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Not every field in math and science is as abstruse and inaccessible as higher category theory. For example, look up any recent breakthrough in biology: MRNA vaccines, techniques for neural imaging, etc. You don't need to be an expert to be in awe of the clever things people had to come up with to make these work. There's also a ton of beauty being created in recreational math---see for example the elegance of something like this. Anyone can understand that! Even better, popular science/math exposition is also getting better and better so even the "serious" ideas are more accessible than they ever were before---even aspects of your example of higher category theory are open to way more of the population than you claim these days.
Sure not everyone is capable of appreciating every aspect, but this is like saying that novels are a super elitist form of beauty because only English professors have a hope of understanding everything in Ulysses.
I kind of see what you're getting at, there is something profound in using our human intellects to engineer away bodily suffering and codify the processes of doing so, or formulate an elegantly simple solution to a knotty problem, but it lacks the aesthetic dimensions that satisfy the more earthly senses.
There are some fairly simple principles to what most people consider beautiful and aesthetically pleasing and they carry across from art and architecture to music and magazine models, and they can indeed often be codified in mathematical terms. Repetition, rhythm, ratio, harmony, symmetry, dynamics, variation, proportion, and other more human or purpose specific ergonomics, plus any embedded textual and subtextual communication. These are not idiosyncratic preferences. They're timeless, real, and to a degree they're intuitive. It's the same things that make clowns and caricatures funny by getting it wrong via exaggeration. We have thousands of years of practice and improvement in these matters, and while cost constraints are a perennial consideration there's no reason to abandon them entirely or pretend they don't exist.
It's a bit like cookery. Only the most wretched poor, prisoners on punishment, or an ascetic monk would be expected to eat plain grains. But on the other end of the scale even the richest royalty aren't eating an entire bowl of pure saffron. There's a Goldilocks balance of complexity to aim for and a lot of post-war culture has either gone for too little (brutalism, soylent meal replacement drinks), too much (3D cinema, "experimental" ""music"", 87 flavours of hot sauce, Times Square, tinnitus level audio amplification, etc) or a ruthless bean-counting (sub)optimising (I don't know, plastic cutlery? or pockets that are only deep enough for your fingertips). To paraphrase Marie Kondo, those things don't spark joy, or comfort, or contentment. They spark under/over-stimulation and alienation, and those make society a sad panda.
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I'm a midwit. These videos don't do anything for me. At best, they prompt a "well, that's neat" reaction, and nothing else. Without trying to be dismissive, somebody waxing about the beauty of mathematics comes off as very wanky. I can sort of grok what they're getting at, and understand that their brains are wired very differently from mine. It is certainly very interesting, but nothing that can elicit the same gut punch of awe and appreciation from my favorite film or still image; the ceiling of a well-constructed chapel (I'm not even religious) or the stature of an ancient monument; a quaint Shire-like village in the mountains or a barren desert bereft of human imprint. I can imagine myself and many others breaking down in tears when confronted with any of the above. Somebody moved to mania by a formula on a whiteboard and an accompanying 30-minute Youtube explainer would be... completely alien to me. There's way too much thinking involved for me to consider this beautiful in any meaningful sense, when what I think most people are gesturing towards are phenomenon and constructs that could catch one unawares and demand their gaze and attention.
I'm happy that some people can 'get off' on stuff like this, since I'm not sure where we'd be today if they didn't exist. But I don't see the aesthetics, or what the common man should take away from them other than perhaps an eyerolling "Yes, yes, you're so smart that you don't need the beauty of this material Earth - numbers are totally sufficient." Perhaps that only attests to my aforementioned midwittery, but it is honest.
I certainly wouldn't want such people charged with any attempted beautification project. No offense.
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Unfortunately, I’m not able to watch your videos right now, but I’ll give them a look when I can.
In general, while I do appreciate the fact that the beauty found in mathematics and the sciences is becoming more accessible, I still disagree for two reasons. First: as accessible as they might be becoming, I believe that there’s still a large gap between the number of people who can appreciate even a Numberphile video versus the number of people who walk through Grand Central Station and are awestruck.
And that leads me to my second reason: I am inclined to believe that the aesthetic experience that most people get from beautiful architecture is qualitatively different from that which they’d receive from, say, reading about advances in biology. Don’t you think that a medieval peasant is more likely to be floored and filled with the awe of God when they walk into a Gothic cathedral than when they are informed of the finer points of scholastic philosophy? Maybe I’m just typical-minding here, but I wager that for most people monumental and beautiful architecture just hits something primal in a way that more intellectual beauty does not. And if there’s a cross-over point where the latter sort of art does bear greater aesthetic fruit than the former, I would also suppose that it comes at a point inaccessible to the majority of the human population.
I do understand your position. Though I don’t deal in math nearly as advanced as you, there are times when, at the end of a long derivation, some elegant formula will pop out, and I’ll find myself floored. But I fear that it’s unreasonable to expect everyone to find this same joy.
(This is also a reply to @5434a)
I don't think I want to argue that there aren't any aspects of aesthetic preferences that are held universally enough to be objective. I just want to make the narrow claim that the common condemnation of 21st-century Western culture that it is particularly bad at producing beauty is questionable enough that it is completely dependent on idiosyncratic personal preferences that lie on top of these more universal considerations.
To do this, I gave an example of an idiosyncratic preference that I thought was within the bounds of reasonable that also judges modern, western society as exceptionally good at producing beauty. There are others that also suffice, some based on more earthy considerations that may feel more compelling to you. For example, it's not implausible that many medieval peasants may be more in awe of the Manhattan skyline or the Ground Zero memorial than a Gothic Cathedral. It's also not implausible that many might think the dramatically increased accessibility of natural beauty---Banff, Yosemite, the Grand Canyon, Iguazu Falls, things medieval peasants can't even dream of---is worth the cost of having cookie-cutter suburbia everywhere.
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I'm not completely incapable of find aesthetic pleasures in certain weird number sequences but I don't think of MRNA vaccines or neural imaging techniques as beautiful. I think "hey, neat!" or "that's an impressive feat" but beauty never comes top-of-mind for me for a lot of scientific advancements. You and I are probably operating off entirely different definitions of what's beautiful.
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