11 ms·

Emily Riehl is rewriting the foundations of higher category theory

235 points by guerrilla 6y ago

masterofnone1 6y ago
Definitely a great article and the math part was incredibly interesting. At the same time, I had a bit of a nagging fear by this line - > As a semi-androgynous queer woman, I think that I kind of fit in in the mathematics community better than I would if I were a cis, straight female. I think it also means I’m less likely to get hit on, which is a horrible thing that has happened to a lot of young women in fields where there aren’t enough women. Obviously without defining "hit on", I do not want to draw too many conclusions. But as a guy, it makes me quite scared that just asking a someone out for a coffee (which I do to people regardless of gender / sex), might get construed as "hitting on" and a horrible thing. All due respect to the people who have been subjected to sexually predatory behavior though. Would like to hear others opinion on the same.
- dundarious 6y ago
  Just asking if they’d like to go for a coffee and a chat is not intrinsically “hitting on” someone. Obviously tone and context can change everything, but there is no need to be paranoid in general.
  - masterofnone1 6y ago
    I agree, in the context of the article it means something more sinister than just coffee. But regardless, does not leave me with some fear. Thanks for your reply!
  - generationP 6y ago
    > might get construed as > is not intrinsically Your post does not contradict the parent. For better or worse, any type of interaction (professional or not) is occasionally used as a side channel for romantic interests, and so risks getting misinterpreted as one. Cyber-optimist hopes that online dating platforms will pull this ever-present shadow out of everyday socialization, or at least de-mine the workplace, have proven futile; enough people want the ambiguity. The only reasonable option is to grow a thicker skin and learn saying no and laughing it off.
    - munk-a 6y ago
      I've thought on this a lot in the past and the only thing I have hope of addressing it is making any sort of personal/professional relationship spill overs societally verbotten. When folks are at work they intend to work and making any assumption against that line is just going to lead to pain. I really like the team I work with, but I don't ever want them to mix with the group I socialize with solely due to the fact that while at work I want to work.
      - generationP 6y ago
        You want to avoid even social (not just romantical) mixing? Sorry, but I don't think this is viable with the workers I know (including myself). It is in head-on contradiction with the "do what you love" maxim that most people in my generation are trying to follow. We aren't robots and we don't want to live two completely disjoint lives (or, rather, when we do, we have internet forums, video games and what not for that). In order to have a job where I could completely dissociate from my coworkers, I'd need to find a second skill at which I'm good enough to find employment yet don't care enough about to let it bleed into my life. People are struggling enough with building one skill... There is probably some good middle ground to be found (how far should my job be from my interests to avoid crossing the streams too much yet allow me to keep it? how much should I let my colleagues into my life?), but no one seems to have invested much in finding it.
        munk-a 6y ago
        There are some people who lean this way and that's fine - there's nothing wrong with it - but there are other people who don't. This will tend to follow an age distinction (with older folks being less interested in having more personal/professional crossover) but I strongly disagree with it being generational. Your team at work will change over time and new people will join and leave, as you are forced to reconcile changes of employment with the destruction of your social circle I think you'll find that it's easier to move to keeping the two separate. Having children and a strong life partner can also contribute to this - there are a lot of relationships you care deeply about outside of the workplace and you don't want your time at work to be complicated by drama from the fact that you don't value your relationships with your coworker over that of your partner. Social events at work can be fun and build a stronger team, but viewing your coworkers as your primary social circle probably isn't a healthy long term choice since at some point that relationship will be severed (hope that you don't have to fire a bestie) and someone will be left in an emotional lurch without a shoulder to cry on. I've found it quite helpful to be able to empathize with coworkers and chat about what's going on with work bits in a more safe environment but going into work hoping to find good relationships (social or romantic) is placing a large burden on those you're working with and can end pretty terribly. I'd also point out that strong social bonds are a reciprocal thing and that while you may be entering the workplace hoping to form those bonds your coworkers may not and the visible existence of cliques in work that exclude some employees that may simply be uninterested in such social activity can lead just as easily to drama in the workplace.
- loopercal 6y ago
  I'm not sure of your point. You're scared of being seen as a predator while women are scared of being preyed upon? So wouldn't you want to try and make spaces as safe as possible so that women wouldn't have to be afraid?
  - letmevoteplease 6y ago
    Translating "hit on" as "prey on" might be a sign that you have an unhealthy view of human relationships.
    - loopercal 6y ago
      >I think it also means I’m less likely to get hit on, which is a horrible thing that has happened to a lot of young women in fields where there aren’t enough women Do you think my framing is inaccurate given what she said? How would you describe the negative association with being hit on in the quote above? >Translating "hit on" as "prey on" might be a sign that you have an unhealthy view of human relationships. Seeing someone cute at a wedding and making a pass is a far cry from what's been happening in academia for decades where power dynamics are often obvious. There's a reason why very few people would have a problem being (tastefully) hit on in a social situation and why people complain about it happening in a professional situation.
- morty_s 6y ago
  I think there’s a saying, “when in doubt, don’t” or something like that, but seriously As a guy I kind of get where you’re coming from. Sort of. I think being “scared” is a bit much (or can at least be portrayed as the “wrong” connotation to those that care). The way I’d phrase this is, “I want to respect people’s boundaries and certain situations can be trickier to navigate than others and I’d rather not mess it up.” You can’t account for how someone else will perceive your actions/intentions. In fact, they could probably vary (ie what if someone is looking to be hit on on Tuesday but not Wednesday? What if a person thinks “everyone hits on them”). For me, I try to treat everyone with respect. Maybe I want to talk more about something, but the other person doesn’t—I’m aware this could be the case so I always try to leave/create/make space for them (ie always provide a way out of the convo for the other person). I also try to ask myself if “grabbing a coffee” over some conversation is necessary. Interesting people have a ton of people wanting to grab coffee, so maybe a group thing would be better. I also try to consider the persons time (male or female); of course I’d love to steal some time from them or make a professional connection, but you can’t always get what you want.
- dang 6y ago
  This is a generic tangent veering into outright offtopicness. We try to avoid generic tangents in HN threads because such discussions are more or less all the same, and replacing an interesting specific discussion with a repetitive generic one is a bad trade. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=generic%20discussion%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor... That goes 10x when the topic is an ideological one. It's clear you weren't starting an ideological flamewar on purpose but that's what generic ideological tangents lead to. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=generic%20ideolog%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor... The best way to avoid this is to stay grounded in the specifics of the article, especially the ones which have the richest diffs from past repetitive discussion. https://hn.algolia.com/?dateRange=all&page=0&prefix=false&sort=byDate&type=comment&query=diffs%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=false&so...
  - masterofnone1 6y ago
    Apologies. New to HN and I understand this comment did not add to the discussion. Thank you for hiding it and I will try to keep the rules in mind.
    - dang 6y ago
      Appreciated!
- whowe1 6y ago
  I don't think asking someone for coffee is really what she means by "getting hit on"...
mkw5053 6y ago
I went through her book "Category Theory in Context" a few years ago and loved it! It's a great introduction to the field.
- breck 6y ago
  Thanks for the tip! Looks like she put the PDF of the book up here: https://math.jhu.edu/~eriehl/context.pdf https://math.jhu.edu/~eriehl/context.pdf
  - guerrilla 6y ago
    From the same page: > The Mathemagician’s Axiom of Textbook Prerequisites: Let M be the minimum actual prerequisites for an average student being able to read and understand a given presentation of a subject in a mathematics textbook. Let A be the author’s stated prerequisites. Then usually: A <<<<<<< M > ... My intended audience might be described as peri-graduate students, ranging from advanced mathematics undergraduates, to graduate students, to perhaps even research mathematicians in other disciplines.
    - einpoklum 6y ago
      So, you're saying a well-read Ph.D. in abstract math is the pre-requisite for reading that book?
      - tooltower 6y ago
        Regardless of your level, just remember to set your pacing expectations. It's perfectly okay if you are going slow, it's really information-dense. I have no background in abstract math. It took me three days to make it through the first paragraph. I'd still recommend it.
      - howling 6y ago
        I think the prerequisite for "Category Theory in Context" is a grasp of basic category theory ((co-)limits, Yoneda lemma, adjoint functor theorems, etc). You should also have some interest in an abstract maths field that requires all these category theory machinery. So a graduate student in abstract maths sounds about right.
munk-a 6y ago
I can really identify with finding Ian Malcolm as inspirational for the positive sides of science. In Jurassic Park the contrast between the do-er scientists (those engineering the dinosaurs) and the think-er scientists (the more abstract theoretical scientist) was pretty starkly and, now that I've been working for a while, correctly portrayed in exposing the motivations those two classes of folks will tend to be working. If science is a career to acquire cash then it's quite easy to get compromised into focusing on the wrong motivations even if your intentions are quite pure - abstract fields tend to be rather "useless" and thus the same influencing power and money isn't available leading those folks to have a much clearer ability to ethically reason about problems. When you've got co-workers depending on a project going forward to keep a roof over their heads it's a lot easier to compromise morals.
generationP 6y ago
> I’m not sure whether Lurie realized that it was possible to give rigorous model-independent proofs laying the foundations of infinity category theory. Part of the reason that Dom and I are able to establish something along the lines that I suspect Lurie would have wanted is that we were coming along later. There is also a sociological component to the history. Lurie was forced by the community to choose a specific model to prove theorems about infinity categories, because the ideas were so new, and people didn’t believe the proofs otherwise. Short version: Even Lurie wasn't ready to generalize from one example :) Nothing to be ashamed of in any other part of mathematics, I'd say.
amyjess 6y ago
> I think there’s more stigma attached to femininity in mathematics than femaleness necessarily. As a semi-androgynous queer woman, I think that I kind of fit in in the mathematics community better than I would if I were a cis, straight female. For anyone who would like to read more on the subject, I'd recommend the works of Julia Serano. She's written extensively about how feminine women are mistreated in academia, even by other feminists and queer women; her most prominent book is Whipping Girl: A Transsexual Woman on Sexism and the Scapegoating of Femininity, but she also has a number of other books and essays on the subject. She's also coined the term "femmephobia" to refer to the phenomenon.
- munk-a 6y ago
  My sister-in-law went through an odd ostracization when trying to get tenure in academia. She and my brother had decided to have children while she pursued her tenure and she ended up getting a lot of friction out of older women in the department who had been forced, when they entered academia, to make a hard choice between being a mother and being a professor. There are a lot of really strange social dynamics that women can get hit by in the workplace and that one was certainly new to me.
morty_s 6y ago
I love category theory. I found out about it through Haskell and as it turns out it is a branch of mathematics that I feel I’ve been missing my whole life. Since taking an interest I’ve worked through a couple books on the topic and have listened to a ton of talks/interviews Emily Riehl has given (as well as others). I really enjoyed her talk at lambda world, “A categorical view of computational effects” (both the content and audio/video quality of this talk are very good!) Stoked to see this article on HN! I can’t tell if category theory is becoming more popular or if I’m just living in a algorithmically curated/tailored world.
- jamiek88 6y ago
  What was the number one thing about category theory that changed your perspective if you don’t mind me asking? You seem very enthusiastic and I’d like to share that enthusiasm one day.
  - bopbeepboop 6y ago
    Not the person you’re asking, but the “aha” moment for me was connecting whiteboard diagrams with type theory. Whiteboard diagrams work because they’re a categorical diagram related to the semantics of the program I’m trying to write. In the sense that CT and TT are “equivalent”, your whiteboard diagrams are your program.
  - type_enthusiast 6y ago
    For me, it was realizing that category theory is the mathematical language of abstraction – almost literally the "principle of least power" in math – and those abstractions often connect to programming abstractions. Even if you're not using words like "Functor" or "Monad" to describe them! And it can be useful to think of them more abstractly than they actually are, even if you're not going to use them that way (or even talk about them that way in your code). Just making some "ridiculously abstract" connections can help provide a missing piece of architecture, even if you keep the math story to yourself (which you likely should). So it can (potentially?) be useful to model various things in terms of what they mean "at the most abstract level", and then find ways to capture chunks of that into various architectural abstractions that make sense without category theory (kind of like a Karnaugh map, in a sense). Sorry if that seems like a lot of "purple prose" or self-important... it really isn't. I think it's the same thing that a lot of people mean when they say "I don't use Haskell but learning it made me a better programmer." I don't use abstract algebra, but learning it made me a better programmer (those statements might even be homomorphic, depending on the Haskell involved)
deleted 6y ago
[deleted]
est 6y ago
The article mentioned a mathoverflow question. I was curious to see if it got closed, so I clicked the link https://mathoverflow.net/questions/43690/whats-a-mathematician-to-do https://mathoverflow.net/questions/43690/whats-a-mathematici... Yes, it's closed
speedbird 6y ago
"the obligation mathematicians have to address the social justice issues of the moment" Huh?
- Grustaf 6y ago
  I was once reading a very good Russian book about the Old Church Slavonic language, when it suddenly started praising the glorious achievements of Lenin or something along those lines. It turns out that all books, no matter how unrelated they were in subject matter, were obliged to glorify the Soviet ideology. Some thing don't change.
  - meepmorp 6y ago
    Are you saying she’s Lenin in disguise? She looks amazingly well for being a dead 150 year old man. Oh, wait, no. You were just dismissing her opinions out of hand by likening her to the founder of an oppressive state.
    - Grustaf 6y ago
      No, in my analogy she would be the author of the grammar book that praises Lenin. Though I haven't read her books so I don't know how political they actually are, I just replied to the comment about politicising mathematics.
      - meepmorp 6y ago
        But the politics she’s talking about have always been in mathematics (and other areas of academia), even if that’s not apparent to people who aren’t negatively impacted by them.
        Grustaf 6y ago
        I’ve read countless math textbooks from introductory to PhD level, from a wide timespan, and never once come across any hint of politics. So no, you are simply wrong.
wrnr 6y ago
I never seem to get CT or what other people get from it. If you told me there is such a thing as geometric algebra where you have a language to talk about multidimensional spaces and that to solve certain practical problems it worth the effort to ask the question if there might be a space where the answer to that problem is trivial. CT on the other had always struck me as a long list of if expressions with if expressions inside at infinitum.

235 points by guerrilla 6y ago

Definitely a great article and the math part was incredibly interesting. At the same time, I had a bit of a nagging fear by this line - > As a semi-androgynous queer woman, I think that I kind of fit in in the mathematics community better than I would if I were a cis, straight female. I think it also means I’m less likely to get hit on, which is a horrible thing that has happened to a lot of young women in fields where there aren’t enough women. Obviously without defining "hit on", I do not want to draw too many conclusions. But as a guy, it makes me quite scared that just asking a someone out for a coffee (which I do to people regardless of gender / sex), might get construed as "hitting on" and a horrible thing. All due respect to the people who have been subjected to sexually predatory behavior though. Would like to hear others opinion on the same.

dundarious 6y ago
Just asking if they’d like to go for a coffee and a chat is not intrinsically “hitting on” someone. Obviously tone and context can change everything, but there is no need to be paranoid in general.
- masterofnone1 6y ago
  I agree, in the context of the article it means something more sinister than just coffee. But regardless, does not leave me with some fear. Thanks for your reply!
- generationP 6y ago
  > might get construed as > is not intrinsically Your post does not contradict the parent. For better or worse, any type of interaction (professional or not) is occasionally used as a side channel for romantic interests, and so risks getting misinterpreted as one. Cyber-optimist hopes that online dating platforms will pull this ever-present shadow out of everyday socialization, or at least de-mine the workplace, have proven futile; enough people want the ambiguity. The only reasonable option is to grow a thicker skin and learn saying no and laughing it off.
  - munk-a 6y ago
    I've thought on this a lot in the past and the only thing I have hope of addressing it is making any sort of personal/professional relationship spill overs societally verbotten. When folks are at work they intend to work and making any assumption against that line is just going to lead to pain. I really like the team I work with, but I don't ever want them to mix with the group I socialize with solely due to the fact that while at work I want to work.
    - generationP 6y ago
      You want to avoid even social (not just romantical) mixing? Sorry, but I don't think this is viable with the workers I know (including myself). It is in head-on contradiction with the "do what you love" maxim that most people in my generation are trying to follow. We aren't robots and we don't want to live two completely disjoint lives (or, rather, when we do, we have internet forums, video games and what not for that). In order to have a job where I could completely dissociate from my coworkers, I'd need to find a second skill at which I'm good enough to find employment yet don't care enough about to let it bleed into my life. People are struggling enough with building one skill... There is probably some good middle ground to be found (how far should my job be from my interests to avoid crossing the streams too much yet allow me to keep it? how much should I let my colleagues into my life?), but no one seems to have invested much in finding it.
      - munk-a 6y ago
        There are some people who lean this way and that's fine - there's nothing wrong with it - but there are other people who don't. This will tend to follow an age distinction (with older folks being less interested in having more personal/professional crossover) but I strongly disagree with it being generational. Your team at work will change over time and new people will join and leave, as you are forced to reconcile changes of employment with the destruction of your social circle I think you'll find that it's easier to move to keeping the two separate. Having children and a strong life partner can also contribute to this - there are a lot of relationships you care deeply about outside of the workplace and you don't want your time at work to be complicated by drama from the fact that you don't value your relationships with your coworker over that of your partner. Social events at work can be fun and build a stronger team, but viewing your coworkers as your primary social circle probably isn't a healthy long term choice since at some point that relationship will be severed (hope that you don't have to fire a bestie) and someone will be left in an emotional lurch without a shoulder to cry on. I've found it quite helpful to be able to empathize with coworkers and chat about what's going on with work bits in a more safe environment but going into work hoping to find good relationships (social or romantic) is placing a large burden on those you're working with and can end pretty terribly. I'd also point out that strong social bonds are a reciprocal thing and that while you may be entering the workplace hoping to form those bonds your coworkers may not and the visible existence of cliques in work that exclude some employees that may simply be uninterested in such social activity can lead just as easily to drama in the workplace.
loopercal 6y ago
I'm not sure of your point. You're scared of being seen as a predator while women are scared of being preyed upon? So wouldn't you want to try and make spaces as safe as possible so that women wouldn't have to be afraid?
- letmevoteplease 6y ago
  Translating "hit on" as "prey on" might be a sign that you have an unhealthy view of human relationships.
  - loopercal 6y ago
    >I think it also means I’m less likely to get hit on, which is a horrible thing that has happened to a lot of young women in fields where there aren’t enough women Do you think my framing is inaccurate given what she said? How would you describe the negative association with being hit on in the quote above? >Translating "hit on" as "prey on" might be a sign that you have an unhealthy view of human relationships. Seeing someone cute at a wedding and making a pass is a far cry from what's been happening in academia for decades where power dynamics are often obvious. There's a reason why very few people would have a problem being (tastefully) hit on in a social situation and why people complain about it happening in a professional situation.
morty_s 6y ago
I think there’s a saying, “when in doubt, don’t” or something like that, but seriously As a guy I kind of get where you’re coming from. Sort of. I think being “scared” is a bit much (or can at least be portrayed as the “wrong” connotation to those that care). The way I’d phrase this is, “I want to respect people’s boundaries and certain situations can be trickier to navigate than others and I’d rather not mess it up.” You can’t account for how someone else will perceive your actions/intentions. In fact, they could probably vary (ie what if someone is looking to be hit on on Tuesday but not Wednesday? What if a person thinks “everyone hits on them”). For me, I try to treat everyone with respect. Maybe I want to talk more about something, but the other person doesn’t—I’m aware this could be the case so I always try to leave/create/make space for them (ie always provide a way out of the convo for the other person). I also try to ask myself if “grabbing a coffee” over some conversation is necessary. Interesting people have a ton of people wanting to grab coffee, so maybe a group thing would be better. I also try to consider the persons time (male or female); of course I’d love to steal some time from them or make a professional connection, but you can’t always get what you want.
dang 6y ago
This is a generic tangent veering into outright offtopicness. We try to avoid generic tangents in HN threads because such discussions are more or less all the same, and replacing an interesting specific discussion with a repetitive generic one is a bad trade. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=generic%20discussion%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor... That goes 10x when the topic is an ideological one. It's clear you weren't starting an ideological flamewar on purpose but that's what generic ideological tangents lead to. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=generic%20ideolog%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor... The best way to avoid this is to stay grounded in the specifics of the article, especially the ones which have the richest diffs from past repetitive discussion. https://hn.algolia.com/?dateRange=all&page=0&prefix=false&sort=byDate&type=comment&query=diffs%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=false&so...
- masterofnone1 6y ago
  Apologies. New to HN and I understand this comment did not add to the discussion. Thank you for hiding it and I will try to keep the rules in mind.
  - dang 6y ago
    Appreciated!
whowe1 6y ago
I don't think asking someone for coffee is really what she means by "getting hit on"...

mkw5053 6y ago

I went through her book "Category Theory in Context" a few years ago and loved it! It's a great introduction to the field.

breck 6y ago
Thanks for the tip! Looks like she put the PDF of the book up here: https://math.jhu.edu/~eriehl/context.pdf https://math.jhu.edu/~eriehl/context.pdf
- guerrilla 6y ago
  From the same page: > The Mathemagician’s Axiom of Textbook Prerequisites: Let M be the minimum actual prerequisites for an average student being able to read and understand a given presentation of a subject in a mathematics textbook. Let A be the author’s stated prerequisites. Then usually: A <<<<<<< M > ... My intended audience might be described as peri-graduate students, ranging from advanced mathematics undergraduates, to graduate students, to perhaps even research mathematicians in other disciplines.
  - einpoklum 6y ago
    So, you're saying a well-read Ph.D. in abstract math is the pre-requisite for reading that book?
    - tooltower 6y ago
      Regardless of your level, just remember to set your pacing expectations. It's perfectly okay if you are going slow, it's really information-dense. I have no background in abstract math. It took me three days to make it through the first paragraph. I'd still recommend it.
    - howling 6y ago
      I think the prerequisite for "Category Theory in Context" is a grasp of basic category theory ((co-)limits, Yoneda lemma, adjoint functor theorems, etc). You should also have some interest in an abstract maths field that requires all these category theory machinery. So a graduate student in abstract maths sounds about right.

munk-a 6y ago

I can really identify with finding Ian Malcolm as inspirational for the positive sides of science. In Jurassic Park the contrast between the do-er scientists (those engineering the dinosaurs) and the think-er scientists (the more abstract theoretical scientist) was pretty starkly and, now that I've been working for a while, correctly portrayed in exposing the motivations those two classes of folks will tend to be working. If science is a career to acquire cash then it's quite easy to get compromised into focusing on the wrong motivations even if your intentions are quite pure - abstract fields tend to be rather "useless" and thus the same influencing power and money isn't available leading those folks to have a much clearer ability to ethically reason about problems. When you've got co-workers depending on a project going forward to keep a roof over their heads it's a lot easier to compromise morals.

generationP 6y ago

> I’m not sure whether Lurie realized that it was possible to give rigorous model-independent proofs laying the foundations of infinity category theory. Part of the reason that Dom and I are able to establish something along the lines that I suspect Lurie would have wanted is that we were coming along later. There is also a sociological component to the history. Lurie was forced by the community to choose a specific model to prove theorems about infinity categories, because the ideas were so new, and people didn’t believe the proofs otherwise. Short version: Even Lurie wasn't ready to generalize from one example :) Nothing to be ashamed of in any other part of mathematics, I'd say.

amyjess 6y ago

> I think there’s more stigma attached to femininity in mathematics than femaleness necessarily. As a semi-androgynous queer woman, I think that I kind of fit in in the mathematics community better than I would if I were a cis, straight female. For anyone who would like to read more on the subject, I'd recommend the works of Julia Serano. She's written extensively about how feminine women are mistreated in academia, even by other feminists and queer women; her most prominent book is Whipping Girl: A Transsexual Woman on Sexism and the Scapegoating of Femininity, but she also has a number of other books and essays on the subject. She's also coined the term "femmephobia" to refer to the phenomenon.

munk-a 6y ago
My sister-in-law went through an odd ostracization when trying to get tenure in academia. She and my brother had decided to have children while she pursued her tenure and she ended up getting a lot of friction out of older women in the department who had been forced, when they entered academia, to make a hard choice between being a mother and being a professor. There are a lot of really strange social dynamics that women can get hit by in the workplace and that one was certainly new to me.

morty_s 6y ago

I love category theory. I found out about it through Haskell and as it turns out it is a branch of mathematics that I feel I’ve been missing my whole life. Since taking an interest I’ve worked through a couple books on the topic and have listened to a ton of talks/interviews Emily Riehl has given (as well as others). I really enjoyed her talk at lambda world, “A categorical view of computational effects” (both the content and audio/video quality of this talk are very good!) Stoked to see this article on HN! I can’t tell if category theory is becoming more popular or if I’m just living in a algorithmically curated/tailored world.

jamiek88 6y ago
What was the number one thing about category theory that changed your perspective if you don’t mind me asking? You seem very enthusiastic and I’d like to share that enthusiasm one day.
- bopbeepboop 6y ago
  Not the person you’re asking, but the “aha” moment for me was connecting whiteboard diagrams with type theory. Whiteboard diagrams work because they’re a categorical diagram related to the semantics of the program I’m trying to write. In the sense that CT and TT are “equivalent”, your whiteboard diagrams are your program.
- type_enthusiast 6y ago
  For me, it was realizing that category theory is the mathematical language of abstraction – almost literally the "principle of least power" in math – and those abstractions often connect to programming abstractions. Even if you're not using words like "Functor" or "Monad" to describe them! And it can be useful to think of them more abstractly than they actually are, even if you're not going to use them that way (or even talk about them that way in your code). Just making some "ridiculously abstract" connections can help provide a missing piece of architecture, even if you keep the math story to yourself (which you likely should). So it can (potentially?) be useful to model various things in terms of what they mean "at the most abstract level", and then find ways to capture chunks of that into various architectural abstractions that make sense without category theory (kind of like a Karnaugh map, in a sense). Sorry if that seems like a lot of "purple prose" or self-important... it really isn't. I think it's the same thing that a lot of people mean when they say "I don't use Haskell but learning it made me a better programmer." I don't use abstract algebra, but learning it made me a better programmer (those statements might even be homomorphic, depending on the Haskell involved)

deleted 6y ago

[deleted]

est 6y ago

The article mentioned a mathoverflow question. I was curious to see if it got closed, so I clicked the link https://mathoverflow.net/questions/43690/whats-a-mathematician-to-do https://mathoverflow.net/questions/43690/whats-a-mathematici... Yes, it's closed

speedbird 6y ago

"the obligation mathematicians have to address the social justice issues of the moment" Huh?

Grustaf 6y ago
I was once reading a very good Russian book about the Old Church Slavonic language, when it suddenly started praising the glorious achievements of Lenin or something along those lines. It turns out that all books, no matter how unrelated they were in subject matter, were obliged to glorify the Soviet ideology. Some thing don't change.
- meepmorp 6y ago
  Are you saying she’s Lenin in disguise? She looks amazingly well for being a dead 150 year old man. Oh, wait, no. You were just dismissing her opinions out of hand by likening her to the founder of an oppressive state.
  - Grustaf 6y ago
    No, in my analogy she would be the author of the grammar book that praises Lenin. Though I haven't read her books so I don't know how political they actually are, I just replied to the comment about politicising mathematics.
    - meepmorp 6y ago
      But the politics she’s talking about have always been in mathematics (and other areas of academia), even if that’s not apparent to people who aren’t negatively impacted by them.
      - Grustaf 6y ago
        I’ve read countless math textbooks from introductory to PhD level, from a wide timespan, and never once come across any hint of politics. So no, you are simply wrong.

wrnr 6y ago

I never seem to get CT or what other people get from it. If you told me there is such a thing as geometric algebra where you have a language to talk about multidimensional spaces and that to solve certain practical problems it worth the effort to ask the question if there might be a space where the answer to that problem is trivial. CT on the other had always struck me as a long list of if expressions with if expressions inside at infinitum.