Writing a math research paper: start to finish! 

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.)

This was extremely valuable to me. Thank you for making it.

"Nobody reads this stuff anyw...." 🤣 Very interesting to see how something like this works. I love your videos!

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.

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

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.

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.

It's weird, yeah. But we appreciate it regardless.

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.

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 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 so glad RU-vids algorithm is going crazy recently and I got to see this glimpse into a world I think is incredible

thank you for this! It’s very cool to see the process and thought behind these studies

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.

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.

i like your videos so much! relaxed, informative, with the perfect amount of sass and humour!

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.

thank you for your contributions to the field.

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 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!

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.

Thank you, incredible work and an even better personality!

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

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!

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.

Excellent video! Very helpful and just in time for me. Thank you!

Awesome to get some insight into higher maths. Thanks for sharing.

awesome idea to document the process!

This was really interesting! Please post more in the future

Pretty cool look behind the scenes ... thanks for this awesome video !!

You are awesome. I love your videos. Thank you!

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.

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 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.

This was so helpful for grad students like myself to see. Thank you!

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)

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.

You're insane. I got my first research publication last year and this content is beyond inspiring.. Thanks so much!!

Well done. Congratulations. Thanks for sharing.

such an inventive idea to share this topic thank you

Hope this inspires other researchers to do the same! Thanks for making this.

This was amazing. Thank you so much for sharing

Thank you very much! This video is a gem.

This is amazing thanks. It made my day actually.

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 !

Great video! I m about to finish my bachelor in math and always wondered about the process of creating mathematical papers! Great insight

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.

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!!!

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!

Great works!

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!

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.

Absolutely loved this video! Architype academic. Keep up the good work!

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!

Professor Staecker i am not a graduate student but your video cheered me up! thank you for sharing with us

Very great i am beginning a phd in france and this kind of video is very precious to me thank you for sharing !

I found this highly motivating, the paper also looks quite interesting. The review process seemed really unusual though, glad you made it.

Valuable video, thank you!

It would be amazing if you could make more of these types of videos.

I have no idea what i just watched but found it thoroughly engrossing!

Thank you for sharing. Congratulations 🎉.

This is very interesting, thank you for sharing

this it the most interesting i've watch today. always wondered match research is done

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 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!

"They had food so I went but they can't make me pay attention" You just described half of my meetings 😩

"...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.

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!

Many thanks for sharing this process and to Professor Lee for the expense to release it.

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.")

Congratulation Chris. It was great looking you go through the process. Thanks for sharing. Looking forward for more content like this.

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.

Great video man!!!

great video! learned alot

I am in fact going to read this stuff! Applied and computational topology is my jam :)

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

Just started freshman year of college. I hope all math professors are as chill as you my man.

Great content!

Thanks for this--as a math librarian I sometimes get asked for examples of the publishing process and this will be a great resource.

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.

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

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.

Great video.

i really enjoyed this video

Well.... wow.... ok that s really cool in fact ! Thanks for sharing -

Thank you for the video journey. It sounds like the direction of the research might be clear, but the outcome is not. Even after the work is finished! Much appreciate your efforts to advance knowledge in Topology.

This is a gem

Enjoyed the video very much - interesting, informative, and enjoyable to watch. However, I'd like to recommend a few revisions ...

Happy to see you, professor. I met you at Fixed Point Lab, in Bangkok, Thailand.

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.

Great video! I was thinking about making a similar video for the most recent paper I'm working on, but other things got in the way in the end. Maybe I'll give it another attempt sometime in the future!

Congratulations. I'm seeing that the article establishes some parameters and definitions, and several short proofs, almost like properties. I remember two economics professors who were the editors for a journal, and it was nice being on 'that side' of the publishing process.

I am a student in highschool. Im currently taking the IB program and for math we have to write a 20 page paper and this seems like something that might serve me really useful. I have absolutely no experience in writing a math paper and i was thinking on doing an exploration on machine learning. the math is way above my level but I have the time and passion, plus I understand the basic gist of all the math. I like how this video goes into depth on the actual paper writing instead of the math, as im fairly confident in that.

I'm a PhD student in Plant Science. Thank you for sharing this! I still wasn't able to set up a collaboration (hope to do so!) and for sharing the true part of doing science of trials and errors.

I'm gonna have to read the paper now!

This was a fun watch lol. I’m currently working on cubical homology and I was surprised to know how somewhat interconnected our works are but not quite the same.