Timeline for How do mathematicians conduct research?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2015 at 16:42 | comment | added | BCLC | Nate, actually that's kind of what I was wondering. If a PhD is original research and bachelor's and master's are not, does that mean bachelor and master level mathematicians don't prove? I mean when you prove something no one else has proven before it sounds like original research...? What do you mean by expository thesis? Sounds interesting | |
| Apr 4, 2015 at 15:11 | comment | added | Nate Eldredge | @Jack: I'm not sure what to say about master's programs. Around here most master's programs are based on coursework and/or expository theses, and don't have original research as a requirement. | |
| Apr 4, 2015 at 15:10 | comment | added | Nate Eldredge | @Jack: The goal of pure mathematics research at any level is as I described: to be able to prove or disprove statements whose truth or falsity was not previously known. At the undergraduate level, it often begins with computations (by hand or computer) to try to evaluate whether a conjecture is plausible, and sometimes it doesn't get any further than that. There will also be a lot more interaction with an advisor. | |
| Apr 4, 2015 at 11:40 | comment | added | BCLC | Nate, pardon the dumb questions, but does this apply for undergraduate (pure) mathematical research as well? What about for master's? | |
| Dec 13, 2014 at 17:04 | comment | added | Federico Poloni | You forgot "meet with a colleague, stare at a blackboard together and argue passionately on which definition looks the most beautiful". Pretty accurate nevertheless. | |
| Dec 12, 2014 at 5:04 | vote | accept | Fraïssé | ||
| Dec 11, 2014 at 23:31 | comment | added | Oswald Veblen | Rather than starting with a conjecture (although I sometimes do that), I more often start with an idea: some specific thing that I'd like to understand. This is based on my intuition about what problems seem likely to have interesting results. As I work through the thing I am studying, I come up with specific conjectures and theorems. But the beginning of the project rarely has specific conjectures, just goals. | |
| Dec 11, 2014 at 21:23 | comment | added | Andreas Blass | In my own experience, it's not that common to begin with a specific problem. More often, I begin with a feeling that something I've read or heard about could be done more elegantly or more clearly. My initial goal is then just to understand better what someone else has done, but if I can really achieve a better understanding, then that often suggests improvements or generalizations of that work. Indeed, it sometimes makes such improvements obvious. If the improvement is big enough, it can constitute a paper; if not, it can sometimes become part of a paper, or of a talk. | |
| Dec 11, 2014 at 16:21 | comment | added | Dan Bryant | What's interesting is that sometimes in the course of proving something, you might invent an entirely new kind of mathematics, which in turn winds up being useful for other purposes. This is very loosely analogous to inventing new programming languages for the purpose of more efficiently expressing your intention and hence developing things more quickly. Many of the names of our everyday mathematical abstractions come from the names of the living, breathing people who spent their lives constructing and refining them. | |
| Dec 11, 2014 at 11:03 | history | edited | David Richerby | CC BY-SA 3.0 |
Lemmas not interesting enough to publish *on their own* but most papers will contain several.
|
| Dec 11, 2014 at 7:38 | history | answered | Nate Eldredge | CC BY-SA 3.0 |