r/PhilosophyofMath • u/TemporaryAd7700 • 2d ago
Math in Future education
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.
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u/StressCanBeGood 2d ago
In order for mathematics to thrive, it’s going to have to go through a transition, just like every other career in the history of the world. Specifically, from solving abstract equations to inspiring others to learn math.
The theory of neuroplasticity suggests that the brain is a muscle-like organ like the heart and lungs. Put the heart and lungs through the right kind of stress, like going for a run, and they become stronger and faster.
The same appears to go for the brain. Challenge the brain in the right way and it becomes stronger and faster. And it would appear that silly and fun brain games won’t do the trick. The brain needs to challenged in a kind of/sort of painful way. Just like the body needs to be challenged in a kind of/sort of painful way in order to become stronger and faster.
Do an online search for brain games don’t work and you’ll see dozens of results confirming this. However, when the brain is truly challenged, there’s some evidence that it does indeed become stronger and faster, as indicated by this article:
Future mathematicians will be those who inspire others to learn math. Turns out that numbers are real trip. All kinds of fascinating things that could inspire people of all ages to want to learn math.
But it’s entirely on mathematicians to do this. Stop complaining (not suggesting that OP is complaining but I hear a lot of mathematicians whining about all kinds of stuff) and start inspiring.
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u/TemporaryAd7700 1d ago
To inspire other to abstract equations? Inspire to mistake? To stress?)
This is mistake of thinking which I'm talking about, and that it's also not develop enough, that it's too limited and detached even for mind development, even not for brain
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2d ago edited 1d ago
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u/TemporaryAd7700 1d ago
The elements are not the same: they can change a lot becoming
And in context of culture rules is like main former of elements... Maybe not main, but maybe it's enough word for perception of conditions that can be changed Or in context of math chose may be former or predictor And what I guess we need is this space of chose not as flat and limited which math able to control with it's evidence obligatory right now
So it feels like people can become smarter or wiser out or above the school and math: sure math made some effect for intellect. Also writing or literacy may too. But I'd the goal of education is development and growth of people I guess it can't be founded around math. Maybe around spark or deeper understanding themselves, but about spark I think that people are not just and only sparks or stars for gobelin: they have their own being that could be more important than only this outer attribution.
Or what exactly do you mean about spark?
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u/Not_Well-Ordered 2d ago
I’ll only deal with last few questions.
I’d say math is still heavily needed for society even today e.g. operation researches, etc. as well as for science, to have a consistent computational system that can use to model or approximate objects and those boost technological progression usually in the good direction, from a holistic view as people will gradually regulate.
Also, even in the age of AI, LLMs are unable to craft new insightful tools/theories or conjectures on their own without any human guidance. LLMs have no clue of what’s an “important” result and what is not. It can be easily stuck there proving very trivial statement like 1+1 =2 2, 1 + 2 =3…
We also still need mathematicians collaborating with scientists in order to examine whether mathematical models fit the descriptions of certain phenomena or not, and what “fits” would depend on collective (human) observations and data.
So far, AIs are still maybe 10-20 years away at least from covering the non-verbal intelligence and creativity that humans have.
However, AIs definitely surpass humans in combining existing (formal) tools to push the current math conjectures and expand the knowledge.
But that does not mean mathematicians are not needed, and maybe we would need more mathematicians to explore, relate, and explain the results, and to craft new theories or tools that can encapsulate new patterns. You can say like AIs provide new sources of inspiration at quicker rate, which is actually good for math community.
But what’s problematic is if the society thinks we don’t more mathematicians, when in fact, we would need more as there are more potential for major breakthroughs in pure and applied fields if more people investigate. That would be until maybe AGI or ASI actually comes into play, when the key questions about consciousness and cognition have been partially solved from scientific PoV.
At last, I’d say mathematics can be a formal science because its symbolic manipulations can be empirically verified and analyzed via statistics (funnily back to math itself again but about its semantic contents) e.g. Lean, computational modeling...