You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Daniel Geisler (Dec 16 2024 at 18:36):I just recieved a question from a programmer who loves mathematics and was interested in a quote I made on Hacker News.
A large portion of mathematicians have little coding ability, so I help some amazing people out, learn lots of mathematics and have lots of fun.
I find learning mathematical etiquette to be both important and difficult. I believe this is something typically learned in the process of gaining a Ph.D. in mathematics. I'd love to read anything already written about mathematical etiquette. I'm still giving the question thought and would like to see if others here could contribute their own advice or even direct me to an article covering the subject.
John Baez (Dec 16 2024 at 18:49):I don't think I've ever seen anything about "mathematical etiquette". I can certainly spot violations of it. I imagine a lot of it applies to academia in general, while some is particular to math. But I'd like to read anything anybody has written about it.
I have a page called Advice, which is advice mainly for young mathematicians and physicists - and people who don't know whether they want to go into math or physics. I wrote it a long time ago, and in several different stages where I had different things on my mind. I don't have the energy to improve it now. But anyway, it's not mainly about "etiquette", but it may have some overlap.
Emilio Minichiello (Dec 16 2024 at 22:11):I think there is something really interesting here. I don't know if I would call this mathematical etiquette, but I've had many attempted mathematical conversations with people who were not trained as PhD mathematicians that left me annoyed or frustrated. Now I've certainly done the same to others countless times, but upon reflection, I think there are a couple of really key points that can make mathematical conversations go better. Here are some of my thoughts, I'm curious what other people think.
Tips for talking with a mathematician:
Be as rigorous as possible. Know what mathematical objects you are talking about. Give them letters. My advisor used to drill this into me as a student, we used to go for walks and I would have to explain to him what I had learned just using my voice. This was an incredibly helpful practice for me. I would actually practice saying out loud "Let M be a finite dimensional smooth manifold such that ..." In other words, know how to make a mathematical statement.
Example: "I learned that if you've got a space, then at every point there's an R^n attached to it" versus "I learned that if M is an n-dimensional smooth manifold, then at every point x in M you can define a vector space T_x, called the tangent space at x, defined as ..."
Don't bullshit. If you don't know something, or don't understand it well enough to talk about at a level of rigor, just say that and figure out what common ground of understanding you can find.
Mike Shulman (Dec 16 2024 at 22:27):As a mathematician, I'm probably biased, but I think those are pretty good rules for all human communication (with minor modifications)... (-:
Peva Blanchard (Dec 16 2024 at 22:36):As a minor source of comfort, it's good to remind programmers that mathematical etiquette is way more friendly than computer etiquette (full of screens of deaths and segfaults). :smile:
Peva Blanchard (Dec 16 2024 at 22:50):Daniel Geisler said:
I find learning mathematical etiquette to be both important and difficult.
Do you have specific examples of experiences where mathematical etiquette turned out to be difficult? Maybe people here could then give more tailored advises.
Daniel Geisler (Dec 16 2024 at 23:14):@Peva Blanchard good question, but not so easy to answer. :smile: The statement you quoted was about learning mathematical etiquette more than having difficult experiences. I will say personally that I no longer use forums like mathoverflow because of being flamed so often. It feels like a number of members have a vested interest in burning people down to the ground.
I find the messages about mathematicians passing away often has a common theme. While these people have made significant advances in mathematics, many times their impact as a fine human being is more important.
John Baez (Dec 16 2024 at 23:23):I've hardly ever gotten flamed on MathOverflow, but I don't know if it's because people know me (and therefore like me :grinning_face_with_smiling_eyes:) or because I've spent a lot of time thinking about how to ask questions mathematicians like.
John Baez (Dec 16 2024 at 23:25):I hope it's the latter. On MathOverflow they want questions that are crisp, parse correctly, are phrased in terms of known mathematical concepts, and are not questions whose answers you could easily look up in a textbook. Also, they don't like drama.
Mike Shulman (Dec 16 2024 at 23:36):My experience and hopes on mathoverflow are like yours, John, and while I may be relatively well-known now, I was just a barely minted PhD when it started out. It's possible that different subcommunities of mathematicians behave differently on mathoverflow. I do think there's probably a something else, whether we call it etiquette, culture, or what, that you and I do without thinking about it but that's hard for others to break into. I have had quite negative experiences on other stackexchange sites; perhaps the people there are nastier, but perhaps I just don't know their shibboleths.
Peva Blanchard (Dec 16 2024 at 23:43):In my understanding, Mathoverflow is more for professionals, which would explain the level of scrutiny (and perhaps the flames), whereas Math stack exchange aims at a broader audience.
John Baez (Dec 16 2024 at 23:46):Yes, that's correct - here's how the site describes itself:
MathOverflow is a question and answer site for professional mathematicians. It's built and run by you as part of the Stack Exchange network of Q&A sites. With your help, we're working together to build a library of detailed answers to every question about research level mathematics.
John Baez (Dec 16 2024 at 23:46):I believe the adjectives "professional" and "research level" are supposed to serve as filters: if you don't know how to act like a "professional mathematician" asking a question about "research level mathematics", I think you'll get in trouble there.
John Baez (Dec 16 2024 at 23:49):Math Stack Exchange is very different:
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's built and run by you as part of the Stack Exchange network of Q&A sites. With your help, we're working together to build a library of detailed answers to every question about math.
Now we've got the phrases "at any level" and "every question".
Daniel Geisler (Dec 16 2024 at 23:51):@John Baez What you are talking about is exactly what I mean by mathematical etiquette. Not being able to be a part of mathematics academia, I had fundamental issues with communicating mathematics. That can be very frustrating for a number of mathematicians, but even more importantly it indicates a major avenue of possible growth which I have embraced. Instead of being upset with getting flamed, I should have focused more on understanding what was frustrating the people I was communicating with. I have felt lost in the woods for decades due to my lack of understanding the needs of the people I was dealing with. Having been a moderator of a mathematics forum I would like to provide people with the roadmap that I never had.
David Egolf (Dec 17 2024 at 00:34):I think talking on this zulip helps provide opportunities to learn some mathematical etiquette! At least, I feel that I've learned a lot about how mathematicians communicate from my time here.
John Baez (Dec 17 2024 at 00:48):Can you say anything interesting about what you've learned.... without being rude? :upside_down:
John Baez (Dec 17 2024 at 00:49):I think it would be fun to hear about it. Having been talking to mathematicians all my life (or so it feels), there's probably a lot that I take for granted and don't notice anymore.
I do recall a huge transformation in how you talk here, @David Egolf. You now seem very good at what we might call the "game" of talking about math, which is a very efficient way to uncover a lot of facts through conversation, where two or more people ask each other questions, work on these questions together, keep track of what's being assumed and what's been shown at any stage of the conversation, point out each other's mistakes and clearly admit when they've made mistakes, decide jointly to temporarily give up on some questions because they're too hard, etc.
David Egolf (Dec 17 2024 at 01:17):Sure, I'd be happy to share some things I've learned about mathematical communication! Just now, I scrolled all the way back to the start of my messages on this zulip, and I think that helped spark my memory a bit.
Daniel Geisler (Dec 17 2024 at 01:29):By its innate nature, it is important to have good modeling of communication to master it. That happens here a great deal.
Jean-Baptiste Vienney (Dec 17 2024 at 01:40):John Baez said:
I do recall a huge transformation in how you talk here, David Egolf. You now seem very good at what we might call the "game" of talking about math, which is a very efficient way to uncover a lot of facts through conversation, where two or more people ask each other questions, work on these questions together, keep track of what's being assumed and what's been shown at any stage of the conversation, point out each other's mistakes and clearly admit when they've made mistakes, decide jointly to temporarily give up on some questions because they're too hard, etc.
The way you're describing a mathematical conversation makes me think to the way Socrates wants to discuss with Gorgias in the dialogue Gorgias by Plato. So it must be a good time for me to throw out my favorite extract from this book:
SOCRATES: You, Gorgias, like myself, have had great experience of disputations, and you must have observed, I think, that they do not always terminate in mutual edification, or in the definition by either party of the subjects which they are discussing; but disagreements are apt to arise – somebody says that another has not spoken truly or clearly; and then they get into a passion and begin to quarrel, both parties conceiving that their opponents are arguing from personal feeling only and jealousy of themselves, not from any interest in the question at issue. And sometimes they will go on abusing one another until the company at last are quite vexed at themselves for ever listening to such fellows. Why do I say this? Why, because I cannot help feeling that you are now saying what is not quite consistent or accordant with what you were saying at first about rhetoric. And I am afraid to point this out to you, lest you should think that I have some animosity against you, and that I speak, not for the sake of discovering the truth, but from jealousy of you. Now if you are one of my sort, I should like to cross-examine you, but if not I will let you alone. And what is my sort? you will ask. I am one of those who are very willing to be refuted if I say anything which is not true, and very willing to refute any one else who says what is not true, and quite as ready to be refuted as to refute; for I hold that this is the greater gain of the two, just as the gain is greater of being cured of a very great evil than of curing another. For I imagine that there is no evil which a man can endure so great as an erroneous opinion about the matters of which we are speaking; and if you claim to be one of my sort, let us have the discussion out, but if you would rather have done, no matter;–let us make an end of it.
David Egolf (Dec 17 2024 at 01:49):I'll list below some things I've found helpful in communicating with mathematicians in text format, coming from an engineering background. I've formatted the list as if I was giving advice to my younger self:
David Egolf (Dec 17 2024 at 02:04):Oh - one last thing comes to mind:
Mike Shulman (Dec 17 2024 at 02:11):Wow, that's an impressive list!
Alex Kreitzberg (Dec 17 2024 at 02:57):I'm taking notes from Egolf's list :sweat_smile:.
Regarding mathoverflow vs this Zulip. I want to add the pros here seem to have a very strong grasp on when and why conventions get broken, and often patiently guide an asker "back on track".
If an asker breaks conventions on mathoverflow, something about the structure or culture makes it hard to help the asker communicate better. This seems to be an issue across all the exchanges in my experience.
John Baez (Dec 17 2024 at 03:09):MathOverflow is different because it's not for conversations - it's pretty close to a strict one-question, many-answer format. People can and do leave "comments" to help questioners fix their question, but the whole setup is not aimed at dialogue: free-ranging conversation is discouraged.
Peva Blanchard (Dec 17 2024 at 05:47):I've just noticed that the word "etiquette" could be more revealing than I thought. The word reminds me the rules that governed people's behavior at Versailles, rules that were strongly informed (I guess) by the nobles' ranks and titles.
I don't know about other countries, but in France, mathematics, as it is taught to children from a very young age up to, at least high school, is mostly used to select people. This creates strong feelings of "being too dumb for maths", of not "being worth it", and "being excluded". I find this very sad.
It is true that the craft requires a certain way of talking about it, as very well illustrated by the various lists above. It might be interesting to also present a counter-etiquette, for how members of the math community should behave w.r.t. "outsiders".
Daniel Geisler (Dec 17 2024 at 08:18):Reviewing my earlier writings I see a transformation from self promotion to a neutral point of view that promotes mathematics itself. With this in mind I have rewritten my mathematics website to represent the mathematics community. Even though I am the sole author of the website, I can no longer tell that. I have removed myself from the "equation."
Over time my interest has shifted from developing mathematics to developing mathematicians. I see much of etiquette as not just the intelligence to do mathematics but also the wisdom to interact with people while not expressing any ego. I spent a decade as a monk where I learned about serving others.
@John Baez said
I don't think I've ever seen anything about "mathematical etiquette". I can certainly spot violations of it.
Self knowledge and self mastery can elevate etiquette to the level of art.
Maybe the highest form of etiquette is to demonstrate growth from others effort to advance their understanding.
Morgan Rogers (he/him) (Dec 17 2024 at 11:13):Mike Shulman said:
As a mathematician, I'm probably biased, but I think those are pretty good rules for all human communication (with minor modifications)... (-:
A sandwich S is defined to be perfect if its filling F(S) has properties S1, S2, S3... :rolling_on_the_floor_laughing:
Morgan Rogers (he/him) (Dec 17 2024 at 14:53):I found your points very well thought out @David Egolf, I will be sure to point people to them in future.
Mike Shulman (Dec 17 2024 at 16:06):Those are the sorts of "minor modifications" I meant.