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fosco (Oct 22 2025 at 18:16):https://www.youtube.com/watch?v=P4iiNpkClRU it was a very saddening six minutes. I could spend some time replying in the merit of some of the things that even I see she is getting wrong, but there are other people who already devoted their career to joining category theory and physics, broadly intended. If anyone wants to "rectify names" about this monodimensional, prejudicial take on the mathematics we do, I'm happy to co-sign it.
fosco (Oct 22 2025 at 18:20):There's a general bad taste that this video leaves me with, I see the quality of Sabine's outreach degrading over the years, probably by the month. It is saddening that even someone with a PhD in highly abstract physics can derubricate category theory to some sort of void uuh buuh abstract jargon here's a diagram; and it is worrying that someone with a PhD in physics struggles to understand the meaning of "a complex algebraic variety, plus a closed semi-algebraic region whose interior is a d-manifold"
Kevin Carlson (Oct 22 2025 at 18:49):I didn't find this offensive; to summarize the CT-related part, she observes there was a burst of interest in CT in physics a couple of decades ago but that "nobody" thinks it's going to revolutionize physics anymore. Of course "nobody" is not a strictly accurate descriptor, the existence of Urs disproves the strict negation, but it seems like basically the normal situation that participants in a paradigmatic science predict that any given putative paradigm-breaker won't succeed in breaking the paradigm until it actually does. And the concern that excessive generalization via CT leads to the risk creating a "theory of anything" rather than a "theory of everything" seems like a very legitimate issue we have to grapple with in category-theoretic applications. Note that Sabine didn't put CT on her bullshit-o-meter or anything, and even explicitly agrees that it's useful in certain more abstract areas, such as presumably cohesive linear homotopy type theory.
fosco (Oct 22 2025 at 18:56):Kevin Carlson said:
the concern that excessive generalization via CT leads to the risk creating a "theory of anything" rather than a "theory of everything" seems like a very legitimate issue
this is an issue that has nothing to do with physics; in general, it seems to me people might misinterpret the content of category theory and its role in the mathematics of the past century, mistaking it for "some snake oil that was supposed to solve the problems of physics but in the end didn't"
fosco (Oct 22 2025 at 19:00):I think this attitude is dangerous and prejudicial --especially for someone who listens to this video superficially, in passing (=the totality of people watching youtube); plus, as I said, the bad taste I've been left with after this inclines to think she doesn't get what CT is ultimately about (or wouldn't even when explained), given that she struggles understanding the keywords defining "positive geometry".
Generally, it is bad to let people who ignore what your work is about, but have a stage with followers, take it and talk about your work.
fosco (Oct 22 2025 at 19:02):I concede I am maybe more irked than average by this trope (category theory seen as an ancillary tool to do X, but ultimately not powerful enough to truly tackle hard problems in X). Still, I think it's a sad misrepresentation to hear.
David Michael Roberts (Oct 23 2025 at 00:10):Does she mention Urs' work? I'm not going to watch the video, want to preserve my mental state.
Kevin Carlson (Oct 23 2025 at 00:48):No, she's very vague, really didn't say any more than I paraphrased.
David Michael Roberts (Oct 23 2025 at 01:01):I think that whatever one thinks of his -categorical approach to M-theory qua theory of reality, and how this relates to the quantum computation work, the non-abelian cohomology formalism being (apparently) able to model bits of solid state physics in a conceptually clean way
Kevin Carlson (Oct 23 2025 at 01:09):Yeah, I'm not at all informed about this stuff but I'm sure it's cool, and she doesn't seem to rule out that level of coolness.
Paolo Perrone (Oct 23 2025 at 07:57):I wonder how many people in this community have originally a background in high-energy physics, for sure I'm not the only one.
Paolo Perrone (Oct 23 2025 at 07:57):Product placement aside, I don't think the video is particularly too harsh on category theory. Sure, it clearly shows she doesn't understand it, but that's about it. Her critique was mostly about how it didn't revolutionize physics despite the initial hype. (Hype thanks to which, by the way, I heard about category theory while studying gauge theory, and pretty much never left.)
Paolo Perrone (Oct 23 2025 at 07:58):Personally I think that the main reason why high-energy physics is so stagnant is because the majority of the community, a long time ago, stopped being interested in figuring out what is really going on, and started just 'calculating things'. (Not everyone is like that, thankfully, for example Urs Schreiber is not.)
With this attitude, no amount of fancy math is going to help, not category theory, not positive geometry, not non-commutative geometry, and so on: you just go from 'calculating' to manipulating more abstract symbols and shapes.
Paolo Perrone (Oct 23 2025 at 07:58):I see the same risk all the time in my work on probability: occasionally, just moving the right shapes in a string diagram does solve the problem, but that's not the point of categorical probability to me. After all, also analytic calculations would solve the problem. Category theory's value is to help you understand what's going on by focusing on the core ideas and removing all the pesky details. It's important, while manipulating abstract ideas, not to forget what we are trying to model.
Paolo Perrone (Oct 23 2025 at 07:59):(That, and let's also keep in mind that just because something can be expressed using category theory does not mean that category theory will 'solve' that field. We are not 'solving probability' with Markov categories, nor will probability, or high-energy physics, AI, etc, ever be 'solved' just by adding new mathematics.)
Morgan Rogers (he/him) (Oct 23 2025 at 09:53):It's always frustrating to see CT dismissed as essentially irrelevant, usually because of the popping of a CT hype bubble in some domain of application. I agree with Kevin's summary that she wasn't particularly harsh. What's most frustrating to me (which aligns with fosco's assessment of the degrading quality of Sabine's work) is that it doesn't seem like she made any effort whatsoever to look into whether CT did actually produce meaningful contributions to theoretical physics (such as what David mentioned) before dismissing it...
John Baez (Oct 23 2025 at 13:57):I won't watch the video: I quit paying attention to Hossenfelder when in February this year she did a video called "Academia is Communism," approvingly citing Musk, Marc Andreessen and Peter Thiel saying that universities are enemies of progress - without even mentioning that at the very moment Musk's DOGE team was chopping apart the US government, including the Department of Education. (She could have at least celebrated that fact, if she thought it was a good thing.)
But I wonder why she said there was a burst of interest in category theory in physics 20 years ago but nobody thinks it's going to revolutionize physics anymore.
In fact there's a lot more work on categories in physics right now! Look at a few of these recent papers on fusion 2-categories in quantum physics. This is the kind of thing I was vaguely dreaming about back in the 1990s! It's all come true, but it's being applied to condensed matter physics instead of pie-in-the-sky quantum gravity. Maybe that's why she doesn't know or care about it.
Abstract: We use a 2-categorical version of (de-)equivariantization to classify (3+1)d topological orders with a finite G-symmetry. In particular, we argue that (3+1)d fermionic topological order with G-symmetry correspond to SuperVect-enriched G-crossed braided fusion 2-categories. We then show that the categorical data necessary to define these theories agrees with that arising from a fermionic generalization of the Wang-Wen-Witten construction of bosonic topological theories with G-symmetry saturating an anomaly.
We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is based on defining 2D coproducts through horizontal and vertical maps that satisfy compatibility and associativity conditions, enabling the consistent growth of vector spaces over lattice sites. We present several examples of 2D bialgebras, including group-like and Lie algebra-inspired constructions and a quasi-1D coproduct instance that is applicable to Taft-Hopf algebras and to quantum groups. [...] Our results establish a local and algebraically consistent method to embed quantum group symmetries into higher-dimensional lattice systems, potentially connecting to the emerging theory of fusion 2-categories and categorical symmetries in quantum many-body physics.
We study how the fusion 2-category symmetry of a fermionic (2+1)d QFT can be affected when one allows for stacking with TQFTs to be an equivalence relation for QFTs. Focusing on a simple kind of fermionic fusion 2-category described purely by group theoretical data, our results reveal that by allowing for stacking with as an equivalence relation enables a finite set of inequivalent modifications to the original fusion 2-categorical-symmetry. To put our results in a broader context, we relate the order of the symmetry modifications to the image of a map between groups of minimal nondegenerate extensions, and to the tangential structure set by the initial categorical symmetry on the background manifold for the QFT.
John Baez (Oct 23 2025 at 14:04):The reason I quit talking about this stuff is not because it doesn't work - it's because it's too mainstream to need my advertisements!
Matteo Capucci (he/him) (Oct 25 2025 at 09:16):fosco said:
and it is worrying that someone with a PhD in physics struggles to understand the meaning of "a complex algebraic variety, plus a closed semi-algebraic region whose interior is a d-manifold"
omg it's even worse:
image.png
Matteo Capucci (he/him) (Oct 25 2025 at 09:16):She managed to quote ChatGPT and be racist at the same time, truly a marvelous display of stupidity.
Matteo Capucci (he/him) (Oct 25 2025 at 09:22):On a less serious note, I take issue with the diagram she chose to disparage CT
image.png
Matteo Capucci (he/him) (Oct 25 2025 at 09:23):Very badly typeset and not even that crazy, we should send a join letter with some serious deranged nonsense
Matteo Capucci (he/him) (Oct 25 2025 at 09:26):Also she is criticizing CT on the basis of an extremely shallow understanding of it... which is irksome. 'It's just diagrams with arrows'... how tiring.
Cole Comfort (Oct 25 2025 at 12:44):Matteo Capucci (he/him) said:
Also she is criticizing CT on the basis of an extremely shallow understanding of it... which is irksome. 'It's just diagrams with arrows'... how tiring.
It is really frustrating to hear people disparage things they don't understand. I have heard people talk like this about category theory, and I have also heard category theorists talk about physics, logic and computer science in similar way. Of course some research programmes are inchorent or ill-motivated, but if you don't try to understand and learn, it is usually impossible to tell.
It is my belief that academia incentivises specialization to the detriment of breadth, and often-times a deeper understanding. I can not understand when people seem to be proud that they don't know something because it isn't what they do. Of course we can't know everything, but at least in principle I would like to know as much as possible.
James Deikun (Oct 25 2025 at 15:40):People on Mathstodon have pointed out that comparing things to Chinese is a common idiom in Germany for incomprehensibility, making it the kind of cultural racism we all (to some extent or other) partake of, rather than conscious racial disparagement/othering, and that she was probably applying this to GPT5's attempt at an explanation rather than the concept since she continued trying to understand positive geometry and ultimately gave a 1/10 on the "bullshit-o-meter" where lower is lower-in-bullshit. I can't defend her stance on academia-in-general but it seems like some of the complaints against this video in particular are overblown.
(It is important to call out the harmful effects of elements of cultural racism like this idiom, but it's also important to take it for what it is and not what it isn't and take a measured, empathetic approach if you actually want to induce change. Being too accusatory and acerbic causes people to focus on themselves rather than the people who may be hurt by cultural racism.)
David Michael Roberts (Oct 25 2025 at 20:16):comparing things to Chinese is a common idiom in Germany for incomprehensibility,
Ah, the "It's all Greek to me" analogue.
Cole Comfort (Oct 25 2025 at 20:21):David Michael Roberts
https://en.wikipedia.org/wiki/Greek_to_me
There is no source for this one on the wikipedia page, but I find the one of the German idioms most amusing:
All I understand is "train station."
Maybe that one wouldn't resonate with the international audience.
David Michael Roberts (Oct 25 2025 at 22:49):I've seen a comparison of different European languages' versions of this and a few refer to Chinese.
David Michael Roberts (Oct 25 2025 at 22:52):The directed graph of references to other languages being the incomprehensible one is interesting :-)
Noah Chrein (Oct 25 2025 at 23:38):One may retain humility and gratitude despite a lifetime of rejection. We can show those in pain, such as Sabine and others, grace.
And let me just say, in dwelling with those on the periphery of mathematics (silicon valley tech types) for a few months this summer, it's quite obvious that the LLMs will try to convince you that category theory is the answer to all your questions.
There's a whole huge demographic of people who just came across category theory in the last year, and definitely not through algebraic topology. This demo is prone to believe they totally understand the depth of category theory after reading 1 intro book like Maclane (again, not algebraic topology or geometry or algebra etc).
However, they are for the most part very eager to learn, I decided to make a big signal group chat with every one of them that I met (and some of you are in it). I feel as though outright rejection of these folks causes lasting animosity, so I urge you to have grace despite their potential rudeness, reduction of the field, and unearned hubris. Have patience for the flip side as well: their category theory idolatry, saying that every problem is category theory (which it is but the reason why is so much deeper and none of us have touched it, maybe Grothendieck glanced upon it).
For among this demo are several serious people who have really surprised me with their natural grasp of the field, including some who are very young.
Morgan Rogers (he/him) (Oct 26 2025 at 10:31):James Deikun said:
Being too accusatory and acerbic causes people to focus on themselves rather than the people who may be hurt by cultural racism.
If Matteo's comment on the CT Zulip is somehow the first place that Sabine discovers that her comment comes off as racist, I would certainly need to retract my earlier comment about her lack of engagement with CT.
Morgan Rogers (he/him) (Oct 26 2025 at 10:35):Noah Chrein said:
And let me just say, in dwelling with those on the periphery of mathematics (silicon valley tech types) for a few months this summer, it's quite obvious that the LLMs will try to convince you that category theory is the answer to all your questions.
It seems like you didn't watch the video; Matteo's screenshot is the only one involving ChatGPT; it's Sabine that makes the connection with category theory (as an abstract mathematical discipline she claims previously took the interest of theoretical physicists).
Nonetheless, I'm glad you're taking the time to help people understand CT better!
John Baez (Oct 26 2025 at 10:38):It seems to me the issue of people of displaying "grace" to people just learning category theory is largely orthogonal to Hossenfelder, since she's not teaching anyone category theory and probably not learning any either.
(Btw, I think Hossenfelder paid more attention to me, and also to category theory, back in the 1990s - back when I was more visible and loudly touting the possible applications of category theory to quantum gravity in my series This Week's Finds. I don't feel she's been following the recent dramatic applications of category theory to condensed matter physics.)
James Deikun (Oct 26 2025 at 11:06):Morgan Rogers (he/him) said:
If Matteo's comment on the CT Zulip is somehow the first place that Sabine discovers that her comment comes off as racist, I would certainly need to retract my earlier comment about her lack of engagement with CT.
It's not only about her, but about people who may identify with her. It's important to make clear that the problem with this comment is:
and not:
Morgan Rogers (he/him) (Oct 26 2025 at 12:24):I agree with all of those points, but I was taking issue with your criticism of Matteo's comment, which made no reference to the speaker's "overall character".
James Deikun (Oct 26 2025 at 12:35):A lot of people would take "display of stupidity" that way, and most people outside the progressive activist community seem to take "be racist" that way.
Morgan Rogers (he/him) (Oct 26 2025 at 14:03):A behaviour can be racist (in the ways you have explained) or stupid. Racism and stupidity are no more of less than patterns of behaviour; making a racist comment, inadvertently or not, is one of the acts that constitutes being racist. So Matteo's comment was a description of the act: in making the comment, Hossenfelder was 'being racist'; in quoting directly from ChatGPT she was 'displaying stupidity' (according to Matteo, anyway). If "a lot of people" were to extrapolate from that assessment an unrepresentative broader judgement of Sabine Hossenfelder's character, that would be on them, not on Matteo.
Jencel Panic (Oct 26 2025 at 14:12):That's a truly awful take, we all know that bashing other people and being smug about stuff that didn't work out pays better than actually try to explain a concept, or try to figure out how things work, but if you have to do it, at least you should maintain some professional integrity, not quote chatGPT...
James Deikun (Oct 26 2025 at 14:14):I'm sure if someone else wanted to be defensive of Sabine, as you are being defensive of Matteo, they would say that "Chinese is merely a language that Sabine does not understand; if a 'lot of people' were to extrapolate from that any sort of attitude toward Chinese people, never mind Asians in general, that's on them, not Sabine." In a diverse community, you cannot merely declare that your preferred communication style is the objectively correct one and it is everybody else's job to divine and respond to (only) your true intentions; you must make the effort to communicate in a way that so that others will understand your intentions.
Noah Chrein (Oct 26 2025 at 17:03):John Baez said:
It seems to me the issue of people of displaying "grace" to people just learning category theory is largely orthogonal to Hossenfelder, since she's not teaching anyone category theory and probably not learning any either.
I'm talking about having grace for people who are in pain, like Sabine. Grace here might look like an un-offended response video to this, made in good fun.
Alex Kreitzberg (Oct 26 2025 at 17:38):Hossenfelder has made a career out of undermining other's credibility. But putting that aside, It's okay to get angry or frustrated if somebody implies your work is overly complicated.
Ben Kaminsky (Oct 28 2025 at 07:17):Hi, not to harp too much on the issue, but Geometric Computability Theory was created precisely to fill this exact "gap in the market" for the "shut up and calculate" types like Sabine. It's a kind of "Constructive Computational Gauge Theory."
I've already got the manuscript outlining all that's really needed being reviewed at a respected Springer journal by the way. Once it's published, the complaints about the usefulness of CT in physics by this particular crowd should more or less start to go away by the end of this decade, so please, I ask you all just be patient. Hearts and minds don't change overnight.
If Dr. Sabine insists that our foundations for physics be based on a deterministic, computational, 4D theory, well then, I'm more than happy to provide her with such a research program, so she won't be able to complain about lack of alternatives in the HEP-th space anymore, I can assure you all of this. (The catch is that she has to learn what a geometric bordism is).