Timeline for Nature of pure mathematics research
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2020 at 10:23 | comment | added | Federico Poloni | Maybe it's a problem of definitions. What percentage of your phd thesis is work you were competent enough to do also when you were 18, after a little training? | |
| Jan 21, 2020 at 2:23 | comment | added | Kimball | @AlexanderWoo Math research has no grunt work. - Really? I feel like a lot of PhD theses, and about half of the work I do in my own research, are grunt work. | |
| Jan 20, 2020 at 18:31 | comment | added | Dave L Renfro | @Alexander Woo: "Math research has no grunt work." --- Well, at the beginning there's the sometimes lengthy "library research" on a certain problem/topic (now mostly done outside the doors of an actual university library) that might need to be undertaken, and at the end there are the many successive theoretical refinements that one considers once the main method/idea is established/proved in the most important special case(s) (although given present-day publication quotas, these might be left for follow-up papers). | |
| Jan 19, 2020 at 21:54 | comment | added | Federico Poloni | "An idea that can be used only once is a trick. If one can use it more than once, it becomes a method.” --George Pólya and Gabor Szegö, Problems and Theorems in Analysis, 1972. | |
| Jan 19, 2020 at 21:08 | comment | added | Alexander Woo | S_Mitter: Math research has no grunt work. There are no experiments to do. Once someone figures it out, it's been figured out, and there is no more research to do on that question. So topics that have nothing mysterious or unexplained about them tend to be solved, and are not research questions anymore. Now it does frequently happen that a subject that originally looked like a bunch of tricks gets organized and becomes something that doesn't look like a bunch of tricks anymore, and that is part of the work of research in mathematics. | |
| Jan 19, 2020 at 20:23 | comment | added | S_Mitter | Tricks: Coming up with clever ways to prove certain things/attain certain results. Common example is high school combinatorics. It's not built upon rigorous structures. Different problems using same principles often require clever "strategies" which are difficult to think of from scratch, the leaps here from problem to the trick that solves it is not exactly explained, always. Whereas take for example Isomorphism theorems is built upon definitions and smaller results, there's nothing mysterious or unexplained about it. | |
| Jan 19, 2020 at 20:14 | history | answered | J Fabian Meier | CC BY-SA 4.0 |