I have trouble explaining to my parents how my job is a real thing. I can only imagine trying to explain ‘I study shapes, but only ones that don’t jut inwards’.
I've found it's best to explain my job using unintelligible jargon.
There are three choices, really:
You can give a quick explanation in terms they understand, which makes your job sound easy and makes them wonder how anybody gets paid to do it.
You can explain what you do and why it's important in terms they understand, but it'll take so long they'll get bored and wish they hadn't asked.
Or you can give a quick explanation using jargon that they don't understand, which will leave them bored but impressed, which is the best of the bad options.
When I meet people who immediately use hyper-specific jargon with strangers, I either distrust them, or assume they’re not emotionally intelligent (because it’s a choice demonstrates little respect for the person they’re addressing). It also projects that they may be compensating for some emotional insecurity on their own end, trying to assert intellectual “superiority” in some way.
The first option (explaining things simply) might make your job sound easy to a very small minority of extremely uneducated, under-stimulated people, who also have unaddressed insecurities around their own intelligence. But that’s not most humans.
Moderately-to-very intelligent people appreciate how difficult (and useful) it is to explain complex things simply. Hell, most “dumb” people understand, recognize, and appreciate this ability. Honestly, I think not appreciating simple explanations indicates both low mathematical/logical and social/emotional intelligence. Which makes explaining things simply a useful filter for, well… people that I wouldn’t get along with anyway.
With all that said, I prefer to first explain my job in an “explain like I’m 5” style and, if the other party indicates interest, add detail and jargon, taking into account related concepts that may already be familiar to them. If you take them into account, they won’t get bored when you go into detail.
>You can give a quick explanation in terms they understand, which makes your job sound easy and makes them wonder how anybody gets paid to do it.
What is the problem with this?
Most jobs, when simplified, sound like "anybody can do it". I think it's generally understood among adults who have been in the workforce that, no, in fact anybody cannot do it.
The way I think about it is this. There are roughly two groups of people:
- Some people will not care / be dismissive of what I have to say. I probably don't want to talk to these people much.
- Some people will be interested! I probably will like these people.
If I use technical jargon, I am optimizing to impress people I don't really care about impressing - and I will be pushing away the people that I would actually be interested to spend time with.
If I speak respectfully, i.e. the simple explanation, it will resonate more with the people I like. I will push away the people who don't care, but I didn't really want to talk with them anyways.
I don't see what's hard about threading the needle, or maybe I'm completely lacking in EQ
"I'm a mathematician, I study how shapes fit together, which surprisingly, is being used for new methods of secure communication by so and so university, but I just love the math"
I think you can explain the product you work on rather the what you actually do.
I personally say I work on Bluetooth support for Google Home assistant devices. "It's like Alexa, but Google.
Even if you work on some absurdly down stack thing, this seems to work. You work on making sure the internet is as fast as possible, or files are stored in the cloud properly, or the graphics on your computer are displayed correctly.
I once told my dad that if the subject of my thesis was something I could easily explain then it wouldn't be interesting enough to do a PhD in. I said it half-jokingly and he laughed about it, but he stopped asking me what I'm studying after that so maybe he did take it more seriously.
>You can explain what you do and why it's important in terms they understand, but it'll take so long they'll get bored and wish they hadn't asked.
Yes, don't fall into this trap. The other two options are still better. Everyone says, "no, no, I really want to know" and then tunes out two minutes later; then four minutes later they start doing the George Carlin lean: "Surgery! I am having my ears sewn shut!".
I work at many levels and on many different projects, so usually I give a very simple explanation of the most interesting one, in very simple terms, and add, 'that's a small part of my job'.
People that are interested can ask either to give more details on what I have explained, or what about the rest. If they are not interested, they say something and I usually ask what about them, no hard feelings.
I don't have that problem ("I work with computers / I am a computer programmer") but I usually follow with "I'm a race driver. I drive the car as fast as I can, I don't change the tires nor the oil in it" when I get the usual "can you fix my computer?" request.
For reasons that I care not to ask people get seriously annoyed by that.
Really? When I see that all I think is it's one of "them" - the kind that takes some kind of perverse pleasure in needlessly mystifying, complicating, and obfuscating things as much as possible - especially the trivial.
Blowing smoke around simple things to gatekeep them is not impressive and not cute.
I have my own micro business where I make equipment for high energy physics machines.
I have yet to figure out a way to tell people what my business is in a way that is even slightly accessible. Everything about it is so esoteric and multiple steps removed from regular life. It's not necessarily complex, it just contains a ton of details that the average person has no familiar contact with, and don't really have everyday analogues.
> I make equipment for high energy physics machines
> I have yet to figure out a way to tell people what my business is in a way that is even slightly accessible.
You ... just did? In a remarkable short, concise, and very accessible way. I can ask as many follow up questions as I want and we might even have an engaging conversation. Sounds interesting!
At least in the case of sphere packing it's closely related to some core problems in information theory that helped make the Bell phone system so reliable.
Yeah I'd definitely explain that one as "I study ways to make wifi faster", doesn't cover all the nuance, but it's definitely better than the alternative.
Convex shapes, well, annoyingly it's too broad. It has way more applications than sphere packings but it's hard to pick a good example. It's like trying to explain you design screwdrivers to someone who doesn't know what a screw is.
There is a way to explain to neophytes and it's generally to be more emotional problem-solving and intuitive, and less logical or scientific. There's a toxicity that can rise up in talking in a seemingly over-specific manner which puts people off.
Explain it from the perspective of, "well, in order to get XYZ done, we are frustrated by it being hard, so we make an easy guess .. we try thinking about the problem in this crude way way because that's easy to think about, and then we make ABC because we know about ABC's ... and we are excited when using it gets us closer to working than anything else we've tried before".
Emotion-laden explanations are a viable way to explain to non-techs. They may be more comfortable thinking emotionally, whereas we are steeped in the logic and sometimes mathematics of our practice. So we must reintroduce emotion into the explanations.
It worked for me, explaining to my family, they followed on and actually understood.
FTA: “in 100-dimensional space, his method packs roughly 100 times as many spheres; in a million-dimensional space, it packs roughly 1 million times as many“
Nice example of how weird large-dimensional space is. Apparently, when smart minds were asked to put as many 100-dimensional oranges in a 100-dimensional crate as they could, so far, the best they managed to do was fill less than 1% of its space with oranges, and decades of searching couldn’t find a spot to put another one.
“Fill less than 1% of its space” becomes a very counter intuitive statement in any case when discussing high dimensions. If you consider a unit n-sphere bounded by a unit cube, the fraction occupied by the sphere vanishes for high n. (Aside: Strangely, the relationship is non monotonic and is actually maximal for n=6). For n=100 the volume of the unit 100-sphere is around 10^-40 (and you certainly cannot fit a second sphere in this cube…) so its not surprising that the gains to be made in improving packing can be so large.
> (Aside: Strangely, the relationship is non monotonic and is actually maximal for n=6)
For this aside I crave a citation.
When n=1 the sphere fit is 100% as both simplex and sphere are congruent in that dimension. And dismissing n=0 as degenerate (fit is undefined there I suppose: dividing by zero measure and all that) that (first) dimension should be maximal with a steady decline thereafter thus also monotonic.
I’m familiar with this example of hyper-geometry. Put more abstractly, my intuition always said something like “the volume of hyper geometric shapes becomes more distributed about their surface as the number of dimensions increases”.
It's rather crazy that we humans can't really even intuit about a single extra dimension. Or even a single fewer! There's a lot of people who will say that they can visualize things in the 4th dimension but I've yet to find someone who can actually do this. This includes a large number of mathematicians (it's never the mathematicians that claim this...)
I really like the animation in this Math Overflow post[0], because it has a lot of hidden complexity that most people don't think about. The animation is actually an illusion, and you are "hallucinating". That top image projecting a cube down onto a plane? Well... that isn't a cube. We've already projected the cube into 2D! Technically this is 3D. But the 3rd dimension isn't a spacial dimension, it is a time dimension. Which itself is a helpful lesson in learning about the abstraction of dimensions! So we hallucinate a cube, rotating, and then see the projected image on a plane, which we hallucinate as a square that isn't skewed but instead has depth. This is all rather wild in of itself.
The truth is that we struggle to imagine 2D! And most people will claim to be able to visualize 2D and the claim will go uncontested.
If you haven't read Flatland[1], I'd encourage everyone to do so. A lot of people get it wrong. They read it as an analogy 1 dimension down. Where we 3 dimensional creatures are analogous to the 2D creatures and a 4D creature would be as baffling as a 3D creature is to the Flatlander. While that is true, there is a trick being played on you. You think understanding 2D is really easy. But I guarantee you what you're visualizing is inaccurate. Frankly, the book isn't perfectly accurate either.
But really put yourself in the Flatlander's shoes. In a real Flatlander's shoes, not the ones of the book. Be the Square Flatlander and imagine yourself looking at a Triangle. What do you see? I'm betting it is a line? But this is incorrect. You've given it thickness, you've given it a third dimension. Try this again and again, adding more depth and challenging yourself to imagine a real Flatland. You'll find you can't.
Instead, we can visualize and reason about a 2D space embedded within 3D. You might say I'm being nitpicky here, but if I weren't then it would be perfectly fine to say that this[2,3] is a 4-dimensional hypercube instead of a representation of a 4D hypercube.
I actually think understanding this goes a long way to help understanding very high dimensions. If you are forced to face the great difficulty of accurately visualizing one more or one fewer dimension, you are less likely to fool yourself when trying to reason about much higher dimensions.
And as Feynman once said:
The first principle is that you must not fool yourself and you are the easiest person to fool.
[3] Good video of Carl Sagan where he holds a 3D projection of the hypercube. The shadow. But anything I show you has to be embedded in 2D... He picks it up at 6:20 https://www.youtube.com/watch?v=UnURElCzGc0
Neat. I spent a month trying to use sphere packing approaches for a better compression algorithm (I had a large amount of vectors, they were grouped through clustering). Turned out that theoretical approaches only really work for uniform data and not any sort of real-world data.
The usual trick is to use domain-specific knowledge to translate that asymmetry to uniformity.
E.g.: Suppose the data has high-order structure but is locally uniform (very common, comes about because of noise-inducing processes). Compute and store centroids. Those are more uniform than your underlying data, and since you don't have many it doesn't really matter anyway. Each vector is stored as a centroid index and a vector offset (SoA, not AoS). The indices are compressible with your favorite entropic integer scheme (if you don't need to preserve order you can do better), and the offsets are now approximately uniform by assumption, so you can use your favorite sphere strategy from the literature.
I'm sure you've already explored this, but is there some precompression operation that you could do to the vectors such that they're no longer sparse, and therefore relatively uniform?
They weren't sparse, they were dense but the "density" was quite non-uniform (think typical learned ML vectors). Not too far from an N-dimensional gaussian (I ended up reading research on quantizing Gaussian distributions, but that didn't help either as we didn't have a perfectly gaussian thing).
_May_ be a case for extending out what has been explored by theory to cover more useful ground (or not, depending on whether real-world usecases like yours are too heterogenous for effective general techniques).
I feel like mathematicians should be able to do a second doctorate level degree a few years after their first PhD, that must be in a adjacent field of their own, but not the same.
The purpose of a PhD is to certify that you're able to do independent research. Many researchers retrain (or just add a research interest) in adjacent fields during their postdocs or later. At that point it's just research.
Beside the habilitation example of rando234789 (https://news.ycombinator.com/item?id=44498702), in Russia (and Ukraine) there indeed exist two "doctorate levels": кандидат наук [Candidate of Sciences] and доктор наук [Doctor of Science].
> For a given dimension d, Klartag can pack d times the number of spheres that most previous results could manage. That is, in 100-dimensional space, his method packs roughly 100 times as many spheres; in a million-dimensional space, it packs roughly 1 million times as many.
Those numbers sound wild. For various comms systems does this mean several orders of magnitude bandwidth improvement or power reduction?
I think not, because moving to a higher dimension is exponentially worse (density ~ n^2/2^n) than this linear improvement.
So it's only helpful for naturally high dimensional objects. Digital objects do not have a natural dimension (byte length), so you can choose a small dimension.
That density is the volume density. For most applications, you care about the density in terms of number of hyperspheres instead. The largest hypersphere that fits inside an n-dimensional unit hypercube has radius 1/2 and volume π^(n/2) (1/2)^n / Γ(n/2 + 1), https://en.wikipedia.org/wiki/Volume_of_an_n-ball#Closed_for... so the number of hyperspheres in a given volume scales as n^2 Γ(n/2 + 1) / π^(n/2). Of course the dominant term is the factorial growth of the Gamma function, so even without the recent improvement by Klartag, using more dimensions to encode multiple values simultaneously was already preferable.
Error-correcting codes in signal processing are naturally high dimensional object, also mentioned there. Don't see any reason why this research would not be applicable, we haven't found optimal error correcting code for 100 bits yet.
The addition of a dimension can be thought of as adding another variable or "axis" in simpler terms.
Due to the added variable aka axis, you have increased the size of complexity.
2d shapes packed in a 2d boundary vs 3d objects in 3d space. The difference is fitting quarters on a paper vs marbles in a perfect cube.
Now imagine having to find the most optimal method of packing for objects of Nth degree in Nth constraint. For example packing object that have 256 dimensional or variables into a constraint that also is 256 of complexity.
I feel as your dimension aka variable increases....the amount of information to compute grows quite quickly.
We can rule out some things as non optimal or non perfect, but we can also get close to perfection via trial and error. I see this as an example of the traveling salesman issue.
Do you stick with a randomly selected answer, do you go with the current most optimal solution, or do you invest time and effort into finding a new solution but you risk finding a worse solution. At the end of the day is the packing efficient gains worth the computational complexity of N dimension of N constraint given it will take an unknown amount of time to find a more efficient packing solution, and the new solution could be anywhere from 0.1% to 80% more efficient.
Sure Klartag isnt a sphere packing specialist by training, but he's one of the best problem solvers around. He just resolved the Hyperplane Conjecture earlier this year and has contributed to progress on related problems in convexity theory such as: KLS Conjecture, Mahler Conjecture, Central Limit Theorem for Convex Bodies, to name a few. His student Eldan's work on Stochastic Localization has also proven critical in log-concave sampling algorithms (related to the KLS conjecture, and he gave a talk at the ICM).
Also, the toolkit one uses in convex geometry, especially some of the harmonic analysis tools are quite handy in the study of sphere packing.
> Klartag is convinced that this makes them extremely powerful: Convex shapes, he argues, are underappreciated mathematical tools.
I agree with this and I'm not even a mathematician, I've seen convex hull algorithms pop up in unexpected places to solve problems I would never have thought of using convex hull algorithms for, like a paper on automatic palette decomposition of images.
For other dimensions, this is an open question; it seems unlikely to be true in general. For some dimensions the densest known irregular packing is denser than the densest known regular packing.
> For some dimensions the densest known irregular packing is denser than the densest known regular packing.
I thought that was one of the important results from the paper, the most efficient packing for all dimensions is symmetrical again and this increase was significant enough it seems unlikely that existing non-symmetrical methods will be able to beat it.
Not necessarily—in 3d there are uncountably many non-lattice packings. They all have the same density as the FCC lattice though. To construct these packings, shift horizontal layers of FCC horizontally with respect to each other.
It is conjectured that in higher dimensions, the densest packing is always non-lattice. The rationale being that there is just not enough symmetry in such spaces.
Well these new results (denser packings than before) are regular lattices which might suggest that the optimal packing could be a lattice. (Until the record is broken again by a irregular packing ;-)
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There are three choices, really:
You can give a quick explanation in terms they understand, which makes your job sound easy and makes them wonder how anybody gets paid to do it.
You can explain what you do and why it's important in terms they understand, but it'll take so long they'll get bored and wish they hadn't asked.
Or you can give a quick explanation using jargon that they don't understand, which will leave them bored but impressed, which is the best of the bad options.
The first option (explaining things simply) might make your job sound easy to a very small minority of extremely uneducated, under-stimulated people, who also have unaddressed insecurities around their own intelligence. But that’s not most humans.
Moderately-to-very intelligent people appreciate how difficult (and useful) it is to explain complex things simply. Hell, most “dumb” people understand, recognize, and appreciate this ability. Honestly, I think not appreciating simple explanations indicates both low mathematical/logical and social/emotional intelligence. Which makes explaining things simply a useful filter for, well… people that I wouldn’t get along with anyway.
With all that said, I prefer to first explain my job in an “explain like I’m 5” style and, if the other party indicates interest, add detail and jargon, taking into account related concepts that may already be familiar to them. If you take them into account, they won’t get bored when you go into detail.
What is the problem with this?
Most jobs, when simplified, sound like "anybody can do it". I think it's generally understood among adults who have been in the workforce that, no, in fact anybody cannot do it.
- Some people will not care / be dismissive of what I have to say. I probably don't want to talk to these people much.
- Some people will be interested! I probably will like these people.
If I use technical jargon, I am optimizing to impress people I don't really care about impressing - and I will be pushing away the people that I would actually be interested to spend time with.
If I speak respectfully, i.e. the simple explanation, it will resonate more with the people I like. I will push away the people who don't care, but I didn't really want to talk with them anyways.
"I'm a mathematician, I study how shapes fit together, which surprisingly, is being used for new methods of secure communication by so and so university, but I just love the math"
"I teach computers what sounds different aminals make."
This is always the right answer. It is the only answer that respects the listener and contains a seed to further conversation.
What's wrong with this? Making it look easy is why you get paid for it.
I personally say I work on Bluetooth support for Google Home assistant devices. "It's like Alexa, but Google.
Even if you work on some absurdly down stack thing, this seems to work. You work on making sure the internet is as fast as possible, or files are stored in the cloud properly, or the graphics on your computer are displayed correctly.
There is another:
Give away as little information as you can about it.
Don’t say or agree that it’s secret or that you can’t talk about it- just be tight-lipped, and don’t divulge.
If you do it right, you will seem mysterious.
If you do it wrong, they probably won’t talk to you much again.
Win-win.
Yes, don't fall into this trap. The other two options are still better. Everyone says, "no, no, I really want to know" and then tunes out two minutes later; then four minutes later they start doing the George Carlin lean: "Surgery! I am having my ears sewn shut!".
People that are interested can ask either to give more details on what I have explained, or what about the rest. If they are not interested, they say something and I usually ask what about them, no hard feelings.
It works smoothly for me.
For reasons that I care not to ask people get seriously annoyed by that.
Eg you can focus on what you actually do, or you can focus on the benefits you bring to other people.
Blowing smoke around simple things to gatekeep them is not impressive and not cute.
I have yet to figure out a way to tell people what my business is in a way that is even slightly accessible. Everything about it is so esoteric and multiple steps removed from regular life. It's not necessarily complex, it just contains a ton of details that the average person has no familiar contact with, and don't really have everyday analogues.
> I have yet to figure out a way to tell people what my business is in a way that is even slightly accessible.
You ... just did? In a remarkable short, concise, and very accessible way. I can ask as many follow up questions as I want and we might even have an engaging conversation. Sounds interesting!
(not sure about convex shapes)
Convex shapes, well, annoyingly it's too broad. It has way more applications than sphere packings but it's hard to pick a good example. It's like trying to explain you design screwdrivers to someone who doesn't know what a screw is.
This is a suitable description of possibly 70 % of all jobs.
Explain it from the perspective of, "well, in order to get XYZ done, we are frustrated by it being hard, so we make an easy guess .. we try thinking about the problem in this crude way way because that's easy to think about, and then we make ABC because we know about ABC's ... and we are excited when using it gets us closer to working than anything else we've tried before".
Emotion-laden explanations are a viable way to explain to non-techs. They may be more comfortable thinking emotionally, whereas we are steeped in the logic and sometimes mathematics of our practice. So we must reintroduce emotion into the explanations.
It worked for me, explaining to my family, they followed on and actually understood.
How do I concisely describe the long chain between a fundamental research and something tangible?
Deleted Comment
You ask me what it is I do. Well, actually, you know,
I'm partly a liaison man, and partly P.R.O.
Essentially, I integrate the current export drive.
And basically I'm viable from ten o'clock till five.
convex hulls your car
Nice example of how weird large-dimensional space is. Apparently, when smart minds were asked to put as many 100-dimensional oranges in a 100-dimensional crate as they could, so far, the best they managed to do was fill less than 1% of its space with oranges, and decades of searching couldn’t find a spot to put another one.
For this aside I crave a citation.
When n=1 the sphere fit is 100% as both simplex and sphere are congruent in that dimension. And dismissing n=0 as degenerate (fit is undefined there I suppose: dividing by zero measure and all that) that (first) dimension should be maximal with a steady decline thereafter thus also monotonic.
I really like the animation in this Math Overflow post[0], because it has a lot of hidden complexity that most people don't think about. The animation is actually an illusion, and you are "hallucinating". That top image projecting a cube down onto a plane? Well... that isn't a cube. We've already projected the cube into 2D! Technically this is 3D. But the 3rd dimension isn't a spacial dimension, it is a time dimension. Which itself is a helpful lesson in learning about the abstraction of dimensions! So we hallucinate a cube, rotating, and then see the projected image on a plane, which we hallucinate as a square that isn't skewed but instead has depth. This is all rather wild in of itself.
The truth is that we struggle to imagine 2D! And most people will claim to be able to visualize 2D and the claim will go uncontested.
If you haven't read Flatland[1], I'd encourage everyone to do so. A lot of people get it wrong. They read it as an analogy 1 dimension down. Where we 3 dimensional creatures are analogous to the 2D creatures and a 4D creature would be as baffling as a 3D creature is to the Flatlander. While that is true, there is a trick being played on you. You think understanding 2D is really easy. But I guarantee you what you're visualizing is inaccurate. Frankly, the book isn't perfectly accurate either.
But really put yourself in the Flatlander's shoes. In a real Flatlander's shoes, not the ones of the book. Be the Square Flatlander and imagine yourself looking at a Triangle. What do you see? I'm betting it is a line? But this is incorrect. You've given it thickness, you've given it a third dimension. Try this again and again, adding more depth and challenging yourself to imagine a real Flatland. You'll find you can't.
Instead, we can visualize and reason about a 2D space embedded within 3D. You might say I'm being nitpicky here, but if I weren't then it would be perfectly fine to say that this[2,3] is a 4-dimensional hypercube instead of a representation of a 4D hypercube.
I actually think understanding this goes a long way to help understanding very high dimensions. If you are forced to face the great difficulty of accurately visualizing one more or one fewer dimension, you are less likely to fool yourself when trying to reason about much higher dimensions.
And as Feynman once said:
[0] https://math.stackexchange.com/a/2286226[1] http://www.geom.uiuc.edu/~banchoff/Flatland/
[2] https://en.wikipedia.org/wiki/Tesseract#/media/File:8-cell-s...
[3] Good video of Carl Sagan where he holds a 3D projection of the hypercube. The shadow. But anything I show you has to be embedded in 2D... He picks it up at 6:20 https://www.youtube.com/watch?v=UnURElCzGc0
EDIT: groped -> grouped
E.g.: Suppose the data has high-order structure but is locally uniform (very common, comes about because of noise-inducing processes). Compute and store centroids. Those are more uniform than your underlying data, and since you don't have many it doesn't really matter anyway. Each vector is stored as a centroid index and a vector offset (SoA, not AoS). The indices are compressible with your favorite entropic integer scheme (if you don't need to preserve order you can do better), and the offsets are now approximately uniform by assumption, so you can use your favorite sphere strategy from the literature.
Try doing that in the modern academic environment tho..
But I can imagine that drawing connections between different branches of maths would be especially powerful, yes
Those numbers sound wild. For various comms systems does this mean several orders of magnitude bandwidth improvement or power reduction?
So it's only helpful for naturally high dimensional objects. Digital objects do not have a natural dimension (byte length), so you can choose a small dimension.
https://en.m.wikipedia.org/wiki/Sphere_packing
Due to the added variable aka axis, you have increased the size of complexity.
2d shapes packed in a 2d boundary vs 3d objects in 3d space. The difference is fitting quarters on a paper vs marbles in a perfect cube.
Now imagine having to find the most optimal method of packing for objects of Nth degree in Nth constraint. For example packing object that have 256 dimensional or variables into a constraint that also is 256 of complexity.
I feel as your dimension aka variable increases....the amount of information to compute grows quite quickly.
We can rule out some things as non optimal or non perfect, but we can also get close to perfection via trial and error. I see this as an example of the traveling salesman issue.
Do you stick with a randomly selected answer, do you go with the current most optimal solution, or do you invest time and effort into finding a new solution but you risk finding a worse solution. At the end of the day is the packing efficient gains worth the computational complexity of N dimension of N constraint given it will take an unknown amount of time to find a more efficient packing solution, and the new solution could be anywhere from 0.1% to 80% more efficient.
Also, the toolkit one uses in convex geometry, especially some of the harmonic analysis tools are quite handy in the study of sphere packing.
So "unexpected"? Not quite.
I agree with this and I'm not even a mathematician, I've seen convex hull algorithms pop up in unexpected places to solve problems I would never have thought of using convex hull algorithms for, like a paper on automatic palette decomposition of images.
https://www.rose-hulman.edu/class/cs/csse451/Papers/DILvGRB....
See also https://www.ams.org/journals/notices/201702/rnoti-p102.pdf
For other dimensions, this is an open question; it seems unlikely to be true in general. For some dimensions the densest known irregular packing is denser than the densest known regular packing.
I thought that was one of the important results from the paper, the most efficient packing for all dimensions is symmetrical again and this increase was significant enough it seems unlikely that existing non-symmetrical methods will be able to beat it.
It is conjectured that in higher dimensions, the densest packing is always non-lattice. The rationale being that there is just not enough symmetry in such spaces.