Non-mathematicians build mathematics buildings, harvest and press chalk into sticks, grow the food and coffee we process into theorems (mathematicians are significantly more likely to od on amphetamines, btw), attend the calculus courses we desperately need for funding, clean our chalkboards and empty our wastebins... the list goes on and on.
And yes there are mathematicians who vote for Trump. All you've proven with that tirade is a bound on the radius of your own filter bubble.
Mathematicians are perfectly capable of doing all those self-care things, as monks do in every monastery. (By contrast, non-mathematicians are unable to build anything larger than a small hut without help from mathematicians in the form of geometry.)
I don't know of a single mathematician who has ODed on amphetamines, although of course amphetamines have been popular with mathematicians since they were discovered; and I know of only one who voted for Trump (Dan Kleitman), although undoubtedly others exist. The doses of amphetamines conducive to doing mathematics are about two orders of magnitude lower than the lethal doses, so it seems unlikely that someone who takes them to improve concentration rather than for euphoria would OD accidentally, as heroin users frequently do.
Funding is only necessary to the extent that it helps keep the torch-wielding villagers away from the gate. To the extent that it subjects mathematical research to political tests, it is not only unnecessary, but counterproductive.
If my filter bubble includes Bruno, Socrates, Mozi, Gödel, Turing, and Archimedes, I think its radius is adequate.
I think the downvoting of my "tirade" to -2 has shown that non-mathematicians hate and fear mathematicians, think that all those killings of mathematicians I listed were reasonable and justified, and would like to silence any criticism of them.
Mathematicians should make an effort to reach out to non-mathematicians because that category also includes people like, you know, physicists, engineers, computer scientists, students who may want to one day become mathematicians, those kinds of people.
The point about professions wasn't that mathematicians don't have the ability to do those things (although I'm quite certain most don't have the constitution to do many blue collar jobs), it was that if they were spending 40-50 hours a week collecting the town's garbage, working at a water treatment plant, or doing hot tar roofing, they would no longer have the time or energy to be doing math for a living.
You are truly delusional to think that funding is "only necessary to the extent that it helps keep the torch-wielding villagers away from the gate". Taxes collected from the people you seem to have so much contempt for (basically everyone) are what allow mathematicians to live in ivory towers doing research mathematics for a living. The patronage system of old (which allowed for people like Bruno and Gauss to get any education at all) was even worse, as the money they were receiving was the product of borderline or outright slavery.
Your bizarre characterization of mathematicians as saint-like figures levitating above the unwashed masses is indicative of a pretty poor understanding of history and a shocking lack of ability to empathize. I hope you understand that people who think like you (people who are disgusted by those who built and paid for the ivory towers in which your heroes reside) are the reason why people support things like defunding universities.
It's definitely not necessary to have taxes or a 21st-century-level GDP to do mathematics. Current world GDP is about US$17500 per capita PPP, three times the income I've been living on for years, and 1500 times the world GDP in the time of Archimedes. Computers do help, but they aren't essential, and most of the economy isn't devoted to producing computers or other mathematically useful goods anyway; most of it is devoted to things like the steak I just ate, tearing down buildings and putting them back up, killing people in senseless wars, destroying the atmosphere, team sports, junk food flavorings, surveillance capitalism like Facebook, literal prostitution, disposable fashion, toys, furniture, second cars, daytime TV, and so on.
Admittedly, a significant fraction of world GDP is devoted to essentials like child care, elder care, primary food production, housing, and education. But an enormous amount of it is just wasted and counterproductive effort.
However, you weren't talking about those parts; you were talking about truly essential services. Garbage collection and water treatment are essential but are not significant fractions of the GDP. Let's consider garbage collection, using US statistics. The US has 118520 garbage collectors, including the people who work at recycling plants and dumps, out of a population of 328 million people. If this difficult, dangerous, and sometimes unpleasant work were shared equitably among everyone, it would average 52 seconds per person per week, ¾ hour per year. In practice, even with good coordination, you'd probably lose an order of magnitude in efficiency to the lack of specialization, so probably sharing it equitably would mean that everyone would spend an hour or so every couple of months sorting the recycling at the recycling plant. This would have several salutary effects: people would learn not to put milk bottles in the recycling bin without rinsing them, the social stigma attached to garbage collection would disappear, and garbage collection contracts would no longer be an appealing way for mafias to dispose of clandestine murder victims' bodies.
As for construction work, although I'm not a journeyman electrician or anything, I've poured concrete a few times, I've bent and tied rebar, and I've repaired roofs; and when I was volunteering at the Casa de María in the slums near here, almost everybody I knew there had built their own house (or married or been born to someone who had.) With modern materials, you can build a perfectly adequate and livable house in a person-month, and it can house a family for several lifetimes. Even inefficient construction techniques like adobe, which I've also done, require less than a person-year per family dwelling. There is absolutely no need for people to specialize in hot-tar roofing as a career. That's senselessly exploitative oppression, and it destroys people's physical health as well as their intellectual potential.
Maybe you think that, if some people don't spend 40–50 hour weeks destroying their health breathing in construction dust, then other people will have to go homeless, because there won't be enough housing. The simple ratio I gave above should clarify why that isn't the case: one person-month of construction work per lifetime is more than enough to supply everyone with adequate housing, and that's even without 3-D printing in concrete to build new houses. The reason people go homeless is that they're not allowed to build houses, or the government bulldozes their houses (this happened to a group of my friends), or they're socially isolated and have sufficient mental or physical health problems that they can't take care of themselves.
In the US, about 3% of the population raises food full-time. If this labor were distributed across the population as a whole, it would amount to an hour or two per week. Gardening for an hour or two per week is not enough to seriously impact your mathematical productivity, whether you're driving a combine or tying tomato plants to the fence.
The big time commitments — which mathematicians often do end up doing — are child care, elder care, and education. The kibbutzim have shown that it's possible to collectivize these in a useful and humane way; school and nursing-home systems in places like the US have shown that it's possible to collectivize them in destructive and unbelievably cruel ways. The economy and government the non-mathematicians have constructed makes it very difficult to evade these curses, whether or not you are a mathematician.
As for slavery, slavery does not help education; not only is it inhumane and degrading to both the slave and the owner, it's an inefficient way to satisfy material needs. If the serfs had been liberated before Bruno (who had no patron) and Gauss were born, they would have had greater opportunities to educate themselves, not less.
You say that students of mathematics, physicists, engineers, and so on are "non-mathematicians". I'm not entirely in agreement with that but I'm willing to stipulate it for the sake of this conversation. I still don't think there's any reason for mathematicians to care about their opinion. If a student of mathematics thinks they have squared the circle or that differential forms are useless, [other] mathematicians have no reason to care, except that it might be a fun conversation with someone who might grow into a future collaborator, or that the conversation might sharpen their own understanding of differential forms or whatever. Students of mathematics, physicists, and engineers have motives of their own for caring about mathematics, though. I don't think [other] mathematicians have any responsibility for convincing them of that, nor any real benefit in doing so, except, again, insofar as it might result in interesting new mathematics. But if physicists by and large don't care about category theory (though I've met at least one exception), that doesn't really affect the category theorists, much less the consistency or beauty of category theory. Certainly category theorists wouldn't be doing themselves any favors by writing grants that pretend they're doing some kind of industrial R&D.
I don't think of mathematicians as saint-like figures levitating above the unwashed masses. I think of the unwashed masses as totally depraved screaming degraded chimpanzees throwing turds, and the mathematicians as slightly less depraved, screaming a bit less, slightly less degraded, but still basically chimpanzees.
> (By contrast, non-mathematicians are unable to build anything larger than a small hut without help from mathematicians in the form of geometry.)
If being a mathematician requires this sort of arrogant attitude, then I am all for locking those people up in an ivory tower and willingly foregoing the fruits of their labor.
The idea of applying mathematics and science to the efforts of people doing things instead of thinking about things is actually quite recent--maybe 300-ish years ago. Medieval Europeans didn't need a deep understanding of geometry or physics to discover flying buttresses or build Gothic cathedrals. Go back further in time and look at the majesty of Stonehenge or the Pyramids; the people who built those had no concept of tangents or pi and yet built what they did.
> I think the downvoting of my "tirade" to -2 has shown that non-mathematicians hate and fear mathematicians
No. I like mathematicians quite a lot, but I think you have your head stuck up your own ass.
> Go back further in time and look at the majesty of Stonehenge or the Pyramids; the people who built those had no concept of tangents or pi and yet built what they did.
The Sumerians were doing geometry in 2450 BCE, and the Egyptians were in contact with them. Older Sumerian texts (from before 3100 BCE) don't have a lot of geometry but do contain numerical measurements and arithmetic used for accounting.
The Moscow Mathematical Papyrus, from Egypt, is from the 13th Dynasty (ended 1649 BCE), and it has a problem in it about the volume of the frustum of a pyramid. The Rhind Papyrus (around 1550 BCE) contains six problems about building pyramids, some problems about granary design, and a number of problems about real estate. The pyramids analyzed therein are building-sized. At this point the Egyptians had been building pyramids for a millennium, but no older mathematical texts have survived (aside from a diagram from 1000 years earlier showing how to measure off the slope of a mastaba), but few papyri last even the 4000 years of these papyri. Papyrus is fragile.
Nevertheless, it seems that the ancient Egyptians considered the knowledge of mathematics important to building pyramids, at least by the end of the pyramid-building period.
As for Stonehenge, we have no idea. The folks who built it didn't have a writing system, so we don't know much about how they thought. Still, it does seem pretty plausible that you could roll a big stone lintel up a hill of sand, or carefully balance it onto progressively higher stone pivots, without knowing the Pythagorean theorem. I guess Stonehenge is bigger than a small hut, so you've got me there.
There are Babylonian and Egyptian sources describing how to solve quadratic and some cubic equations from about 1600 BCE, but that is unfortunately at the end of the pyramid-building period. I think it's likely that they had this knowledge much earlier, but it's possible that they built the Pyramids, or most of them, before anyone had figured that out.
> I don't know of a single mathematician who has ODed on amphetamines, and only one who voted for Trump (Dan Kleitman)
I'm a mathematician who thinks that your sequence of posts here isn't serving the purpose you seem to think it does. I don't think that addressing it point by point serves much purpose, but these two claims bothered me particularly, so I single them out for response.
I speak to your second point first: surely you don't think that there is only one mathematician who voted for Trump? Unless you do, it is irrelevant that you only know one; there are surely lots of others out there. I didn't, and I don't know any mathematician that I know did, but I know at least a few mathematicians who I know voted for GWB, and I imagine that there have to be at least a few other Trump voters in my mathematical circle.
The first part in particular, in addition to the same quibble about what it matters whether or not you personally know such people (as opposed to whether or not they exist), probably requires an overly restrictive definition of 'mathematician' as "someone with academic credentials, or other official recognition, as a practitioner of mathematics". I personally don't think that's a good definition of a mathematician, and I don't think that advancing such definitions is a good thing for the future of our profession.
Who is "a mathematician"? I definitely don't mean "someone with academic credentials or other official recognition"; surely Erdős was a mathematician when he was a teenager, Ramanujan was a mathematician before he wrote to Hardy, and Lagrange was a mathematician when he discovered the variational calculus with Euler; I think it's even reasonable to assert that Socrates was a mathematician when he taught Menon how to draw a line of length √½, because he demonstrated the correctness of the construction mathematically rather than just asserting it, even though he surely did not discover it at that moment. I think it's sufficient to be doing mathematics as an end in itself.
But that doesn't help much; what does it mean to be "doing mathematics"? Is it sufficient to read a proof? How about reconstructing a proof you vaguely remember? How about working some exercises in a textbook? Does it matter if the exercises are arithmetic or differential equations? What about when Martin Gardner rediscovered some well-known theorem or other? Might it even be sufficient to be doing mathematics for some other purpose, such as predicting the motions of the planets or the flight of an artillery shell, rather than an end in itself?
It seems that there's unavoidably a gray area; the toddler who counts "one, two, three, seven, ten" is definitely not "doing mathematics", while Scholze was surely "doing mathematics" when he discovered perfectoid spaces. Somewhere in between, there are cases where you can plausibly make an argument either way. (I don't think Ramanujan before his contact with Hardy is one of them, but perhaps that's self-serving bias on my part — I have no academic credentials of any kind, other than publications.)
But that's okay. Language isn't math, so we can't expect people to come to a perfect consensus about what it means, although we can of course attempt to clarify our thinking, however much the non-mathematicians may detest and attempt to sabotage such activity.
So, what do you think is a good definition of "a mathematician"?
> So, what do you think is a good definition of "a mathematician"?
It depends on the context. The definition I'd like to advance is that a mathematician is someone who does mathematics (and that what one usually means by "a mathematician" is something more like "one who habitually does mathematics, or one whose profession is the doing of mathematics"); the toddler, while counting "one, two, three", is a mathematician, who may turn into a new-language learner when continuing "seven, ten", or may still be a mathematician if that toddler is fascinated by and exploring number patterns. By this definition, almost everyone is a mathematician at some time or other, so that making claims about what the population of mathematicians does is little more than making claims about what everyone does.
There are at least two problems with this definition: (1) it shifts the question from "who is a mathematician?" to "what is doing mathematics?"; and (2) it blurs meaningful distinctions between people who are habitual or professional mathematicians, among amateurs, dabblers, and tyros, and other distinctions that one might want to make. My answer to (1) is that I would give an equally broad answer to the latter question, and my answers to (2) are twofold, namely (a) tough, and (b) the distinctions can be preserved by including additional modifiers, as I have done. This resolves these problems to my satisfaction, but I don't expect them to satisfy everyone, or even many.
> I don't think Ramanujan before his contact with Hardy is one of them, but perhaps that's self-serving bias on my part — I have no academic credentials of any kind, other than publications.
That sounds self-defeating, rather than self-serving! Why not recognise Ramanujan as a mathematician before Hardy? Surely the same genius was there, just not expressed in familiar ways; so what Hardy can be said to have done to Ramanujan is surely not to have turned him into a mathematician, but instead to have taught him the common language of mathematics in which to express what he already knew but couldn't fully communicate to others.
I didn't mean to assert that young Ramanujan was clearly not a mathematician — rather the opposite!
Perhaps in practice my definition of "a mathematician" is "someone who, when wrong, responds to disagreement by changing their mind rather than becoming defensive or downvoting you", an event I see on a daily basis in lectures on mathematics and very rarely outside of them.
> Perhaps in practice my definition of "a mathematician" is "someone who, when wrong, responds to disagreement by changing their mind rather than becoming defensive or downvoting you", an event I see on a daily basis in lectures on mathematics and very rarely outside of them.
Mathematicians are often OK at this within their discipline, but we're as bad as anyone else at it when dealing with human affairs. (At least, I am.) I might rather suggest the less flattering characterisation of a mathematician who will argue with a statement with which they agree, just to see if it breaks. (At least, I do.)
> Mathematicians are perfectly capable of doing all those self-care things, as monks do in every monastery
Are they, though? In the pursuit of my PhD, I met plenty of mathematicians who could barely wipe their own ass, let alone cook a meal or, god forbid, build a simple hut. Did you know that most mathematicians use computers? Do you expect these same people to manage the chemistry, physics, engineering, mining and logistics necessary to build their own computing devices?
> I think the downvoting of my "tirade" to -2 has shown that non-mathematicians hate and fear mathematicians, think that all those killings of mathematicians I listed were reasonable and justified, and would like to silence any criticism of them.
That's quite a chain of conjectures... you may be a mathematician, but you certainly aren't holding yourself to mathematical standards here.
Here's a counterexample. I downvoted you. I'm a mathematician. And fwiw Galois died in a duel, which is, by definition, a consensual affair. His killing was an unreasonable, unjustified tragedy, but he brought it on himself. Oded Schramm did himself on a mountain; by the way -- you're shit-talking "non-mathematicians" for taking senseless risks, but missing the obvious and playing victim while referring to non-mathematicians as "torch-wielding villagers."
I downvoted you for your insufferable superiority complex and mindboggling narrow-mindedness.
You seem to be under the misconception that I am a mathematician. I think that's a bit of a stretch of the term, although I do enjoy math; as far as I know, I've never published or discovered a single novel mathematical result, and I certainly don't have any academic mathematical credentials. Very few of the humans would call me a mathematician.
Everyone is born incapable of carrying out self-care tasks. Some of us remain that way for our entire lives, but most don't. I haven't observed a strong correlation between mathematical ability and potty-training or cooking ability, so surely any community of mathematicians would have enough people who could cook a meal that they'd get along okay, in the improbable scenario where they were forced into strict autarky.
Duels are not consensual except in the sense that it's consensual to surrender to the police when they tackle you. Struggling against the police, or fleeing the duel, is overwhelmingly likely to get you killed.
I'm not sure where you're getting this idea that I'm "shit-talking non-mathematicians for taking senseless risks"; one mathematician I know went to Italy for a week to stay in the house of a man she'd just met in Argentina to dance in his tango show, while another juggled his baby to illustrate a lecture about siteswaps (and, perhaps more shockingly, gave up tenure for the baby's mother). I think mathematicians tend to take more long-term risks and less short-term risks than non-mathematicians. None of those examples is quite in the same category as "he grabbed the cop by her bulletproof vest", for example, which is something I saw a non-mathematician do as I helped the cops to arrest him.
What I'm shit-talking non-mathematicians for is killing mathematicians, burning the Academy and the works of the Mohists, destroying the German universities in the service of a stupid self-congratulatory racist ideology, and destroying democracy in America for the same reason. None of those amount to "taking senseless risks"; their undesirable results were nearly guaranteed and indeed intended by the perpetrators.
You're not wrong about the insufferable superiority complex, but you ought to consider the way in which my "tirade" is actually correct, even if my insufferable superiority complex annoys you. As a mathematician, you undoubtedly have a great deal of experience changing your mind after hearing arguments from people you don't particularly like. I suggest you try doing it in this case.
> Duels are not consensual except in the sense that it's consensual to surrender to the police when they tackle you. Struggling against the police, or fleeing the duel, is overwhelmingly likely to get you killed.
The history is quite unclear with regard to the fateful duel of Galois, and historical record suggests that it's quite possible he was the one who laid the challenge!
> As a mathematician, you undoubtedly have a great deal of experience changing your mind after hearing arguments from people you don't particularly like. I suggest you try doing it in this case.
I admit that I'm wrong when it's demonstrated that I'm wrong. This is common among mathematicians, and makes me insufferable in my own way. I would suggest you reconsider your characterization of the downvotes you've received -- multiple mathematicians are responding to you, and there's lots of us here on HN: your audience is not comprised of torch-wielding villagers. And yet you continue to dig in -- this sort of conversation is undesirable here, and I'd recommend you to consider the site guidelines and your fellow conversational partners' opinions before continuing. (I'll desist after this comment, and bid you farewell)
> Duels are not consensual except in the sense that it's consensual to surrender to the police when they tackle you. Struggling against the police, or fleeing the duel, is overwhelmingly likely to get you killed.
That's not how duels work. A challenge for a duel is usually issued in response to a perceived insult or injury to one's honor, and the request for a duel would often be delivered in writing. The only penalty for refusing a duel is the attendant impact on social standing--you could be seen as dishonorable or cowardly for refusing a duel. And even if you agreed to a duel, you might be able to get out of it simply by being disagreeable as to the actual conditions of a duel.
That definitely was not a thing I had in mind, no, although I'm sure it has cast a shadow over the particular flavors of honor society I've had the displeasure of being subjected to — thanks to Hollywood, if nothing else.
My comment above, in a text color that's easier to read:
Why should mathematicians want non-mathematicians to care? The evidence to date shows that non-mathematicians do things like starting wars, electing Trump, dying of heroin overdoses, circulating conspiracy theories about climate change, sentencing Socrates to death, chopping down the Academy for firewood, putting Archimedes to the sword, burning the books and burying the scholars under Qin Shi Huang, burning Giordano Bruno, killing Galois in a duel, only recognizing Leonardo for his paintings, stripping the German Jewry of their professorships (those they didn't simply murder first, like Gödel's mentor Moritz Schlick), and drugging Turing until he grew breasts and killed himself. The best the mathematicians can hope for is to evade the attentions of the non-mathematicians so they can be left in peace with their theorems and their olive groves. The theorems are true and beautiful whether the non-mathematicians care or not.
Governments burn libraries. Governments manifest the will of the common people.
I, too, believe that academia has lost its way. Over the entry of the Academy it said, "Do not enter, non-geometers." We should return to that policy; allowing theologians and such peddlers of nonsense into the academy was an unavoidable concession during medieval times, but it is one we should walk back.
And the part below, which apparently people also want to silence:
Mathematicians are perfectly capable of doing all those self-care things, as monks do in every monastery. (By contrast, non-mathematicians are unable to build anything larger than a small hut without help from mathematicians in the form of geometry.)
I don't know of a single mathematician who has ODed on amphetamines, although of course amphetamines have been popular with mathematicians since they were discovered; and I know of only one who voted for Trump (Dan Kleitman), although undoubtedly others exist. The doses of amphetamines conducive to doing mathematics are about two orders of magnitude lower than the lethal doses, so it seems unlikely that someone who takes them to improve concentration rather than for euphoria would OD accidentally, as heroin users frequently do.
Funding is only necessary to the extent that it helps keep the torch-wielding villagers away from the gate. To the extent that it subjects mathematical research to political tests, it is not only unnecessary, but counterproductive.
If my filter bubble includes Bruno, Socrates, Mozi, Gödel, Turing, and Archimedes, I think its radius is adequate.
I think the downvoting of my "tirade" to -2 [outdated: now -4] has shown that non-mathematicians hate and fear mathematicians, think that all those killings of mathematicians I listed were reasonable and justified, and would like to silence any criticism of them.
