Hardy would agree with the viewpoint that you espouse but it would be pushed back against by Arnol'd, Poincare, Gauss, Von Neumann, and even Grothendiek: Arnol'd and Poincare were vituperatively against the division between "pure" and "applied" mathematics; they considered mathematics and physics interchangeable, and Arnol'd lamented that the field had lost a large amount of funding/prestige/relevance due to groups like the Bourbaki that took a purely aesthetic view; Gauss had a critical view of problems like Fermat's last theorem (he felt that you could construct infinitely many such problems, and felt that attempting to prove it was a generally useless endeavor), along with outright calling pure mathematics worthless; but while Von Neumann and Grothendiek were more moderate, both were critical of the field losing motivation/quality as it strayed away from empirical science into—quoting Von Neumann—"abstract inbreeding".
Arnold's polemics are perhaps the most infamous and easily found online (see "On Teaching Mathematics"), but the written opinions of Poincare et seq. are also easy to find. Even today the vast majority of research funding for mathematics, at least in the United States, is dolled out for highly applied fields like partial differential equations. The field does not even close to unanimously (contemporarily or historically) "explicitly take pride" in working on problems that have no obvious application, or being a "jobs program for nerds": the notion of such "pure" or "nonapplied" mathematics is at the very least a highly fractious and controversial subject, with a number of big names taking opposing viewpoints (often vehemently).
I think your picture of the field is over-represented on the internet, much like the fixation on certain niche fields: Category Theory, Homotopy Type Theory or, worst of all, outright dubious fields like Geometric Algebra; fields with a large number of online promoters, but with much less funding and relevance in the actual academic space. Of course there are reputable people with PHDs that feel this way,—but I can only imagine that there's a legion of tyros, pop math consumers, and undergraduate students who disproportionately promote this viewpoint.
Am I misunderstanding your post?: you're implying that HYPSM increase their matriculation by ten times? These "elite" colleges,—one of which I've attended for graduate school,—have serious issues already with becoming degree mills; degrees have depreciated enormously in value over the last several decades: consider the collapse in being able to find a tenure track research position, even from one of these colleges. If we wanted elite colleges to provide the benefits that they are supposed to; then we would, if anything, want to reduce matriculation.
Stanford,—and I would hazard a guess many other HYPSM schools,—are already minting out too many students; this is especially true when it comes to non-PHD masters degrees, which are essentially an unbecoming cash cow for departments. Actual "quality of education" mostly comes from a low staff/student ratio and direct access of students to elite researchers: this difference in education mostly takes the form of better research labs to work in, with some spillover into office hours; increasing matriculation would only lead to more auditorium-sized classes that are run by lecturers or postdocs—these classes are essentially at the same level as trudging through online material.
Your proposed "solution" would have a Procrustean effect: I can't speak for Chinese or Indian universities, but while schools like UC Berkeley, UT Austin, University of Michigan, et seq... have good reputations, they have a noticeably lower reputation than the ivy leagues and certain private colleges like Stanford, MIT, and Caltech—and a worse reputation for being degree mills.
If you think that Stanford having 180,000 students matriculated will give everyone a quality education, then I think that you fundamentally misunderstand the markers that make an in-person education higher quality. The only benefit that would come of it would be popping the degree bubble and prematurely ending the current moribund trajectory that universities are on; where they are already treating degrees as if they were artificial-scarcity NFTs, rather than providing the actual scarcity that is access to,—and direct training from,—high-level researchers.
Stanford has a $40 billion endowment for 8k undergrads. UCLA has a $10 billion endowment for 34k undergrads. Naturally, the class sizes will be much larger. The UC system does not put 100% of students at UC Berkeley and UCLA, they distribute it across several campuses and distance education and maintain a leveling system that helps promising research talent be in the room with experienced researchers
Despite rising costs, a college degree is still a positive lifetime investment for students (not to mention the positive externalities educated populations have on society at large). The bulk of US college students attend colleges who do not have the resources to build high-quality, industry relevant curriculum, train teachers to teach with modern pedagogy, and efficiently manage dorms, student affairs, and other administrative infrastructure
HYPSM choosing to share land, curriculum, expertise, and administrative infrastructure through network'd partnerships would lead to massive economies of scale and a broad reduction of educational costs. Another way to think about this - is one city of 1 million people more efficient to run per capita than 10 cities of 100k people? The answer is a resounding yes due to urban scaling. Colleges are effectively mini-cities
"I think that you fundamentally misunderstand the markers that make an in-person education higher quality" -> I founded an in-person college with regional accreditation that had a lot more 1:1 and small group teacher time than HYPSM and an average starting salary on par with CS grads from these schools. Our alumni have gone on to become YC founders and can be found at most top tech companies and startups
It is a choice to value exclusivity for exclusivity's sake (eg. withholding JSTOR data from students of colleges who can't afford those costs). The best institutions (eg. YC, Apple) care a lot more about what you can build than what school you got into at age 17
The solution is to hoard ideas, organize them, review them and experiment. I for example suspect that giving students more time for everything would improve results. I have nothing to show for this but it would be good science to run the experiment. Unless of course there are better sounding ideas that should be tried first.
"The bulk of US college students attend colleges who do not have the resources to build high-quality, industry relevant curriculum, train teachers to teach with modern pedagogy, and efficiently manage dorms, student affairs, and other administrative infrastructure"
I would like to see a source on this: your claim appears ungrounded when considering American colleges.
It is generally understood in the industry that around half of universities are in significant debt / financial distress (started prior to Covid // the demographic peak // recent DoE cuts). Graduate underemployment is also quite high due to a lack of alignment (or perhaps slow alignment) of degree programs to career outcomes
Can we take a minute to consider that degrees aren't supposed to be aligned to career outcomes to begin with? That's what vocational schools are for. Somehow academia became conflated with both a job training program and an adult daycare service and (at least in the US) the result is a confused, inconsistent, expensive mess whose exact purpose isn't clear.
You want them to go back to being finishing schools for the wealthy, as they were before Hopkins (funnily enough) founded the first institute in the US that would be seen as a form of a modern university today?
For people who aren't financially independent, education is a means to an end. Pretending that's not the case or worse, shouldn't be the case, is absurd to ask of anyone running a school and highly damaging to society in general, and the mix of "vocational training" and "classic academia" provided by most US universities seems to work extremely well.
You're putting words in my mouth. I merely pointed out that they have a very confused mission thus I think it is not surprising that there is dysfunction.
We have vocational trade schools. We have professional guild schools (medical, dentistry, etc). At least some subset of students attends school with the intention of becoming professional researchers (ie pursuing a PhD, then a postdoc, then finally general employment).
I think it would be reasonable to expect undergraduate institutions to set unambiguous goals for each program. Students should know what they are signing up for. It would be fine to graduate with a certain amount of time spent explicitly on general education and a certain amount spent explicitly on vocational training with a specific target.
If you claim that education is a means to an end then what of (for example) history majors? I think the bachelors diploma itself is what became a means to an end much to the detriment of "pure" academia. The CS program at my undergrad spent time teaching us how to use version control. That's fantastic for a professional programmer but how does that have anything to do with CS as an academic pursuit? You can literally do much (perhaps all) of actual CS with nothing more than a pen and paper.
> You're putting words in my mouth. I merely pointed out that they have a very confused mission thus I think it is not surprising that there is dysfunction.
I'm not trying to put words in your mouth, but I don't see what other conclusion can be drawn from your statement.
> We have vocational trade schools. We have professional guild schools (medical, dentistry, etc). At least some subset of students attends school with the intention of becoming professional researchers (ie pursuing a PhD, then a postdoc, then finally general employment).
> I think it would be reasonable to expect undergraduate institutions to set unambiguous goals for each program. Students should know what they are signing up for. It would be fine to graduate with a certain amount of time spent explicitly on general education and a certain amount spent explicitly on vocational training with a specific target.
I agree that undergraduate institutions should be required to set unambiguous goals for each program, but what are done with the many, many attendees who have no goals for themselves beyond "go to college and get a job when I'm done"? I think there is value in having these multi-faceted institutions that are a combination of finishing school, classical academic study, and vocational training that can (and do) produce sufficiently educated and mature adults who can independently function in society.
That is the mission of the undergraduate portion of the Arts and Sciences school at basically every college/university. Professional schools have a slightly more specific mission.
> If you claim that education is a means to an end then what of (for example) history majors?
Excellent question, and it's one for the history department to answer. Maybe things stay as they are now and it's a home for the many people who don't have specific career goals while attending college, and that is their goal.
> I think the bachelors diploma itself is what became a means to an end much to the detriment of "pure" academia.
"Pure" academia only exists for those with a patron (which could be themselves), which is non-existent at any meaningful scale.
> The CS program at my undergrad spent time teaching us how to use version control. That's fantastic for a professional programmer but how does that have anything to do with CS as an academic pursuit? You can literally do much (perhaps all) of actual CS with nothing more than a pen and paper.
Good for them, because anyone applying their CS knowledge in any capacity needs to know that.
If you want to go major in purely theoretical CS at a place that offers only courses that are effectively a specialization of a math major, there is value in it but the department offering them has to answer the same questions as the history department.
It seems we largely agree. For example I wasn't criticizing the CS program at my undergrad, simply observing the mismatch between the label on the tin and what was actually inside.
Observations of inconsistencies, dysfunctions, and similar are not necessarily calls for any particular course of action.
> I'm not trying to put words in your mouth, but I don't see what other conclusion can be drawn from your statement.
I merely observed that many of the issues people point out can be traced back (at least IMO) to having a set of confused and inconsistent goals. I wouldn't expect it to be a particularly controversial observation to anyone who's had significant contact with US academia within the past few decades.
> what are done with the many, many attendees who have no goals for themselves beyond "go to college and get a job when I'm done"?
They probably don't belong there. Most of them only attend because you need a diploma to land a job. Not because the education is particularly useful to the job, but rather because of what diplomas historically signaled about a candidate before everyone had them. Now it seems to just be a holdover (ie we require them because we've always required them and at this point everyone worthwhile has one). At least that's my (admittedly quite cynical) view.
I'm all for a more educated populace but if that's what we want then we should directly implement that.
I notice that you didn't address my remark about "adult daycare service". The presence of directionless "students" attending only to tick a box has serious negative impacts on the rest of the system. Add in student loans that can't be discharged and you've created an absolutely bizarre and (IMO counterproductive) set of economic incentives.
> I notice that you didn't address my remark about "adult daycare service". The presence of directionless "students" attending only to tick a box has serious negative impacts on the rest of the system. Add in student loans that can't be discharged and you've created an absolutely bizarre and (IMO counterproductive) set of economic incentives.
I didn't, because it seemed like a cheap insult. I don't know that directionless students have serious negative impacts on the rest of the system. They can have serious negative impacts on themselves due to student loan debt and a lack of a financially viable skillset when they stop attending college (with a degree or not).
What do you propose people who are 18 - 22 or so do to figure out what they want to do with the rest of their lives? And I'm not defending the status quo, which certainly can be improved.
Classes and more importantly practices get watered down to accommodate them. The situation gradually looks less like university of the 1950s and more like highschool.
Loans that can't be discharged removes lender hesitancy thus removes some degree of downward price pressure from the market. Institutions then have an incentive to capture this money due to the sheer quantity of it - ie not to let marginal students wash out. Hence the changes.
They even start attempting to attract based on amenities rather than prices. I won't belabor the subject. Others have written about it in incredible detail over the past several decades.
> What do you propose people who are 18 - 22 or so do to figure out what they want to do with the rest of their lives?
I don't know but bending what were once rigorous academic programs to accommodate them seems like the wrong answer to me. Do these people see any real benefit from taking on debt rather than working for that period? It seems to me the "benefit" is the diploma and that the requirement of a diploma to apply for a job is most often an arbitrary one these days.
As a thought experiment. Is there any particular reason an AA wouldn't have sufficed for the jobs that don't require specialized knowledge?
> Classes and more importantly practices get watered down to accommodate them. The situation gradually looks less like university of the 1950s and more like highschool.
Fair, though the solution there is to just flunk them out.
> I don't know but bending what were once rigorous academic programs to accommodate them seems like the wrong answer to me. Do these people see any real benefit from taking on debt rather than working for that period? It seems to me the "benefit" is the diploma and that the requirement of a diploma to apply for a job is most often an arbitrary one these days.
I'm not convinced this is happening at the scale you think it is, but higher education is an arms race to some extent and you'd need to get all parties to agree to de-escalate, but only for the ones who don't get much value out of the experience (a group that is somewhat hard to identify a priori).
> As a thought experiment. Is there any particular reason an AA wouldn't have sufficed for the jobs that don't require specialized knowledge?
For the jobs, probably not. I still think a portion of the "college experience" is just maturing, which I agree could be done while working in theory but there is some personal opportunity cost there.
It's not an easy problem or one that can be solved individually IMO. Something like mandatory public service could be an answer, but I don't have high hopes of that being enacted.
As I understood the grandparent post, the idea is that a highest-level university should 10× its student throughput, and 9 other, lower-level universities would be made redundant by that.
This would make sense if all what an elite university did were providing elite-level education. Of course exclusive schools provide other benefits, often more valuable for the target audience than the education proper: a highly filtered student body, networking and bonding with the right, upwardly mobile people (either mega-talented, or just smart kids of rich and influential parents), a luxury-grade diploma that few can afford. Maybe you could theoretically 10× Stanford or MIT, but likely not Yale.
I see the value of the students, it just seems like an odd thing for a government to subsidize via NIH/NSF funding. We don’t really have anything analogous to that in Canada and it just seems awfully weird that it exists in the US without the “it’s older than the country” excuse that Oxford/Cambridge have.
>Actual "quality of education" mostly comes from a low staff/student ratio and direct access of students to elite researchers: this difference in education mostly takes the form of better research labs to work in, with some spillover into office hours
I don't agree with this at all. Quality of education imho comes from being surrounded by fellow elite students so that the pace of the syllabi can remain high.
lower tier universities have excellent faculty, they are selected from applicants from the elite universities as well as excellent students from lower tier universities who have floated to the top. Their problem is, as the elite-ness of the students goes down, the pace needs to drop.
Not trying to be a jerk, but we see the same thing in athletics, elite athletes are significantly above the next tier, and so on. the worst professional team can beat the best college team, because the worst professional team is still made up of the cream of the college teams, with experience (i.e. more education) added on.
at a lower tier university, a dedicated student can still work in labs if they want, but as you move down the tiers you simply get fewer autistics and more partiers. University of Michigan is an excellent univeristy, but do you think the students are studying on weekends, like they do at MIT? no, they're not.
>Their problem is, as the elite-ness of the students goes down, the pace needs to drop.
Only if the school mandates a quota of passing grades. Not sure about HYPSM but anecdotally at my (Canadian) alma mater no such quota existed: the pass rate for 3rd year fluid dynamics was in the 40% ballpark, for example.
I don’t know what the hell you’re talking about, but neither do you. Students at universities ranked similarly to Michigan absolutely do spend a significant amount of time studying on the weekends, especially if they’re not business majors. And MIT has parties and pranks, too.
I mean, is the goal of an elite college to educate? Or is the benefit to sift through the population and pluck out its masters?
I don't really care that UC has a lower "reputation" than Harvard or Stanford. The fact is, the UC system has produced more fundamental research and more actual value for the population and the world at large than Harvard or Stanford. Even if a UC degree is not quite the "golden ticket" that an Stanford degree is.
Concentrating individuals into a smaller and smaller elite benefits them and only them. The U.S. has done this with capital allocation in its economy and it has and will continue to be a century long arc bending toward utter disaster.
I totally agree. Folks here seem to be under some misapprehension that elite = better education. Based on my experience earning my PhD at a public R1 and then working as faculty at a selective private institution, this is not the case. For starters, just consider the incentives for grade inflation at a private vs a public institution. Harvard has famously out of control grade inflation.
My public alma mater was a tremendous force multiplier for upward mobility. Many of my peers were first generation college students. They’re now scientists, doctors, and engineers. Few of them will become famous—they mostly just make the world tick.
My current private institution concentrates already wealthy people. These folks mostly go out and become consultants. They’re consumed with the idea of becoming “thought leaders.”
Which one really provides more value? I have strong opinions.
Pretty much agree but may I also add that Santa Clara County would probably not allow Stanford to increase its student body by any real sizeable amount due to restrictions in traffic, building, parking, etc, etc.
I don't think they're suggesting we reduce the amount of faculty. They're suggesting that you ask all the faculty to share less space, increasing the efficiency of the real estate holdings. Also by reducing the number of schools, you reduce the amount of expensive ancillaries.
Great article. I recently went through Crying of Lot 49 by Pynchon; the sequence of eccentric personalities in this article reminded me of a similar section that Pynchon has in the bay area. Unfortunately the personages interviewed here are not only real but climb beyond any fictional parody.
You would forget that this would cause exponential growth: in a couple decades, a single lab could produce more people seeking tenure track than an entire country's worth of positions; there need to be smarter ways to provide the requisite labor for science, since this is clearly unsustainable praxis. Running a pyramid scheme of this magnitude is only going to cause an implosion—which we may already be witnessing.
There's a big difference between cutting off all foreign-born talent—and addressing the serious issue of graduate school turning into an immigration racket; the current issue with graduate degrees is a very close mirror to the issue with H1b worker visas. The abuse of both systems has harmed Americans—and to some extent the long-term health of the tech industry and the academy.
American is built on immigration, and nearly all of us are immigrants or very recent descendants of immigrants. How in the world has immigration harmed Americans?
It's a NIMBY policy, pulling up the ladder. It's rooted in zero-sum thinking, that can't imagine "make the pie bigger" and can only imagine a fixed-size pie where their slice is getting smaller.
Given the impact the economy has on people's lives, it's an understandable fear. There's plenty of evidence for this not being the case (and in fact evidence for the "brain drain" strategy having substantial positive impact), but getting people to let go of a fear typically requires more than just hard evidence that it's unfounded.
(There's a separate branch of that fear, that imagines immigrants to be a drain on public assistance programs, but there's plenty of evidence that that is not the case.)
(Also, as always, policy is complicated and no comment that fits on a page is going to capture all the nuance of it or facets of it.)
I think if you're going to argue that we shouldn't have contemporary immigration because of the harm to native Americans, then you should show what harm is caused _now_, that native Americans actually oppose immigration, and probably that you support other ways of helping them like giving them land back.
Who cares if it's an easy path if the person graduates with the degree. It should be easy to immigrate here if you get an advanced degree. If you get a degree not in demand then you should be just as unhireable
A degree from Bullshit University in bullshitting should not grant any extra immigration rights because it doesn't mean anything. Although... the current administration must have high demand for bullshitters.
I know absolutely nothing about string theory, or the culture of high-energy physics, but I don't buy the pecuniary argument you are making. You aren't considering the downwind effects of allowing academic rot. The Bourbaki—and their acolytes—also sponged up only a tiny amount of academic funding, but a fever in the pulpit can spread out into the pews; we've seen the "New Math" paradigm damage a generation of primary-and-secondary-school students. Even today, we have issues with engineers not understanding that a derivative is a slope and an integral is an area—due in no small part to a cartel of bad actors in mathematical research. Allowing bad behavior in high-value and influential positions has consequences beyond a waste of government expenditure; a president could turn a democracy into a banana republic, and we would have issues beyond his salary of a few hundred thousand dollars being wasted.
How many primary school students can't add fractions because string theory may be a less promising approach to a ToE versus loop quantum gravity or geometric unity? I know nothing about this stuff. You know nothing about this stuff. Since we both do know about the Bourbaki school of mathematics despite having different opinions on the value of building mathematics upward from foundational principles I'd say we are in the top .5% of the planet re general mathematical/scientific literacy. So I don't buy that even if string theory is wrong there is some massive spillover effect.
I was driving from Sacramento to Reno, and there was a bad snowfall up in the mountains. I ended up getting struck in a small country town, and couldn't get up an iced hill. I thought I was going to be stuck there the entire day (at least), but a stranger pulled up in their pickup truck—with four wheel drive—and towed me up the hill and to safety. That's the most significant act of kindness I can remember—from a complete stranger.
This is cool to look at, but isn't this just obtained by taking the absolute value of the first equation minus the second? These are very pretty visualizations—but trying to present them as some kind of "sea change" in perspective feels unhelpful.
I'd like to know about your experience in modern academe. I've gone to top-ranked schools in America (UT Austin, Stanford). My experience with the average foreign graduate student is not "top research talent." Most of the time you have a mid-level grifter that wants a green card, a work visa, or something else that simply lets them immigrate here. The work that they produce in exchange for that is low quality. The decline in the quality of graduate degrees may in many ways mirror the issues that tech workers have had with H-1Bs: they were intended to attract high quality talent, but became a corrupt racket.
Wonderful, now we're at a point where Hacker News has people defending a fundamentalist antisemitic hate group that's quite literally performed suicide bombings and launched rockets at civilians.
Maybe you haven't felt terror from them because you aren't one of the innocent Jewish civilians who have been deliberately targeted. Can you go back to reddit where your similarly deranged opinions are tolerated, and stay off of what is meant to be a relatively sane forum?
Arnold's polemics are perhaps the most infamous and easily found online (see "On Teaching Mathematics"), but the written opinions of Poincare et seq. are also easy to find. Even today the vast majority of research funding for mathematics, at least in the United States, is dolled out for highly applied fields like partial differential equations. The field does not even close to unanimously (contemporarily or historically) "explicitly take pride" in working on problems that have no obvious application, or being a "jobs program for nerds": the notion of such "pure" or "nonapplied" mathematics is at the very least a highly fractious and controversial subject, with a number of big names taking opposing viewpoints (often vehemently).
I think your picture of the field is over-represented on the internet, much like the fixation on certain niche fields: Category Theory, Homotopy Type Theory or, worst of all, outright dubious fields like Geometric Algebra; fields with a large number of online promoters, but with much less funding and relevance in the actual academic space. Of course there are reputable people with PHDs that feel this way,—but I can only imagine that there's a legion of tyros, pop math consumers, and undergraduate students who disproportionately promote this viewpoint.