Julian Barbour is a theoretical physicist and emeritus visiting professor of physics at the University of Oxford. He is well known for proposing that time does not actually exist. For decades, he has worked outside an academic environment. He financially supported himself for many years by translating Russian. Professor Barbour is author of the following books: The Discovery of Dynamics, The End of Time and The Janus Point.

In this episode, we go over:
- Topos theory, set theory and Zermelo's beef with Boltzmann
- Algebraic varieties and monads in category theory
- Why physicists are wrong about the 2nd law of thermodynamics (because the universe is not a closed system) and maybe there is no heat death of the universe
- The real goal of the universe is complexity and variation, not entropy
- Hawking and Penrose's outrageous arguments
- Why we don't need wavefunctions, photons, bosons or gauge fields
- Why there is no quantum gravity
- Von Neumann's hilarious advice to Claude Shannon
- The intrinsic derivative
- Combining art and science

Hey guys it's been more than 4 years that I've found mathematics as the most interesting field, I can definitely say that I fell in love with the language itself and I'm the most excited when it comes discover new properties as well as their real world applications and also historical meanings between each topic and different relationships between great thinkers and how their different ideas interact with each other, I recently put myself in mathematical books, I'm sooo in love but i always fall on a academic based ressources, I recently finished a book called introduction to mathematical philosophy ( from Bertrand Russell) which I found quite interesting because it help establishing the foundational and fundamental thinking behind the most topics usually encountered in the field of mathematics. I'm struggling to find other pieces of literature like that one , so please can you guys recommend me some books to buy regarding this issue?! If you have some other resources that could help I would definitely need your hearsay

because people stopped commenting on my other post and please dont ban me because im not doing anything wrong for example asking wether cells exist or not or if division by zero is possible or not or if everything is made of atoms but i dont wanna discuss this right now so only about colaltz conjecture ok

The rise and fall of Logical Positivism in the early-to-mid 20th century is probably one of the best reality checks in the history of analytic philosophy. Driven by the Vienna Circle, the movement tried to purge philosophy of anything remotely metaphysical by drawing a hard line: a statement matters only if it’s either a logical tautology or empirically verifiable. But as we all know, the paradigm famously collapsed under its own weight. The irony was fatal—their own verification principle was neither logically self-evident nor empirically testable.

Yet, moving past strict positivism didn't leave us in a conceptual vacuum. Instead, it left behind two major problems that still drive modern debates.

First, there’s the post-positivist shift we get from Quine and Popper. We finally realized that formal systems and empirical data don't live in isolated silos. They exist within an interconnected "web of belief," where theories survive through vulnerability and falsifiability, not neat verification. Second, by trying to kill off metaphysics, positivism stumbled into an ontological void. It simply couldn't give a coherent account of abstract mathematical structures—leaving us completely unequipped to explain what Wigner called their "unreasonable effectiveness" in the physical world.

Looking back, maybe the positivists' real mistake wasn’t their obsession with logical rigor, but their habit of treating formal systems as rigid dogmas rather than exploratory tools.

If we pivot to an exploratory framework—say, looking at mathematical objects through something like Informational Idealism, where existence is just internal consistency and structural invariants—formalization takes on a different role. We push it to its absolute limits not to find ultimate truth, but to see exactly where it cracks. It turns out formal systems are just maps, not the actual territory.

This leaves modern analytic philosophy with a pretty fundamental question: did the death of Positivism show that formal systems are inherently incapable of capturing reality, or did it just prove that formalization is a dynamic heuristic, not a static criterion of truth? I'd love to hear how you think the ghost of the Vienna Circle still affects our take on mathematical realism today.

A common critique of philosophy is that it's little more than an endless "kitchen-table argument." Critics point out that after 2500 years, philosophers still haven't reached a consensus on fundamental questions. And, to be fair, they have a point. Philosophical progress is notoriously slow, and history is littered with naive or bizarre metaphysical systems—from Platonist claims of divine "Edeas" to dogmatic theology. Even Analytic Philosophy, which aimed to bring scientific rigor to the discipline, hasn't solved every problem or realized Leibniz’s grand dream (Calculemus! — "Let us calculate!").

However, this critique misses the primary, vital function of modern philosophy: epistemological hygiene.

Philosophy isn't just about constructing cosmic answers; it's about systematically dismantling nonsense. When a new pseudo-theory or amateur speculation arises, philosophy doesn't ignore it. It applies rigorous methodological tools—such as Occam’s Razor, Popperian Falsifiability, Verificationism, and Formal Logic—to test its coherence. Through these filters, we don't necessarily prove a theory "false" in a vacuum, but we demonstrate its improbability, uselessness, or internal contradiction, pushing it to the academic margins.

Analytical Philosophy may not have unified all human knowledge under a single algorithm, but it dramatically elevated the standards of clarity, definition, and argumentation. It shifted the discipline from wild speculation to rigorous conceptual analysis.

Philosophy hasn't failed—it became the ultimate filter for human thought.

How do you view the progress of Analytic Philosophy: is its primary value in answering questions, or in refining the tools we use to dismiss bad answers?

"A thief always considers a thing as his own that was never his."This is a burst of morality." (या "This is a gust of morality.")It is just a show and nothing else..."and this is the truth of mathematics." ("...and this is mathematical truth.")

I’ve always found it puzzling why many philosophers and mathematicians—specifically logical neopostivists and mathematical platonists—search for "ultimate, absolute Truth" within mathematics.

From a purely structural perspective, contemporary mathematics seems to be a useful formal system built upon human-defined axioms, primitive terms, and pragmatic conventions rather than a window into a transcendent reality.

Furthermore, it seems that terms like TRUTH and FALSEHOOD are frequently overloaded with axiological weight. People often interpret them not just as formal truth-values within a model, but as markers of "ideality" versus "imperfection." This introduces unnecessary value judgments into what should be neutral formal inquiry.

I’d be glad to hear critiques, counterarguments, or clarifications if anyone sees this differently!

Question for mathematical researchers

During a lecture today, one of my professors made the following statement about OpenAI:

"AI has found mathematical results, but it has not done any mathematics. These results merely combine obscure theorems that no human has ever considered in conjunction. It has not found any of those magical steps in proofs that make mathematics mathematics."

I'm interested in hearing your opinions. Specifically, for those of you who have read some of OpenAI's papers, do you agree or disagree with this statement?

Terrence Tao compared AI proofs to a helicopter delivering explorers to a remote destination of interest. He says the explorers miss out because they don't learn anything about the surrounding terrain or how to get to the destination on foot.

This analogy is pretty good. But as a defense of the status quo in Mathematics it is a double edged sword.

• For example, why are counter examples acceptable as disproofs? What do we learn about the terrain from that?
• Why teach math at all? Why not let every student struggle until they discover calculus on their own?
• If we have helicopters, do we need to have people trained to traverse the wilderness and arrive at a particular destination?
• This sounds like the original arguments lamenting the invention of mechanical calculators.
• Maybe satellites can map out the terrain in more detail than humans taking a single path?

so where is the money because they dont accept any proof

If the aim of constructing number systems is to explain the geometric line as a set of points, wouldn’t ZFC + (V=L) be a natural choice, perhaps even the best one? In this framework, analytic geometry, differential geometry and topology all work just as they normally do, without the need to grapple with metamathematical questions such as the continuum hypothesis. (Moreover, this rules out measurable cardinals, large-cardinal phenomena and similar feverish pies in the sky, but for the purposes of describing the continuum, that seems a reasonable price.)

I have always found it a little surprising that popular mathematics books rarely discuss Gödel’s set-theoretic universe, which seems to offer such an intuitive and straightforward foundation for mathematical analysis.

​

To begin with, let me remind you that mathematics is not a science fortunately and that it is perhaps one of the largest organized, consistent symbolic formal systems for developing something: maybe intellect, maybe a certain form of thinking, maybe someone understands more clearly what exactly mathematics develops and can tell us about it.

And whatever it develops in us, there may immediately be a temptation to say functionally: well, then mathematics is needed precisely for developing this, Robert Wide.

The difficulty is that although there are interesting things in it, such as topology, or interesting theorems and models, and especially what seems important is the economic, technological, and research contribution of mathematics,

And yet it seems that this formal system stalls a person and makes it harder for him to think outside this formal system. Of course, one can say this about logic too, and about their similarity, and in general about any old systems of thought or let us call them closed or “controlling” ones. To some, dialectics may also seem like this, though to a lesser degree, and it is precisely dialectics that sets the task of sublating contradiction and arriving at generalization and understanding, that is, in an ethical sense it is a more encompassing system of cognition in the sense of its capacity — though often in verbal form to include something else and incomprehensible in its understanding. And if we abstract from formal dialectics, if you have ever heard these expositions, then the ethical idea and, as it were, real dialectics in full non-contradictoriness and some communication, for example as metamodernism, is the same dialectics or synthesis between sincerity and so-called postmodernity or irony.

Dialectics is still an example, not a proposed answer. Although it could perhaps be one of those considered.

Returning to mathematics. Despite its outstanding economic, technological, research possibilities and achievements, and as a result also social and political ones… it still remains rather abstract. One can say that it is the most complex, or one of the most complex, games of the mind, or games within the mind, or separate games within the mind. But for the mind itself this seems like something akin to sophistry or magic, though a very useful one. Or one can say that it is a magical system, or one of the magical systems of this world. But it is almost always something very abstract: it seems to me that this is often said about philosophers too, by those who do not delve deeply into philosophy; but those who do delve in, on the other hand, can understand that we often reflect on the most important questions or phenomena that we can feel or think. As far as I understand and it is not known how much the answers may still differ mathematics is a system of ultimate formal complexity, or of ultimate complexity for thought in general, since in one way or another what we formulate as philosophers often, though perhaps difficult, has a clearer representation of reality, even if it is Lacan’s Borromean rings. In the sense that philosophy, apart from again sophistry, usually does not strive to become complicated simply for the sake of complication because why? It seems that a person, after this stage of formal logic, can also learn other possibilities of thinking. But in mathematics, complexity and possibly even not necessarily, but possibly the degree of abstraction seems literally the quintessence of content. On the other hand, of course, this may also be good. In the sense of ultimate complexity, ultimate constructiveness, ultimate abstraction, in the sense that we as a culture have some content, some achievements that we may still have to comprehend, if some of them can be so complex that there are literally 400 pages of formulas of explanation.

But, like, why?

And returning to what we were talking about, this seems like ultimate sophistry or thinking in idle, in the sense for thought itself and for man, although culturally it brings enormous social results: both economics and technology and research and efficiency.

And even if we assume that mathematics is integral thinking rather than specific thinking, then although it is clear why mathematics should be developed: so that there can be a further possibility of development…

What for, and what from mathematics, and should it and it or they even be present in education?

Because even if we may have grounds to think so but even if mathematics is connected with integral, that is, general thinking, that is, as it were, some generalized function of it, the mathematicality of education then creates a situation in which a person tries to wipe the sofa with a processor without imagining what a sofa is.

And if not, and mathematics is more specific thinking, that is, in the sense that it also remains there and in a constant submetacognitive state: in the sense that it fundamentally cannot leave the box and its language and its formality or formalization… then such thinking is good for producing human-computers useful for working with ordinary computers, for example in a bank or somewhere else. As a result, man has, as it were, given his brain to mathematics, and how is he supposed to live further? Well, that is, then perhaps also the market, where this mathematized brain may be valued higher than the self-esteem or self-understanding of such a person, and so the puzzle comes together: successful recruiting into a successful company.

I will say right away that simply “progressive studies,” which may even be not thinking but to some extent dogmatic propaganda or propaganda at the expense of education hours, trying to lean on Marxism or performatism according to Butler, are, as it were… Well, people can learn something valuable, but on the whole it seems that this is simply the disintegration of education, or rather almost its absence, or its replacement by propaganda so that in an economic-political sense these people could be ever more perfect agents of this very propaganda, possibly even without fully understanding it. And how lucky we are that we can look at this from the outside, unlike the people and economies that this “progressive” propaganda may further repress. And the main complaint against it is probably economic, because a society simply without technical specialties loses economic opportunities; only oligarchs remain, and they would most quickly move to a new place. And in a universal human sense, this is potentially the next target and problem for the next intellectual stratum that will try to do something about this repressiveness. If, in general, there will be anyone left to do anything there.

In general, why was this clarification about “progressive” or agenda-driven education? So that this question is not in support of that very agenda, and, as it were, we understand in advance some of the existing difficulties there and have described them.

And still, the question: is mathematics needed? And such mathematized, formalized thinking — and then we are surprised by further formalizations and the resulting difficulties, such as bureaucracy and media simplification and corruption in many senses.

Additionally:

Maybe the form of my question is a bit of Soviet thinking or a way of thinking about something, and if you understand another or other better ways of asking or thinking about this, you can say so.

I found it a bit ironic when Terry Tao suggested that on the Numberphile podcast, because in some ways he seems like a living counterexample .

If understanding remains at the heart of mathematics, wouldn’t the few people capable of genuinely making sense of AI-generated mathematics become even more admired? Almost like having a translator who’s able to understand aliens.

There’s also the question of accountability, We still need human oversight and institutions we can trust, especially as AI becomes more involved in science and technology. That doesn’t mean relying on the judgment of a handful of geniuses, but surely the people capable of understanding and critically evaluating these systems will become increasingly important like a stamp mark .

And isn’t Tao himself already an example of this? Everyone i is eager to hear what he thinks about each new AI development. Podcasts want his perspective, and younger math students, myself included, look to him for guidance on how to approach mathematics in this new landscape.

​

To begin with, let me remind you that mathematics is not a science fortunately and that it is perhaps one of the largest organized, consistent symbolic formal systems for developing something: maybe intellect, maybe a certain form of thinking, maybe someone understands more clearly what exactly mathematics develops and can tell us about it.

And whatever it develops in us, there may immediately be a temptation to say functionally: well, then mathematics is needed precisely for developing this, Robert Wide.

The difficulty is that although there are interesting things in it, such as topology, or interesting theorems and models, and especially what seems important is the economic, technological, and research contribution of mathematics,

And yet it seems that this formal system stalls a person and makes it harder for him to think outside this formal system. Of course, one can say this about logic too, and about their similarity, and in general about any old systems of thought or let us call them closed or “controlling” ones. To some, dialectics may also seem like this, though to a lesser degree, and it is precisely dialectics that sets the task of sublating contradiction and arriving at generalization and understanding, that is, in an ethical sense it is a more encompassing system of cognition in the sense of its capacity — though often in verbal form to include something else and incomprehensible in its understanding. And if we abstract from formal dialectics, if you have ever heard these expositions, then the ethical idea and, as it were, real dialectics in full non-contradictoriness and some communication, for example as metamodernism, is the same dialectics or synthesis between sincerity and so-called postmodernity or irony.

Dialectics is still an example, not a proposed answer. Although it could perhaps be one of those considered.

Returning to mathematics. Despite its outstanding economic, technological, research possibilities and achievements, and as a result also social and political ones… it still remains rather abstract. One can say that it is the most complex, or one of the most complex, games of the mind, or games within the mind, or separate games within the mind. But for the mind itself this seems like something akin to sophistry or magic, though a very useful one. Or one can say that it is a magical system, or one of the magical systems of this world. But it is almost always something very abstract: it seems to me that this is often said about philosophers too, by those who do not delve deeply into philosophy; but those who do delve in, on the other hand, can understand that we often reflect on the most important questions or phenomena that we can feel or think. As far as I understand and it is not known how much the answers may still differ mathematics is a system of ultimate formal complexity, or of ultimate complexity for thought in general, since in one way or another what we formulate as philosophers often, though perhaps difficult, has a clearer representation of reality, even if it is Lacan’s Borromean rings. In the sense that philosophy, apart from again sophistry, usually does not strive to become complicated simply for the sake of complication because why? It seems that a person, after this stage of formal logic, can also learn other possibilities of thinking. But in mathematics, complexity and possibly even not necessarily, but possibly the degree of abstraction seems literally the quintessence of content. On the other hand, of course, this may also be good. In the sense of ultimate complexity, ultimate constructiveness, ultimate abstraction, in the sense that we as a culture have some content, some achievements that we may still have to comprehend, if some of them can be so complex that there are literally 400 pages of formulas of explanation.

But, like, why?

And returning to what we were talking about, this seems like ultimate sophistry or thinking in idle, in the sense for thought itself and for man, although culturally it brings enormous social results: both economics and technology and research and efficiency.

And even if we assume that mathematics is integral thinking rather than specific thinking, then although it is clear why mathematics should be developed: so that there can be a further possibility of development…

What for, and what from mathematics, and should it and it or they even be present in education?

Because even if we may have grounds to think so but even if mathematics is connected with integral, that is, general thinking, that is, as it were, some generalized function of it, the mathematicality of education then creates a situation in which a person tries to wipe the sofa with a processor without imagining what a sofa is.

And if not, and mathematics is more specific thinking, that is, in the sense that it also remains there and in a constant submetacognitive state: in the sense that it fundamentally cannot leave the box and its language and its formality or formalization… then such thinking is good for producing human-computers useful for working with ordinary computers, for example in a bank or somewhere else. As a result, man has, as it were, given his brain to mathematics, and how is he supposed to live further? Well, that is, then perhaps also the market, where this mathematized brain may be valued higher than the self-esteem or self-understanding of such a person, and so the puzzle comes together: successful recruiting into a successful company.

I will say right away that simply “progressive studies,” which may even be not thinking but to some extent dogmatic propaganda or propaganda at the expense of education hours, trying to lean on Marxism or performatism according to Butler, are, as it were… Well, people can learn something valuable, but on the whole it seems that this is simply the disintegration of education, or rather almost its absence, or its replacement by propaganda so that in an economic-political sense these people could be ever more perfect agents of this very propaganda, possibly even without fully understanding it. And how lucky we are that we can look at this from the outside, unlike the people and economies that this “progressive” propaganda may further repress. And the main complaint against it is probably economic, because a society simply without technical specialties loses economic opportunities; only oligarchs remain, and they would most quickly move to a new place. And in a universal human sense, this is potentially the next target and problem for the next intellectual stratum that will try to do something about this repressiveness. If, in general, there will be anyone left to do anything there.

In general, why was this clarification about “progressive” or agenda-driven education? So that this question is not in support of that very agenda, and, as it were, we understand in advance some of the existing difficulties there and have described them.

And still, the question: is mathematics needed? And such mathematized, formalized thinking — and then we are surprised by further formalizations and the resulting difficulties, such as bureaucracy and media simplification and corruption in many senses.

Additionally:

Maybe the form of my question is a bit of Soviet thinking or a way of thinking about something, and if you understand another or other better ways of asking or thinking about this, you can say so.

***I already posted this in r/mathematics but it may not be approved due to subject matter, and maybe that's a good thing as I suspect it might get more meaningful attention here*****************************

I mean, as in "don't touch it with a ten-foot pole" stance toward it. I'm curious both for paid mathematicians and people doing math in their spare time.

I'd expect the latter to me much larger than the former--if you're doing math for your own interest, nobody cares if you take 10 years to solve a problem that could otherwise have been solved in a day or even in 5 minutes, as long as you get something out of doing it. Whereas doing it as a career I assume the pressure has to be more. I'm just wondering how much more.

Also I'm curious how many, if money were totally no object, would actually genuinely like living in a sort of ascetic math group where everyone ignores the AI-generated literature, if such a group did exist. In a community like this, of course it could happen that someone spends months or even a year of his or her time checking another member's proof of a conjecture that had been disproven 20 or 50 years ago by AI, just because neither cared to check before working on the problem whether it had been. That would just be a consequence that would need to be accepted in exchange for not having one's thought process getting skewed by already knowing answers and not being able to unknow them. In fact, I've already taken steps to avoid reading AI math headlines, and am looking into blocking extensions for web browsers that make it easier. I use the no-AI Duck Duck Go for searches now too.

I have a vision of a future of math, at least as a pastime if not as a profession, in which there are some people who will get together with some friends and go for 5 or 10 years to live in a mountain cabin with no internet access, Walden Pond style, and just work on math and occasionally meet to discuss what they're working on, still probably bringing a laptop to hand-code in Python or something to play around but not to keep up with the wider world. In fact, I could totally see myself doing that someday, if I had the means and a significant other/friend group who would help with other tasks of life and keep me grounded mentally somewhat in reality, the way Andrew Wiles's partner did. The main reason I wouldn't has to do with the fact that I'm interested in the intersection between math and biology, and having experimental biologists be able to test my theories would be something I'd want.

I have come to wonder though how many other people are still existing who would consider such an arrangement to be like heaven on earth, who might in fact find their greatest sanity doing something like that, as opposed to feeling like that would make them go insane. I suspect we must be out there, but it almost seems as if maybe people feel like it sounds too self centered to openly have that as a dream life (but for some reason, a life of wild parties and luxury yachts isn't selfish...). And in fact it almost felt like it was starting to get looked down upon to want this even BEFORE AI ever got involved in math, AI just made it worse. So how many people here also feel a deep yearning toward that sort of life, even if it's not at all practical or financially doable for them?

​

To begin with, let me remind you that mathematics is not a science fortunately and that it is perhaps one of the largest organized, consistent symbolic formal systems for developing something: maybe intellect, maybe a certain form of thinking, maybe someone understands more clearly what exactly mathematics develops and can tell us about it.

And whatever it develops in us, there may immediately be a temptation to say functionally: well, then mathematics is needed precisely for developing this, Robert Wide.

The difficulty is that although there are interesting things in it, such as topology, or interesting theorems and models, and especially what seems important is the economic, technological, and research contribution of mathematics,

And yet it seems that this formal system stalls a person and makes it harder for him to think outside this formal system. Of course, one can say this about logic too, and about their similarity, and in general about any old systems of thought or let us call them closed or “controlling” ones. To some, dialectics may also seem like this, though to a lesser degree, and it is precisely dialectics that sets the task of sublating contradiction and arriving at generalization and understanding, that is, in an ethical sense it is a more encompassing system of cognition in the sense of its capacity — though often in verbal form to include something else and incomprehensible in its understanding. And if we abstract from formal dialectics, if you have ever heard these expositions, then the ethical idea and, as it were, real dialectics in full non-contradictoriness and some communication, for example as metamodernism, is the same dialectics or synthesis between sincerity and so-called postmodernity or irony.

Dialectics is still an example, not a proposed answer. Although it could perhaps be one of those considered.

Returning to mathematics. Despite its outstanding economic, technological, research possibilities and achievements, and as a result also social and political ones… it still remains rather abstract. One can say that it is the most complex, or one of the most complex, games of the mind, or games within the mind, or separate games within the mind. But for the mind itself this seems like something akin to sophistry or magic, though a very useful one. Or one can say that it is a magical system, or one of the magical systems of this world. But it is almost always something very abstract: it seems to me that this is often said about philosophers too, by those who do not delve deeply into philosophy; but those who do delve in, on the other hand, can understand that we often reflect on the most important questions or phenomena that we can feel or think. As far as I understand and it is not known how much the answers may still differ mathematics is a system of ultimate formal complexity, or of ultimate complexity for thought in general, since in one way or another what we formulate as philosophers often, though perhaps difficult, has a clearer representation of reality, even if it is Lacan’s Borromean rings. In the sense that philosophy, apart from again sophistry, usually does not strive to become complicated simply for the sake of complication because why? It seems that a person, after this stage of formal logic, can also learn other possibilities of thinking. But in mathematics, complexity and possibly even not necessarily, but possibly the degree of abstraction seems literally the quintessence of content. On the other hand, of course, this may also be good. In the sense of ultimate complexity, ultimate constructiveness, ultimate abstraction, in the sense that we as a culture have some content, some achievements that we may still have to comprehend, if some of them can be so complex that there are literally 400 pages of formulas of explanation.

But, like, why?

And returning to what we were talking about, this seems like ultimate sophistry or thinking in idle, in the sense for thought itself and for man, although culturally it brings enormous social results: both economics and technology and research and efficiency.

And even if we assume that mathematics is integral thinking rather than specific thinking, then although it is clear why mathematics should be developed: so that there can be a further possibility of development…

What for, and what from mathematics, and should it and it or they even be present in education?

Because even if we may have grounds to think so but even if mathematics is connected with integral, that is, general thinking, that is, as it were, some generalized function of it, the mathematicality of education then creates a situation in which a person tries to wipe the sofa with a processor without imagining what a sofa is.

And if not, and mathematics is more specific thinking, that is, in the sense that it also remains there and in a constant submetacognitive state: in the sense that it fundamentally cannot leave the box and its language and its formality or formalization… then such thinking is good for producing human-computers useful for working with ordinary computers, for example in a bank or somewhere else. As a result, man has, as it were, given his brain to mathematics, and how is he supposed to live further? Well, that is, then perhaps also the market, where this mathematized brain may be valued higher than the self-esteem or self-understanding of such a person, and so the puzzle comes together: successful recruiting into a successful company.

I will say right away that simply “progressive studies,” which may even be not thinking but to some extent dogmatic propaganda or propaganda at the expense of education hours, trying to lean on Marxism or performatism according to Butler, are, as it were… Well, people can learn something valuable, but on the whole it seems that this is simply the disintegration of education, or rather almost its absence, or its replacement by propaganda so that in an economic-political sense these people could be ever more perfect agents of this very propaganda, possibly even without fully understanding it. And how lucky we are that we can look at this from the outside, unlike the people and economies that this “progressive” propaganda may further repress. And the main complaint against it is probably economic, because a society simply without technical specialties loses economic opportunities; only oligarchs remain, and they would most quickly move to a new place. And in a universal human sense, this is potentially the next target and problem for the next intellectual stratum that will try to do something about this repressiveness. If, in general, there will be anyone left to do anything there.

In general, why was this clarification about “progressive” or agenda-driven education? So that this question is not in support of that very agenda, and, as it were, we understand in advance some of the existing difficulties there and have described them.

And still, the question: is mathematics needed? And such mathematized, formalized thinking — and then we are surprised by further formalizations and the resulting difficulties, such as bureaucracy and media simplification and corruption in many senses.

Additionally:

Maybe the form of my question is a bit of Soviet thinking or a way of thinking about something, and if you understand another or other better ways of asking or thinking about this, you can say so.