Timeline for When is one 'ready' to make original contributions to mathematics?
Current License: CC BY-SA 4.0
34 events
| when toggle format | what | by | license | comment | |
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| Jul 30 at 14:49 | comment | added | Hollis Williams | @NateRiver I think I probably spend something close to 50/50 as well but I mostly read papers rather than books. My main criterion for reading a book or an entire set of lecture notes is that it should really grab me how coherent and well-written it is and how much material it covers (perhaps even how inspiring it is). | |
| Jul 30 at 11:04 | comment | added | Nate River | OP, looking at your now impressive publication record, it seems that you’ve found something that works for you. What kind of system do you use now? I personally do about equal amounts of general reading and problem solving. In my experience the knowledge from books has really helped, nothing I’ve learnt has been wasted so far. | |
| Jun 28 at 20:39 | answer | added | paul garrett | timeline score: 3 | |
| Oct 7, 2021 at 21:04 | history | edited | Hollis Williams | CC BY-SA 4.0 |
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| Jan 18, 2021 at 8:59 | history | edited | Hollis Williams | CC BY-SA 4.0 |
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| Sep 10, 2020 at 8:32 | answer | added | AmorFati | timeline score: 10 | |
| Aug 26, 2020 at 9:12 | answer | added | Per Alexandersson | timeline score: 5 | |
| Aug 26, 2020 at 9:02 | history | edited | YCor | CC BY-SA 4.0 |
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| Aug 25, 2020 at 21:58 | history | edited | Hollis Williams | CC BY-SA 4.0 |
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| Aug 25, 2019 at 0:27 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Aug 24, 2019 at 21:45 | review | Close votes | |||
| Aug 27, 2019 at 16:51 | |||||
| Aug 24, 2019 at 20:30 | answer | added | Gerhard Paseman | timeline score: 15 | |
| Aug 24, 2019 at 19:19 | answer | added | user1318416 | timeline score: 2 | |
| Jul 9, 2019 at 20:04 | comment | added | Sylvain JULIEN | Sometimes it's a matter of luck. As I'm not a professional mathematician, and will probably never be, take this with a grain of salt but some 15 years ago I read a quote by Hermann Weyl, saying the best way to understand the nature of a mathematical entity was to study its automorphism group. I started googling "automorphisms of the Selberg class" and didn't get anything relevant. So I dove into a huge ocean of unknown while trying to define them by myself (I can't say this submarine exploration is over but I already enjoyed the colors of a few species of mathematical fish). | |
| Jul 5, 2019 at 11:57 | answer | added | John Coleman | timeline score: 19 | |
| Jul 4, 2019 at 17:50 | comment | added | Alex B. | @TerryTao: thank you, that's a very nice comic, and a great website/blog! | |
| Jul 4, 2019 at 17:14 | comment | added | Our | when they can ? | |
| Jul 3, 2019 at 23:08 | comment | added | Terry Tao | @AlexB. your model (which I agree with) is nearly identical to this one: matt.might.net/articles/phd-school-in-pictures | |
| Jul 3, 2019 at 21:39 | vote | accept | Hollis Williams | ||
| Jul 3, 2019 at 21:19 | answer | added | Timothy Chow | timeline score: 66 | |
| Jul 3, 2019 at 20:56 | comment | added | Hollis Williams | That was my feeling, in applied mathematics I never ever read textbooks as the problems can always be attacked with basic tools, but sometimes in pure math I do read big textbooks and find that very helpful, as it gives me a sense of the subject, I just find it helpful personally but the consensus seems to be to try to stop doing that. | |
| Jul 3, 2019 at 20:55 | comment | added | Dima Pasechnik | The amount of background reading one needs to do depends heavily on the area; some areas are full of problems which can be attacked by "elementary" tools; for other areas it is much less so (and there it might be essential to have an advisor who can answer your technical questions---which otherwise require dieep understanding of what's in one or more 500-page books). | |
| Jul 3, 2019 at 20:49 | comment | added | Timothy Chow | Some related MO questions: mathoverflow.net/q/35880 and mathoverflow.net/q/27299 | |
| Jul 3, 2019 at 20:46 | history | edited | Hollis Williams | CC BY-SA 4.0 |
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| Jul 3, 2019 at 20:27 | comment | added | Ben Barber | If it is at all reassuring, I have never read a textbook cover to cover. I have probably never read 10% of a textbook. | |
| Jul 3, 2019 at 20:18 | history | became hot network question | |||
| Jul 3, 2019 at 14:50 | review | Close votes | |||
| Jul 7, 2019 at 20:18 | |||||
| Jul 3, 2019 at 14:45 | vote | accept | Hollis Williams | ||
| Jul 3, 2019 at 21:38 | |||||
| Jul 3, 2019 at 14:23 | answer | added | Alexandre Eremenko | timeline score: 47 | |
| Jul 3, 2019 at 14:16 | comment | added | Stanley Yao Xiao | My experience is that reading entire textbooks is a very bad way to start doing research. Read papers instead | |
| Jul 3, 2019 at 12:36 | comment | added | Per Alexandersson | I think it is good if you start with an actual problem, and start working backwards. Read related papers, and then read the definitions needed to make sense of the papers. You do not need to understand papers in detail, but make notes of the main ideas, so that you can return and study the techniques in detail once you believe you need them. | |
| Jul 3, 2019 at 12:29 | comment | added | Geoff Robinson | You don't need to know everything before you can do anything. Also, the nature of Mathematics is such that even people who work at all their lives feel that they know nothing of what is there to be known, so the feeling you mention is not unique to you. It's good to keep learning, and there may well naturally (hopefully soon) come a point when you have an insight which no-one else seems to have had, or you can answer a question that was previously unanswered, or ask an interesting question previously unasked. | |
| Jul 3, 2019 at 12:28 | comment | added | Alex B. | This varies from area to area, but ultimately it is your Ph.D. advisor's job to chart for you a narrowish path throw the literature to a point where you can make an original contribution. I have this model that in your undergraduate you are learning the basics in a ball around 0, but in your Ph.D. you have to start drilling a fairly narrow path through the vast body of mathematics to an accessible point on the frontier, before making that tunnel wider over time. Your Ph.D. advisor should have some idea of which points on the frontier are accessible to you and how to get there. | |
| Jul 3, 2019 at 12:14 | history | asked | Hollis Williams | CC BY-SA 4.0 |