Writing a math research paper: start to finish!

[@ChrisStaecker]

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.)

[@OwenEkblad]

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.

[@Otomega1]

@@OwenEkblad As a complete ignorant in the domain, why don't you just publish your work on the internet instead of a journal ?

[@ChrisStaecker]

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.

[@benjamingross3384]

@@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...

[@baab4229]

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.

[@smartereveryday]

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

[@ChrisStaecker]

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

[@MadaxeMunkeee]

That’s the way man, shoot your shot! 😂

[@cademcmanus2865]

sup destin

[@HarryPotter-kd3bh]

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

[@ladymariaoftheastralclockt2338]

Get this man for one of your videos, Destin! Do iiiiit~

[@DaveMeuleman]

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

[@MrPolyphonicpoi]

hits too close to home... so true.

[@MauricioSalazare]

😂 This background comment made me laugh aaaa lot!!

[@atabac]

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.

[@tugberkk.8402]

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.

[@ChrisStaecker]

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.

[@noahfenech3369]

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

[@matthewburns9629]

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.

[@ChrisStaecker]

Yes- what you're describing is a totally normal part of the process, at least for me.

[@IanLeslies]

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.

[@ChrisStaecker]

Right on! I remember you Leslie- I hope you're doing well.

[@IanLeslies]

@@ChrisStaecker yes, all well :)

[@ryandikdan]

I'm so glad KZbins algorithm is going crazy recently and I got to see this glimpse into a world I think is incredible

[@sphinky1156]

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

[@alexmendel1563]

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!

[@sixthbrokenstring]

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.

[@toryalexander5704]

Cal Newport “Deep Work” states that we max out at around 4 hours of deep thinking. Good read.

[@tahsinahmed7585]

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.

[@PerfectoidJosh]

dont do this, join an institution. No one will take your research seriously

[@___Truth___]

@@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.

[@jarlsparkley]

@@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 “.

[@sumintegrals]

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.

[@MelodiousThunk]

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.

[@vvalerio77]

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

[@cemmy410]

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

[@DTWarrior_]

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.

[@dirichlettt]

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.

[@BrainFreezeWave]

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.

[@onlyonecjb001]

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.

[@theastuteangler]

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.

[@evangibson149]

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.

[@theClaytron]

Very relatable. A nice feeling when the process is over...but then a new one starts again. Thanks for sharing!

[@AndreasHontzia]

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.

[@gangwolfgamer]

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.

[@gangwolfgamer]

Also the longer it takes to publish the longer it takes for mathematicians to build on past works I would assume?

[@ChrisStaecker]

@@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.

[@gangwolfgamer]

@@ChrisStaecker That is wonderful to hear! Thank you!

[@pierQRzt180]

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)

[@spinecho609]

The history of science is basically fights about exactly that for 400 years

[@AdrienLegendre]

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.

[@GreggDurishan]

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.

[@Perezosos309]

true.

[@kurtmueller2089]

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.

[@kurtmueller2089]

@Alexandre-sz2jb what the hell? Is this some new version of whatsapp scam?

[@kostasvasilopoulos6586]

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!!!

[@crxunch3790]

"...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.

[@Aloka145]

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

[@KoobztheShawk]

"I've never met my co-author" only in stem! great video!

[@andrewopenside3224]

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

[@deafharp8944]

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)

[@BsktImp]

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!

[@N.A._McBee]

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.

[@tankfire20]

Thank you for documenting the research process.

[@sebastians7346]

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

[@yeetmaster8050]

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

[@tajmahalfred]

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

[@tajmahalfred]

Alllllso glad to find someone with a taste for obsolescent computing devices and aids

[@ewangoddard7345]

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!

[@anthonymiller6234]

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!!!

[@savantshuia]

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!

[@lmao4982]

Tikz and chatgpt, friend

[@lmao4982]

​@Alexandre-sz2jb can Allah tell us how to make good looking diagrams in LaTex?

[@AryanneHoofler]

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

[@Laundry_Hamper]

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.")

[@gordoawesome8590]

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

[@mahin300]

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.

[@fahadalghamdi9316]

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.

[@arthurpenndragon6434]

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!

[@mohammedfarhaan9410]

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

[@ehfik]

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

[@emmabunch7]

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!

[@ichbindoofhihi1]

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!

[@rickyc46]

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!

[@dst1279]

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.

[@Heccintech]

I have a strong appreciation for your work flow, and modern researchers should utilize people worldwide. I utilize a lot of the topics you discuss in my research and I can tell you that, you documenting this is one of the most impactful things you could do. A lot of these processes are not really discussed and these informal setups are where the true researchers lie and were true innovation exists, I wish you displayed animations of the homorphisms and how you could draw structure to them, but that would be a different video. Because in order to draw light from the abstraction, I don't think words could dignify it and that these complex structures are actually over generalized by words.

[@fish42]

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!

[@coenneedell3908]

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.

[@songokussj2446]

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

[@kedonsiemen]

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!

[@paperheartzz]

The absolute honesty of working during a faculty meeting... but going because they had food. 😅

[@ChrisStaecker]

We have a big all-university faculty meeting at the end of the year. It’s nice to see folks and I do pay attention to much of it, but there’s always plenty of stuff that’s not really important to me. LOTS of folks there doing similar work on the side.

[@paperheartzz]

@@ChrisStaecker A faculty paid "work with me" session, delightful!

[@pygmalionsrobot1896]

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

[@stevenvillanueva]

Woah! Didnt expect to see you popping up in my recommendations. A couple years ago I followed along with your recorded Real Analysis lectures, even doing the homework, while i was at work in high-school. It was great, easily one of the best free courses I've ever seen. It's awesome to see this channel get lots of love🎉

[@drakeramoray7574]

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

[@donallynch]

Thank you, incredible work and an even better personality!

[@globisdead]

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

[@unhearted4510]

thank you for your contributions to the field.

[@trondsi]

Nice summary of the process! I have a PhD in biology, and I have published a few papers. But in the long run (postdoc etc) I couldn't keep it going, at least not at the pace that "they" expect (and I think your video shows why it's hard). I now have a non-tenured 100% teaching faculty position at a university instead. Young me would probably have been a bit disappointed (research sounded so much cooler) but I think I'm happier this way.

[@ChrisStaecker]

Yes everybody needs to find the balance that works for them. I have an old professor who's always pressing me to try to do more research. But I've found a pretty good pace that works for me- living life the way I'm happiest is much more valuable to me than the kind of micro-prestige that academic publishing brings.

[@taraskywalker453]

Thank you for sharing this! As a PhD candidate, it is very insightful!

[@r0hanhs]

Perfect timing! I just figured out the proof for the Reimann Hypothesis... Will contact you if anything else is there to ask... Thank you!!🙏

[@Globbo_The_Glob]

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

[@ChrisStaecker]

I have those same notebooks!

[@bioxbiox]

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

[@the_green_snake4187]

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

[@geheimemartha]

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 !

[@CthulhuW8ingInTheDeep]

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

[@Pindrop22]

such an inventive idea to share this topic thank you

[@jacobkrebs7248]

This is perfect as a PhD student in physics. Even though I have my advisor to lean on, the process is still so convoluted and being able to see it is easier to process.

[@jacobkrebs7248]

@Alexandre-sz2jb there is only one way to the Father, and it is through Jesus Christ alone. Please repent my brother

[@kjquiggle]

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

[@МихаилРудаков-х8и]

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!

[@pierQRzt180]

awesome idea to document the process!

[@MinwooKim-di5sz]

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

[@imsleepy620]

as a math major who's definitely going to pursue theoretical math/physics, this is incredibly informative. the process of math research is completely shrouded in mystery for me, and it's reassuring to see a professional struggling with the same kind of self-doubt and emotional rollercoasters that I've always assumed they don't understand.

[@methandtopology]

Honestly when I talked with some professors of a research department they seemed to think everyone knows how research is done. Some people grew up in environments like that (e.g. parents) but I had no clue what research involves and felt "behind" everyone else

[@imsleepy620]

@@methandtopology Yeah, that makes sense. This kind of video is definitely really useful for someone who doesn't know the process at all (and is the only one of its kind that I've seen). Would you have any advice for an undergraduate trying to get into math research (probably in a field like dynamical systems and PDEs or stochastic processes)?

[@methandtopology]

@@imsleepy620 I'm only in my first year of graduate school, and my focus is on topology and geometry, so I don't know if I am in position to give you very good advice. That being said, I can offer some perspective. One recurring theme in my studies so far is that maths is very interconnected and better seen as a whole instead of a partition into 'fields' (because partitions will make you think they are disjoint). It's definitely worth it to try and get as good as you can in every subject. In particular, my understanding is that the big three--Algebra, Analysis, Topology--are the bedrock of maths and you should really put in the effort to get comfortable with them. Any little thing you learn there will eventually help you, can almost guarantee. I worked really hard to get where I am, and it was 100% worth it. So make sure you have no regrets. Here's some advice I found online before that I found extremely helpful: 1) marktomforde.com/academic/gradstudents/images/GradGuide.pdf This is basically like the ultimate crash course on how grad school works. 2) terrytao.wordpress.com/career-advice/ Career advice by Tao himself. 3) kzbin.info/www/bejne/l2LddaiFhdCAidk One of my favourite motivational and eye-opening lectures by an amazing man. I don't know if you want this or if it will help you, though.

[@gordonramsdale]

As someone who never took the prerequisite maths classes for cs and now finds himself doing research in discrete maths… I’m fuckef

[@ofekharnof]

This was really interesting! Please post more in the future

[@egericke123]

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

[@etaoinwu]

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.

[@ChrisStaecker]

Thanks! I agree the paper is pretty accessible- no real heavy background needed beyond undergrad level.

[@etaoinwu]

@@ChrisStaecker wow that's an impressive response time from a prof. Respect from a terminally online kid

[@joseftrojan7664]

Thank you very much! This video is a gem.

[@sovereignshahid9265]

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.

[@MrChaluliss]

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

[@AishKhan-le7xq]

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

[@ChrisStaecker]

Yes I remember- you made me tea, right? Good stuff. I hope you're doing well-

[@InsideInterpreting]

Surprisingly similar to my, really applied field. Although, we often have the added complication of data gathering, getting site access permissions, analysing the data, realising that theory sucks, and so on.

[@dhickey5919]

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.

[@asifmahmud5646]

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

[@subjectiveobjectiveness5827]

This is amazing thanks. It made my day actually.

[@rossimarti]

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.

[@AhmedMahmoud-km6zd]

then this is the case when when you are a confident idiot

[@lattice737]

This was amazing. Thank you so much for sharing

[@MultiWilliam15]

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.

[@ChrisStaecker]

Yes- (discrete) cubical homology is very important in digital topology!

[@radderek007]

Well done. Congratulations. Thanks for sharing.

[@Eldriitch]

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

[@sitrakaforler8696]

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

[@azertyazerty2763]

Thank you for sharing. Congratulations 🎉.