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What's the point of this comment? It's useful to some people therefore people study it. Why assume it needs to be useful to all mathematicians? It is useful fo

What's the point of this comment? It's useful to some people therefore people study it. Why assume it needs to be useful to all mathematicians? It is useful for my own work, and thus I study it, why isn't this as simple as that?

da39a3ee 6y ago
What an extraordinary comment. You seem to be missing various points: - Mathematics is a very large field. - For beginners, it is necessary to have wiser people than yourself put up some signposts. I found the comment you're referring to very illuminating. I'm not naively assuming the author's view is the only one, or "correct", but s/he certainly like they have some familiarity with graduate/research level mathematics in relevant areas. So it was very helpful to see, at least from the point of view of some mathematicians, that this is not considered an important area. I was left wondering whether the author of that comment understood the importance of this stuff in computer science (i.e. in academic approaches to programming languages, might be the right term, I don't know, I'm pretty ignorant of these areas myself), or whether they were only able to criticize it from the point of view of pure mathematics.
- oisdk 6y ago
  > s/he certainly like they have some familiarity with graduate/research level mathematics in relevant areas You should not assume this about any anonymous person on the internet.
spekcular 6y ago
I don't know what your work is, but for the vast majority of people learning HoTT is a complete waste of time. There are many intelligent and curious people reading HN, who might be tempted to spend time understanding it because its somewhat frequent appearance here gives the (false) impression that it plays some important role in modern mathematics. I regret spending the (large) amount of time I did learning what it is about, only to realize that's not much actual content there, and I would hope my post saves other people that trouble. There is a lot of far more interesting, elegant, and useful mathematics out there, imo.
- oisdk 6y ago
  > I don't know what your work is, but for the vast majority of people learning HoTT is a complete waste of time. This is a bizarre thing to say. Learning any mathematics is a complete waste of time. > gives the (false) impression that it plays some important role in modern mathematics. What are you talking about? HoTT is broadly regarded as an exciting and important new area of mathematics; your view is absolutely the minority view. I mean I don't think I'm going to be able to convince you otherwise if you genuinely think that there's "not much content" in HoTT, but there are loads of well-regarded and prominent mathematicians who hold the opposite view to yours.
  - spekcular 6y ago
    Learning mathematics had been incredibly useful to me. If that hasn't been the case for you, I'm sorry. Your claim that HoTT is "broadly regarded as an exciting and important new area of mathematics" is simply wrong. I suggest talking to a wider variety of mathematicians. In particular, concerning "well-regarded and prominent mathematicians," Steve Simpson and Harvey Friedman are on record on the Foundations of Mathematics mailing list saying, essentially, that HoTT is a waste of time [0]. The other set theory experts I know agree with them but haven't said so publicly. My impression is that this is a fairly common view in the set theory and foundations community. Further, Jacob Lurie, who is perhaps the most talented mathematician currently working in higher category theory, has also written he doesn't think highly of it [1]. [0] I can provide links if it you want, but if you search the archive these arguments are easy to find. [1] View the comments on this blog post: https://mathematicswithoutapologies.wordpress.com/2015/05/13/univalent-foundations-no-comment/ https://mathematicswithoutapologies.wordpress.com/2015/05/13...
    - oisdk 6y ago
      > Learning mathematics had been incredibly useful to me. You have missed my point. We generally don't study only the "useful" things; if we did most of the most important mathematics we have today would have gone unstudied. > Your claim that HoTT is "broadly regarded as an exciting and important new area of mathematics" is simply wrong. According to whom? You? You're making an argument about consensus regarding the importance of a given area, but I have seen nothing to indicate that the consensus among mathematicians is in line with your opinion. > Steve Simpson and Harvey Friedman They are in the minority. Again, if you're arguing about consensus you can't just point to one or two individuals and say "look! They agree with me!" For goodness' sake, the thread your referring to is well-known partially because it was controversial. > Jacob Lurie [...] doesn't think highly of it The content of Lurie's comment and yours are quite different.

da39a3ee 6y ago

What an extraordinary comment. You seem to be missing various points: - Mathematics is a very large field. - For beginners, it is necessary to have wiser people than yourself put up some signposts. I found the comment you're referring to very illuminating. I'm not naively assuming the author's view is the only one, or "correct", but s/he certainly like they have some familiarity with graduate/research level mathematics in relevant areas. So it was very helpful to see, at least from the point of view of some mathematicians, that this is not considered an important area. I was left wondering whether the author of that comment understood the importance of this stuff in computer science (i.e. in academic approaches to programming languages, might be the right term, I don't know, I'm pretty ignorant of these areas myself), or whether they were only able to criticize it from the point of view of pure mathematics.

oisdk 6y ago
> s/he certainly like they have some familiarity with graduate/research level mathematics in relevant areas You should not assume this about any anonymous person on the internet.

spekcular 6y ago

I don't know what your work is, but for the vast majority of people learning HoTT is a complete waste of time. There are many intelligent and curious people reading HN, who might be tempted to spend time understanding it because its somewhat frequent appearance here gives the (false) impression that it plays some important role in modern mathematics. I regret spending the (large) amount of time I did learning what it is about, only to realize that's not much actual content there, and I would hope my post saves other people that trouble. There is a lot of far more interesting, elegant, and useful mathematics out there, imo.

oisdk 6y ago
> I don't know what your work is, but for the vast majority of people learning HoTT is a complete waste of time. This is a bizarre thing to say. Learning any mathematics is a complete waste of time. > gives the (false) impression that it plays some important role in modern mathematics. What are you talking about? HoTT is broadly regarded as an exciting and important new area of mathematics; your view is absolutely the minority view. I mean I don't think I'm going to be able to convince you otherwise if you genuinely think that there's "not much content" in HoTT, but there are loads of well-regarded and prominent mathematicians who hold the opposite view to yours.
- spekcular 6y ago
  Learning mathematics had been incredibly useful to me. If that hasn't been the case for you, I'm sorry. Your claim that HoTT is "broadly regarded as an exciting and important new area of mathematics" is simply wrong. I suggest talking to a wider variety of mathematicians. In particular, concerning "well-regarded and prominent mathematicians," Steve Simpson and Harvey Friedman are on record on the Foundations of Mathematics mailing list saying, essentially, that HoTT is a waste of time [0]. The other set theory experts I know agree with them but haven't said so publicly. My impression is that this is a fairly common view in the set theory and foundations community. Further, Jacob Lurie, who is perhaps the most talented mathematician currently working in higher category theory, has also written he doesn't think highly of it [1]. [0] I can provide links if it you want, but if you search the archive these arguments are easy to find. [1] View the comments on this blog post: https://mathematicswithoutapologies.wordpress.com/2015/05/13/univalent-foundations-no-comment/ https://mathematicswithoutapologies.wordpress.com/2015/05/13...
  - oisdk 6y ago
    > Learning mathematics had been incredibly useful to me. You have missed my point. We generally don't study only the "useful" things; if we did most of the most important mathematics we have today would have gone unstudied. > Your claim that HoTT is "broadly regarded as an exciting and important new area of mathematics" is simply wrong. According to whom? You? You're making an argument about consensus regarding the importance of a given area, but I have seen nothing to indicate that the consensus among mathematicians is in line with your opinion. > Steve Simpson and Harvey Friedman They are in the minority. Again, if you're arguing about consensus you can't just point to one or two individuals and say "look! They agree with me!" For goodness' sake, the thread your referring to is well-known partially because it was controversial. > Jacob Lurie [...] doesn't think highly of it The content of Lurie's comment and yours are quite different.