Timeline for How do you decide whether a question in abstract algebra is worth studying?
Current License: CC BY-SA 4.0
11 events
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| Nov 27, 2022 at 12:38 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Sep 25, 2010 at 9:45 | comment | added | Charles Matthews | My comments can certainly be disregarded, since it is a long time since I have called myself a mathematician. I feel somewhat misread here, in fact. Let me just say that I don't feel that "market research" is always a help in generating interesting mathematics; its role seems more in avoiding dead-ends. The "generality" heuristic is tricky without some factor of "taste", is what I'm saying I suppose, and the burden of understanding what that even means is on general background. | |
| Sep 25, 2010 at 8:41 | comment | added | Alex B. | Thanks, Minhyong! I didn't feel like justifying myself here. Charles, unfortunately, you completely misunderstood my point of view. | |
| Sep 25, 2010 at 7:51 | comment | added | Minhyong Kim | I'm quite sorry for butting into a conversation, but I think it's fairly clear from the post that Alex isn't motivated by a particular need to 'get out of a rut.' In fact, the only 'paradigm in algebra' the question refers to (very lightly) is very far from 'innovation by generalization.' | |
| Sep 24, 2010 at 18:55 | comment | added | Charles Matthews | Well, read good mathematicians before deciding what is interesting, try to do something before assessing on the basis of no experience whether you'll succeed, and get out of your current rut of assuming that "innovation by generalisation" is the basic paradigm in algebra. Mathematics gets done in different ways. | |
| Sep 24, 2010 at 16:15 | comment | added | Alex B. | Sorry about my lack of understanding. I will be grateful if you can clarify your statements a bit. Thanks! | |
| Sep 24, 2010 at 16:15 | comment | added | Alex B. | I also don't quite understand, what parts of your post constitute an answer to my question. E.g., I hope that I have made it clear that I am not talking about "applied algebra" here, so I don't quite see how introducing this distinction would have helped the question. On the other hand, the distinction between "structural" and "combinatorial" issues seems orthogonal to my question. The Burnside problem was proposed when everyone was already convinced that groups are something worth studying in their own right. I'm interested in the period before an algebraic concept reaches that stage. | |
| Sep 24, 2010 at 16:11 | comment | added | Alex B. | Charles, I have to admit that I am having trouble distilling an answer to the question from the post and the above comment. I am not sure how to reconcile your two pieces of advice "follow the masters" and "Don't start off with self-peer-review". If I correctly read the latter as "don't try to predict whether the community will agree with you on your assessment of how interesting a topic is", then it seems to contradict the former. | |
| Sep 24, 2010 at 15:35 | comment | added | Charles Matthews | Yes, the incentives tell you the wrong thing (aiming slightly too low is not as damaging as aiming slightly too high). But this has to be kept a secret if we want those first-rate guys. But this is dangerous ground, given the academic politics of those who imply "I may be hard to please, but this is the only way to make sure that my judgement of what makes the grade carries weight". Don't start off with self-peer-review: try to do a good job of research. | |
| Sep 24, 2010 at 13:02 | comment | added | Gerry Myerson | "Follow the masters" is probably the best advice for second-rate mathematicians (and I am speaking here as a third-rate mathematician of long standing). "Be a master" is probably the best advice for first-rate mathematicians. The tricky thing is figuring out which applies. | |
| Sep 24, 2010 at 7:25 | history | answered | Charles Matthews | CC BY-SA 2.5 |