!" Other moderators, including myself, have been caught saying similar things here and there.
I would like to know how MO is useful for YOU!
(Input from "lurkers" is especially welcome! Note that meta.mathoverflow.net is completely separate from mathoverflow.net. You don't need a MathOverflow account to post on meta. Even if you do have a MathOverflow account, your meta account is not tied to it in any way. Anonymous posts are also welcome.)
I live on an island with few other people, let alone mathematicians. So this gives me a relatively easy place to talk about mathematics that I find interesting.
Besides giving me an opportunity to read and think about mathematics that I probably wouldn't encounter otherwise, MO provides a window onto how others think about mathematics, which is very interesting and useful to me. On occasion, one can see some beautiful and elegant mathematics at play in a relatively informal setting, which is very pleasant indeed. I also like the occasional challenge of answering questions that are not my own.
MO gives a glimpse into problems that are interesting to people outside my own field (and outside my department). I don't mean the big-picture questions from other fields, for which I can read expository accounts elsewhere and for which MO is ill-suited. I mean the subsidiary technical problems which come up in the "real world" (defined in the extremely weak sense of "anything other than the subsubfields of mathematics in which I work, including other subsubfields of mathematics") that may be approachable with methods I know about. Reading, and occasionally trying to answer, such questions is a useful counter to the tendency toward mathematical navel-gazing.
MO hasn't directly helped me solve any problems, but it's definitely helped convince me that certain ideas or approaches won't work (usually something which I would've figured out on my own, but would've taken much longer).
Also, and this is related to Donu's first comment, the big picture expositions that users like Emerton have written have been especially nice. Longer expositions of these topics exist in various places, but a one-page conversational summary is much easier to digest when you're just starting out.
The principal draw of mathoverflow for me is the unending supply of extremely interesting mathematics, an eternal fountain of fascinating questions and answers. The mathematics here is simply compelling.
I feel that mathoverflow has enlarged me as a mathematician. I have learned a huge amount here in the past few years, particularly concerning how my particular area relates to other parts of mathematics. I've read some really great answers that opened up new perspectives for me. But just as importantly, I've learned a lot when coming up with my own answers. It often happens that someone asks a question in another part of mathematics that I can see at bottom has to do with how something I know about relates to their area, and so in order to answer, I must learn enough about this other subject in order to see the connection through. How fulfilling it is when a question that is originally opaque to me, because I hadn't known enough about this other topic, becomes clear enough for me to have an answer. Meanwhile, mathoverflow has also helped me to solidify my knowledge of my own research area, often through the exercise of writing up a clear summary account of a familiar mathematical issue or by thinking about issues arising in a question concerning confusing or difficult aspects of a familiar tool or method.
Mathoverflow has also taught me a lot about good mathematical exposition, both by the example of other's high quality writing and by the immediate feedback we all get on our posts. This feedback reveals what kind of mathematical explanation is valued by the general mathematical community, in a direct way that one does not usually get so well when writing a paper or giving a conference talk. This kind of knowledge has helped me to improve my mathematical writing in general.
So, thanks very much mathoverflow! I am grateful.
MO is useful for me because it provides a better way to waste time on the computer than any other site I visit.
It's like a screensaver with actual human beings trapped inside the screen! :)
(Those interested in continuing the discussion regarding Gil's last comment can do so in this thread.)
MO may have helped me get into graduate school? I think my letter writers mentioned my MO participation.
MathOverflow threads can be used as a focal point for aggregating useful resources on a particular topic, as well as to bring diverse communities together. For example, I just created a thread on applications of the Giry monad in probability and statistics. In that post, I write:
"For the benefit of future researchers, I've created this community wiki thread to aggregate possible applications of the Giry monad in probability and statistics. My hope is that this thread might be a place for the structuralist and probability communities to come together and learn from each other."