Timeline for A starting point for research in Graph Theory as a high schooler [closed]
Current License: CC BY-SA 4.0
27 events
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| Jan 29 at 22:32 | history | closed |
Daniele Tampieri Steve D Bugs Bunny kodlu Andy Putman |
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| S Jan 29 at 22:30 | history | suggested | CommunityBot | CC BY-SA 4.0 |
removed meta & social content
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| Jan 29 at 20:22 | review | Suggested edits | |||
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| Jan 29 at 13:33 | comment | added | Timothy Chow | You might also look into math programs that are focused less on Olympiads and more on cultivating a sense of mathematical discovery, such as the Ross Program or MathCamp. | |
| Jan 29 at 13:31 | comment | added | Timothy Chow | @SakshamSethi See my answer to another MO question. It never hurts to know more math, but de Grey's work really required almost no textbook knowledge. My advice to you at this stage is to try to train yourself to ask and answer your own questions. Don't worry about whether your questions are new or old, easy or hard, interesting or uninteresting (as long as the questions are interesting to you). This attitude of always asking and answering your own questions is far more important to cultivate than any specific textbook knowledge. | |
| Jan 29 at 12:36 | comment | added | Andrea Marino | I suggest you get in touch with professors in graph theory from your area, go to seminars of the group (if any), and propose yourself to make some humble calculations. I think free work is always welcomed, and if you catch a Professor who encourages your ambition, it could also mentor you through your early career. | |
| Jan 29 at 12:33 | comment | added | Andrea Marino | In the same vein of Tian Vlasic, a nice starting point (if you are tailored at publishing) could be working out details of so-called "folklore results". That is, take a result that is almost known to experts, but nobody has ever really worked out the details. Study the involved definitions, make the needed calculations, and submit to a minor journal. While this is not satisfactory from a problem-solving point of view, it would allow you to become at ease with research topics and practices while publishing (it is also a service to the community). Knowing of such results is not easy, but [...] | |
| Jan 28 at 22:38 | comment | added | Tian Vlašić | While I’m sure you already know this, I cannot but stress it. Research does not need to be focused on open problems, you just need to make progress in the field; Be that by introducing new definitions and studying their connections or developing new methods, etc. I must say that I am in a very similar situation as you are. I am also a high school student who has participated in math contests. I am currently working on a paper on metric and abstract convexity and I never let the fact that I am a high school student discourage me from my work. Best of luck to you :) | |
| Jan 28 at 21:35 | answer | added | Per Alexandersson | timeline score: 4 | |
| Jan 28 at 21:02 | comment | added | Alec Rhea | You may find it interesting to pursue connections between random graph theory and LLM’s, as was recently done and written about in a Quanta article. | |
| S Jan 28 at 20:28 | vote | accept | Saksham Sethi | ||
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| Jan 28 at 20:27 | vote | accept | Saksham Sethi | ||
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| Jan 28 at 19:01 | comment | added | Steven Stadnicki | @SakshamSethi One caution: you should not assume that your work at this point will lead to a paper. You are still laying foundations for yourself; writing a paper is an excellent goal to work towards but from where you're at IMHO you should be more focused on the work towards it than the paper itself. | |
| Jan 28 at 18:12 | answer | added | JoshuaZ | timeline score: 4 | |
| Jan 28 at 17:41 | comment | added | Saksham Sethi | Secondly, after gaining a solid foundation, how do I know which open problems in this field are accessible for me? I am willing to spend one or two years working on a problem, but I don't wish to spend an enormous amount of time for my first paper. | |
| Jan 28 at 17:34 | comment | added | Saksham Sethi | @TimothyChow I see. Thank you for the response! However, what do you mean by "very little background knowledge"? I would assume that I need to know basic graph theory from an introductory textbook like "Introduction to Graph Theory" by Richard J. Trudeau. Is even that not necessary? | |
| Jan 28 at 15:17 | comment | added | Timothy Chow | Take a look at Aubrey de Grey's paper, The chromatic number of the plane is at least 5. He made major progress on a long-standing open problem in graph theory despite not being a professional mathematician. The paper illustrates how it is possible to do significant research in graph theory with very little background knowledge. | |
| Jan 28 at 14:34 | history | edited | David White | CC BY-SA 4.0 |
Added links to the three exam names, since users from outside the US won't necessarily know of the AIME etc.
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| Jan 28 at 13:49 | history | became hot network question | |||
| Jan 28 at 13:40 | answer | added | David White | timeline score: 8 | |
| Jan 28 at 12:16 | history | made wiki | Post Made Community Wiki by David Roberts♦ | ||
| Jan 28 at 8:50 | answer | added | Sam Nead | timeline score: 11 | |
| Jan 28 at 8:21 | review | Close votes | |||
| Jan 29 at 22:36 | |||||
| Jan 28 at 6:00 | comment | added | mathworker21 | for some problems graph theory, you don't need to know much. you can start thinking about a problem right now. | |
| Jan 28 at 5:49 | history | edited | Saksham Sethi | CC BY-SA 4.0 |
added 7 characters in body
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| S Jan 28 at 5:48 | review | First questions | |||
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| S Jan 28 at 5:48 | history | asked | Saksham Sethi | CC BY-SA 4.0 |