Writing a math research paper: start to finish!
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- Опубліковано 24 сер 2023
- A quick look at the process of writing and publishing a math research article from start to finish. This paper was typical in some ways, atypical in other ways.
The paper: doi.org/10.1016/j.topol.2023....
Chris Staecker webarea: cstaecker.fairfield.edu/~cstae...
Lattice graphic by Jonny Evans, CC-BY-SA, from www.homepages.ucl.ac.uk/~ucahj...
Real line graphic by Wikimedia user TheNub314, CC-BY-SA 3.0, from commons.wikimedia.org/wiki/Fi... - Наука та технологія
FAQ: "What software did you use?" "What did the referee demand you remove?" "Why can't you submit to more than one journal?" "How did you even 'meet' Lee if you've never met?"
- "What software did you use?" The document itself is written in LaTeX, with diagrams in tikz. The little orange boxed notes are from \usepackage{todonotes}. We housed the document in Overleaf, which is a latex collaboration platform with very basic version controls. I wrote some code to generate the more complicated tikz diagrams (which all got cut)- that was plain python.
- "What did the referee want you to remove and why?" It was an example with a picture- you can still see it in the arxiv version: arxiv.org/abs/2208.10748v1 Figure 3. The referee thought it was confusing and misleading. I think it's a bit counterintuitive but that's why we wanted to include it.
But it was just an example- not a theorem or anything really serious. So no big deal to cut it out. Also (we thought) no big deal to include it against the referees recommendation, since there's nothing "wrong" about it mathematically.
- "Why can't you submit to more than one journal?" This is a very very strong cultural norm. The peer review system relies on the anonymous referees being willing to spend a lot of time reading and checking the paper before it's published. If I submit to several journals, they will all get a referee to read it, but then most of that work will have been wasted when I only publish it with one of them.
The journals always have some kind of rule like "by submitting your article to us, you agree not to submit it anywhere else unless we reject it". Violating this rule will make the journal really mad at you, and immediately tank your reputation with other researchers. It's such a universal rule that I've never heard of someone violating it.
- ""How did you even 'meet' Lee if you've never met?" Lee and I both work in a small research area, so we are both aware of each other's work. I've read several of his papers in the past, and I assume he's read mine. It's common in this kind of community for people to send out their new papers by email to anyone else who they think might be interested, so Lee sent me his "monoid isomorphism" paper, and I responded to him with the idea for this project. (Which ended up being quite different from the paper we wrote.)
Hi Chris! I just stumbled across your channel through this video. Love it! This type of transparency about the process is so valuable to young researchers like myself. I am currently a 4th year math PhD student working in mathematical physics. I was just about to type a comment asking about those nifty little orange boxes, but then saw this FAQ. Thanks a lot! Adding boxes like that to my documents is ABSOLUTELY my style.
@@OwenEkblad As a complete ignorant in the domain, why don't you just publish your work on the internet instead of a journal ?
Some researchers have become so fed up with the system that they just put their stuff online and drop the mic. But this can only work sustainably for people who are already very well-established famous researchers. For the rest of us, I need the venue of a journal for people to take my stuff seriously. The gap between a well-refereed journal article and some random person's writings on the internet is huge.
Even though it's a hassle, the peer review system really does make my work stronger. Almost every time, the referee has something good to say, sometimes very significant things that make the work much better.
And anyway the people writing these articles are basically all career academics, who are constantly under pressure from university deans, etc, to publish. The deans never read the papers and have no real idea how good my papers are, but they control my money. Posting stuff online won't cut it.
@@ChrisStaecker I saw a quote about why someone does math for a living that went something like "There are six people in the world who understand what I do and none of the have the power to fire me." He forgot to mention that implies the people who DO have the power to fire him are clueless...
Thanks for the video. I have a question regarding hours. I have often heard that physics research is very time-intensive and that researchers have to often work for >60 hours a week. But you said you only worked 50 hours over two months. Is it different in math research? Or do you have any other papers you are writing simultaneously? Or maybe your teaching duties take the rest of your time? I'm an aspiring researcher and would be very grateful for clarification.
"Nobody reads this stuff anyw...." 🤣 Very interesting to see how something like this works. I love your videos!
hits too close to home... so true.
😂 This background comment made me laugh aaaa lot!!
i do read stuff like this, though i may not understand everything but enough for me to appreciate how math works even at the smallest level.
This was extremely valuable to me. Thank you for making it.
Thanks! That's how we do it on the Z-List! Maybe you can have me on your channel? Haha jk nah don't worry I know my place. but srsly hmu
That’s the way man, shoot your shot! 😂
sup destin
haha lovely response... I have to agree with smartereveryday. It's a great insight to the way others in adjacent fields work. I've been looking at the law field for some while too (i'm in biomedical research).@@ChrisStaecker
Get this man for one of your videos, Destin!
Do iiiiit~
This video was fantastic! I'm an undergrad and have always wondered what the process of actually writing a paper is. You tell a story really well too
A paper's acception should NOT take this long. This is a very good video to show what academics are dealing with. Thanks a lot.
Unfortunately 1 year submission-to-publication is not at all abnormal in mathematics. For this paper I was very pleased with the wait time- the only bad part was the 6 months for an editor-rejection.
Completed unrelated, but my memories of Differential Equations and Linear Algebra classes with Dr. Staecker still stand out as inspirational decades later. Other classes taught me subjects, but yours taught me passion.
Right on! I remember you Leslie- I hope you're doing well.
@@ChrisStaecker yes, all well :)
I'm a second year PhD student in computer engineering, though my topic intersects heavily with computer science theory and statistical mechanics. Thank you so much for this video, it's invaluable to see that even for "relatively easy" papers the process is far from linear. I particularly appreciated the little notes "it took me X hours to make this figure" or "I spend X hours writing code for an idea that didn't pan out". Whenever I spend time on something like that I assume I'm just an unproductive researcher and I ought to be more time efficient. Hearing about the nonlinearities and obstacles from an established researcher helps assuage the imposter syndrome and self-flagellation.
Yes- what you're describing is a totally normal part of the process, at least for me.
I’m a researcher in education studies. I write mostly philosophy style papers. It was so reassuring to know that you also max out at 3 hours or so of hard thinking/writing work. Sometimes I feel guilty that I’m not spending more time with my research.
Cal Newport “Deep Work” states that we max out at around 4 hours of deep thinking. Good read.
I'm so glad UA-cams algorithm is going crazy recently and I got to see this glimpse into a world I think is incredible
i just accessed this paper through my university
i don't know what to do with it, but i read through it
really appreciate how you documented this! it was funny. takes lots of patience. cool to see the journey. i'm no academic or mathematician, just a random person going to university that stumbled across this video and liked it
I'm a postgrad linguistics student who (by chance) is only now working on his first ever research paper (outside of term papers), and it's reassuring to see a lot of similar points I've realised myself: the "active work" and "idle thinking" that's 100% paying off; the "bogus rabbit hole that leads to nothing"; the feeling of mostly failing and, of course, the "nobody reads it anyway". Maybe I'll do my own take on this format. Cheers!
I love the final statement 😂. Man, researchers' job isn't a piece of cake at all. Loads of dealing with frustration. You are truly giants and the foundation upon which progress is built.
It's weird, yeah. But we appreciate it regardless.
As an independent researcher, I haven't published any papers yet, and I've been feeling quite disheartened and unaccomplished. This video really helped me gain insight into the entire process of taking a research paper from inception to publication, I've come to appreciate the tremendous amount of work and dedication required to produce high-quality research. When I compare my process, I found myself giving up as soon as I came through any sort of obstacle. This video illuminated the fact that it's entirely normal not to see immediate results throughout this journey; it's a continuous process of trial and error.
dont do this, join an institution. No one will take your research seriously
@@PerfectoidJosh Frankly, you'd be more careful giving advice, this person is a stranger and what course of things they're journey outlines is one where you don't know how it may end. I say stay the course & course-correct while documenting your journey. At least then people will see how to go about being an independent researcher along a better path.
@@PerfectoidJoshsome of us joined an institution but were discriminated against for having disabilities and the ones responsible have 0 accountability.
In the history of science and especially math there have been numerous examples of significant contributions being made by outsiders and independent researchers. And in mathematics, if someone gives you an unbelievable equation but your calculator says it’s true, you will take them seriously, regardless of their background.
Obviously there are a lot of cranks out there spamming anyone with a .edu email address their crackpot theories. But, you can totally develop novel mathematics, and maybe demonstrate it to a community college professor who can vouch for you. There are absolutely ways of achieving success as an outsider.
All in all I find your comment rude, insensitive, and inconsiderate of the many reasons why someone may not be able to just “join an institution “.
Thank you for this! As a computer scientist who switched from industrial research to working on my own projects in isolation a few years ago, I found it very reassuring to hear you talk about all the dead ends you hit along the way, and your daily attention limit.
Awesome to see an honest amd well-documented description of the math writing process. Congrats on the paper and maybe someday you'll meet the coauthor.
"They had food so I went but they can't make me pay attention"
You just described half of my meetings 😩
Very cool man. I really appreciate the candid humility noting errors, changes, and other stuff us dumb folk do on a regular basis. Almost as if professors and paper-writers are real people too.
I'm one of those people who joke they can barely count to 5. I truly, on a very deep level, do not understand math and the idea that new math is still being discovered blows my mind. This was so fascinating! Thank you for taking your time to take us through this with you.
Chris, thank you for sharing the insights of the process. Deeply interesting and exceedingly helpful - I love the internet for this as how could any one obtain these insights - as this can be translated to ones own studies, regardless of the level of study. In my humble opinion, I believe this is absolute gold and this should be shared far and wide. My wish is that others in your position share this to their students so they understand it is hard work and putting the shift in each day wins every time and not some magic hack. Congratulations on your paper.
i like your videos so much! relaxed, informative, with the perfect amount of sass and humour!
Great insight for me, very interesting stuff! Thanks for talking about your working process, I love descriptions like this, and I often feel the same: Wandering around with a more or less vague idea, weighing pros and cons in terms of realization and strategy, and at the end of the process it comes to concrete life.
thank you for this! It’s very cool to see the process and thought behind these studies
Thank you so much for this video! I am a 2nd year undergraduate who just finished an REU and I am currently working with my REU advisor online to get our paper published -- it is extremely helpful to see that others understand that feeling of not making any progress from day to day. This video provided me with a lot of hope.
i absolutely love u for making this sir ive been searching for help ever since and immediatley clicked on ur vid when isaw it!! hope ur channel grows
Thank you so much for putting the effort in to make this video! Very helpful! I’m starting my first math research project now and am super excited!
Hello and well done for your whole work!!! It just feels so compassionate of yours showing the real struggle of writing a mathematical paper! Especially for people not accustomed enough to this reality, this video is a valuable treasure trove!!!
Very relatable. A nice feeling when the process is over...but then a new one starts again. Thanks for sharing!
So glad this came onto my recommendations! Great work with your paper! I am a sophomore in high school and I am required to write a 25+ page senior thesis in my field of study (Computer science, mathematics, and engineering) by the time I graduate. This video was very insightful, and I am overjoyed to have been able to watch this journey.
thank you for your contributions to the field.
About 35 years, early in my career. I submitted a paper (medical research), review was 1.5 years, had to call the journal's editor twice begging to get the review done, ultimately paper was rejected, incredibly frustrating. Also early in my career and frustrating was bias; a well regarded author could publish a low quality paper, but my paper would be rejected from the same journal because ti failed to meet a far higher quality standard. In my mid to late career, things got far better. On the positive side, the experience later made me a very sympathetic journal reviewer. We need a better system. For example, when a paper is accepted, the author should agree to review at least paper if needed for the journal. Reviews should be done in 6 weeks or less. Reviews should include constructive feedback. Reviewers should be blinded to the authors of the paper to eliminate bias. Unfortunately, publications are needed for promotion, tenure and overall academic job security.
I'm just a curious math enjoyer so I am not familiar with this process at all. The time difference in writing the paper versus the application/referee back and forth is incredible! It makes me worry that someone could come up with the same idea independently you wrote your paper about, give it to a seperate journal and referee who processes it much faster, and release it before yours! I know its no competition and alls well and good for the discovery of new and better math, but I can't help that I would feel annoyed if someone got credit before me for the idea just because of delays.
Also the longer it takes to publish the longer it takes for mathematicians to build on past works I would assume?
@@gangwolfgamer When we first finished the paper, we also posted it publicly online at arxiv.org, which is a well-known trusted repository for pre-published manuscripts. That version carries a date stamp, so it wouldn't be possible for someone else to copy our paper and beat us to press without being found out. Posting online before publication is common practice now, so this issue isn't really a problem.
This also lets other people see our results and immediately start working on followups. This paper itself is a sort of follow-up to Lee's "monoid isomorphism" paper, which I read in 2021 long before it was actually published in 2023.
@@ChrisStaecker That is wonderful to hear! Thank you!
also consider that if multiple people come to the same idea, then the idea is "healthy". Otherwise one still needs to verify the ideas. With multiple independent works, then it is more likely that the idea is sound (it still requires verification though)
The history of science is basically fights about exactly that for 400 years
Thank you, incredible work and an even better personality!
Thank you for documenting the research process.
10:39 Thank you for graphing this! It is easy to get lost in details, so this is very helpful to understand how things work.
This was so helpful for grad students like myself to see. Thank you!
Excellent video! Very helpful and just in time for me. Thank you!
You're insane. I got my first research publication last year and this content is beyond inspiring.. Thanks so much!!
awesome idea to document the process!
I have no idea what i just watched but found it thoroughly engrossing!
Hope this inspires other researchers to do the same! Thanks for making this.
Awesome to get some insight into higher maths. Thanks for sharing.
This was really interesting! Please post more in the future
such an inventive idea to share this topic thank you
Thank you very much! This video is a gem.
Actually shocked this doesn't have more views, kudos for making something I didn't even understand(the math) super entertaining and now I know what to expect if I ever publish a math paper (I won't)
You are awesome. I love your videos. Thank you!
This is amazing thanks. It made my day actually.
Pretty cool look behind the scenes ... thanks for this awesome video !!
Well done. Congratulations. Thanks for sharing.
This was amazing. Thank you so much for sharing
Hi! I just found this channel. This video was very insightful as a physics person as to how it works in math world. The paper piqued my interest, and you mentioned that the video will probably get more views than the paper. I would love to see a ELI5 or similar (or higher level) explanation of your paper.
As a Masters engineering student, this was very insightful. valuable to see the moments when you hit a wall or find out the rabbit hole did not lead to any gold - relieved it is not just me! Also interesting to see the details of getting papers published. thanks a lot, I hope you make more content like this!
Not a mathematician nor I work in the academia, but I found the video very interesting and enlightening, and kinda inspiring seen through the lenses of co-operation and struggle. Thanks! You made it!
Fantastic video ! I just finished french high school and plan on being a mathematician and teacher in the future, so this was very interesting to me !
three thoughts:
1) as a young person watching the internet grow up and fascinated with how it was going to change people's communication in the future, this (and kids texting like they do) is the kind of thing i anticipated with great joy. i honestly didn't predict the other side of the coin: the modern facilitation of misinformation that's probably making james randi spin in his grave. 2) this how-it-feels as a human to do scientific work at the frontiers of new discoveries (irrespective of how earth-shaking they are) should be more present and earlier in the educational path to such careers. and 3) cris with his eminently deadpan expression and goofy sense of humor might have missed his calling as a born straight-man in a comedy duo.
true.
That was compelling! Two hours a day of attempting novel thinking is probably about my limit, too - that consideration of your time (and the relative value of time) towards the end reminded me of a video by acollierastro about bad data - specifically it's about the Jonathan Pruitt situation, if you're familiar with that. If not, I recommend going in blind, it's a wild ride. (The video is "A Scary Science Data Story.")
This was a brilliant video. I'm a PhD student, not quite at the stage to write a paper yet, and your video was a real eye opener to the process. Also made me chuckle!!!
I too collaborated and published in physics journals with co-authors abroad that I never spoke too let alone met and it worked out just fine. If your work is in a very narrow specialised area, be aware (or beware!) of unscrupulous reviewers who may delay the publication of your work to advance their own position in that field! As for never being read, in the social sciences something like 75% of articles are never citedand half are never read by anyone other than their authors, peer reviewers, and journal editor!
Thanks so much for this video. I worked in computational social science, and it was really interesting to get the mathematics view of how The Work happens.
Great video! I m about to finish my bachelor in math and always wondered about the process of creating mathematical papers! Great insight
Great works!
Absolutely loved this video! Architype academic. Keep up the good work!
Just started freshman year of college. I hope all math professors are as chill as you my man.
Professor Staecker i am not a graduate student but your video cheered me up! thank you for sharing with us
Valuable video, thank you!
Very great i am beginning a phd in france and this kind of video is very precious to me thank you for sharing !
Congratulations on finally publishing!🎉
It would be interesting to hear more about your research area and your opinion on popular/not-so-popular journals in it!
"...part of the regular background hum in my mind..." is the first time I have ever heard anyone reference this other than myself and I almost jumped out of my chair when I heard it. I am a freshman college student doing my own personal research on topics that interest me (not necessarily novel); one such topic is actually in the process of becoming my first publishable research paper! This video couldn't have come at a better time for me. I threw together a rough draft of ideas to send to my professor and am now in the same process that you described. Thank you so much for sharing this, not only as an exploration of the process for creating a research paper, but as an exploration of the human creative process as a whole.
Many thanks for sharing this process and to Professor Lee for the expense to release it.
"I've never met my co-author" only in stem! great video!
This is very interesting, thank you for sharing
this it the most interesting i've watch today. always wondered match research is done
Thank you for sharing. Congratulations 🎉.
I found this highly motivating, the paper also looks quite interesting. The review process seemed really unusual though, glad you made it.
Amazing video!
I think most students in highschool, but even in university underestimate just how much time is "wasted" doing research.
They think, fuelled by movie-versions of science, that scientists just sit down one day and write out stuff like relativity and quantum mechanics in a lazy afternoon session. And when they realize that they cannot do this, they lose hope, they start to think that they are just not smart enough.
@@Alexandre-sz2jb what the hell? Is this some new version of whatsapp scam?
It would be amazing if you could make more of these types of videos.
I don't have a formal mathematics background, only a few low-hundreds courses to complement my CS degree. But this inspires me to study topology for its own sake. Great video!
As an aspiring Computer Science student, I would appreciate if you could drop some links on how to make nice looking diagrams in LaTeX and just general LaTeX guides.
I find it quite amusing you've never even been on a video call with your co-author.
Edit: Lee's a legend for making the paper Open Access.
Cheers!
Tikz and chatgpt, friend
@@Alexandre-sz2jb can Allah tell us how to make good looking diagrams in LaTex?
I'm not a "math guy" by any means, having only passed Calc 2, but I really enjoyed seeing the process of creating a paper. I'd always wondered if it was the kind of thing done all at once or not. It is somewhat reassuring to see that even for professional mathmeticians the process is slow and iterative. Very neat video, thank you for sharing.
I am in fact going to read this stuff! Applied and computational topology is my jam :)
loved the video. I'm a math undergrad in my last semester. I'm hoping to pursue a career in mathematics focusing on group theory and topology. This is a very nice heads up on math research. Thank You.
awesome video
If all goes well, I should start working as a research assistant to a professor here at my school soon. This was really helpful in understanding the entire process of research publication!
I enjoyed this. It sort of reminded me of why I'm not sure I would ever make it in the academic world. I love learning but I'm not sure I could deal with some of the hurdles.
Well.... wow.... ok that s really cool in fact !
Thanks for sharing -
This is a gem
great video! learned alot
Great video man!!!
Looking more into LaTeX and research prep since I'm moving soon to grad school to study economics. This was actually quite helpful. Might not be related to my field, but I was more interested in the research collaboration and work processes
Thank you for your video! This really benefits someone who's just starting out. Really appreciate your margin-note technique and I'll use it in my future collaborations.
Also went to read your paper -- it's very interesting, and written in a concise and understandable manner. I would say anyone with a solid understanding of undergrad discrete math can enjoy it.
Thanks! I agree the paper is pretty accessible- no real heavy background needed beyond undergrad level.
@@ChrisStaecker wow that's an impressive response time from a prof. Respect from a terminally online kid
Great content!
I mean you take pride in your work as a mathematician (and it is well earned and deserved). I'm no where near that level of expertise, "heck i struggle with calc 2" but it is very normal to take a lot of time and energy to demonstrate that expertise to those who might be interested in reviewing it. We the layfolk are just happy to see you be you.
Thanks for this--as a math librarian I sometimes get asked for examples of the publishing process and this will be a great resource.
Alllllso glad to find someone with a taste for obsolescent computing devices and aids
Great video.
i really enjoyed this video
I found great solace in the fact that even people writing real published papers have a hard time with pictures that are suppose to be "easy" haha, great honest documentation. Thank you!
Congratulation Chris.
It was great looking you go through the process. Thanks for sharing. Looking forward for more content like this.
As someone just writing their first paper (albeit in a different field) this was a good perspective to see. I'm going to tackling my own maths ideas in the coming years, so knowing that its a grind and that a lot of the work is left on the drawing board makes me a little happier about the pile of notebooks filled with nothing on my bookshelf
I have those same notebooks!
If you’re wondering who’s seeing this video: I’m a 2nd year Computer Science student (+1 yr of engineering that I switched out of lol). Technical research like this is not something I’ve ever seriously considered doing, but it is fascinating to see your process. Thanks!