imagine yourself living in the 1700s. how would you justify Newton and Leibniz's work on calculus?
all maritime engineering and trade was done with geometry and arithmetic at the time. there were no practical applications, not for likely at least a century until hydrodynamics were incorporated into shipbuilding
now look at today. how many of our modern technologies rely on the field having been birthed? that could only exist because of even further decades-worth of antecedent refinements, extrapolations, applications that had, at their time, no direct utilitarian cause?
there's no KPI to be derived from any academic field of study at the bleeding edge of theory. theoretical underpinnings lead to practical applications much further down the line after many paradigm shifts
semiotics and cultural capital as theoretical concepts is another example - at the time they were purely seen as navel-gazey literary theory work. these days, half a century later, they're in wide use (for better or worse) in marketing and advertising - they birthed the whole concept of 'branding'
not everything needs immediate, quantifiable justification. to believe it does indicates a need for a period of self-reflection, to figure out how and when you became so heavily influenced by the MBA-brained propaganda that the world should revolve around the quarter-by-quarter creation of capital
They didn't have to, as there were no state grants or public research funds for mathematics during the 17th century.
Newton supported himself from his inheritance throughout the Great Plague, while he invented calculus, and then from flat salaries as teacher, then flat salaries from working at the London Mint. He later became fabulously wealthy after his appointment as Master of the Mint.
Leibniz was a diplomat, then a librarian.
Since the state was the wealthy privates, for all practical purposes there was by patronage (or the wealthy elite themselves).
Easy yes: Let's impose a tax on everyone to support at least one mathematician.
Easy no: Let's impose a tax on everyone to support one billion mathematicians.
Where are you going to draw that line? How are you going to convince a majority of voters that you're drawing it at the right place?
Do we support people who aren't using vaccines and are intentionally infecting themselves directly (measles parties)?
Do we support people who are intentionally using axe instead of chainsaw? Police officers and stormtroopers who are intentionally using knife instead of a gun?
With civilization and technology we do loose some mental capabilities - like say the part of the brain Amazonian people use for extremely skillful face recognition we do use for reading/writing while loosing that face recognition skill level that those people in the jungle have. So goes the medieval way of doing mathematics (it is a pity though - I liked it and hoped that mathematics will fall among the last, yet it happened to be among the firsts)
> Do we support people who are intentionally not using GPS and are still using paper maps? Or even the people who do it without any maps, just from their memory?
Yes. We do - it's a sport from way back and ongoing - a good many people want to retain non GPS navigational skills.
> Do we support people who are intentionally using axe instead of chainsaw? Police officers and stormtroopers who are intentionally using knife instead of a gun?
Yes. We do. Proficiency in multiple weapons and non weapon combat is a basic part of service training. Axes and wedges still have their place in tree felling.
a car or a future starship wouldn't climb a tree better than ancient human.
and you don't see any issue here? When it takes people 2 years to understand a proof it means that the old ways are done, they hit cul-de-sac. Like in many situations, it is the highest point as well as it is a crisis at the same time.
>why shouldn't an AI system be able to replace a 1870s mathematician
my point isn't that whether it would be able to replace - i think it would. My point is that it doesn't matter. The tool is needed for the 2020s math with those proofs taking 2 years, not for the 1870s math with proofs fitting a several pages letter.
That is math of 1870s https://en.wikipedia.org/wiki/Cefn-coed-y-cymmer#/media/File... and that is what we need in 2020 https://en.wikipedia.org/wiki/Huajiang_Canyon_Bridge#/media/...
Countless other mathematical curiosities were developed in the 1700s -- and forgotten. Calculus just happens to be the one that found practical applications later, so that's the one that's well known today.
It's difficult to draw the conclusion that "every possible branch of learning ought to be funded" by appealing to "later practical value" based on this cherrypicked example.
On the other hand, clearly _some_ novel theoretical work with no apparent immediate value _does_ yield real world benefit later.
Since we lack the resources to fund every PhD with a crazy theory on what the next new subfield ought to be, how do we decide?
Seems like AI could help massively there, by removing a huge bottleneck around technical elaboration and application seeking.
No, it's an example of why you have to allow people to pursue what at the time look like "curiosities", even though most of them don't go anywhere--because the very small portion that do go somewhere, end up changing the world, and we don't know in advance which ones those are going to be.
It's quite true that the funds we have for this are a finite resource. But that doesn't mean that "foreseeable practical applications" is a useful filter for how to deploy that resource.
Of course someone was. Newton and Leibniz weren't living in autarky an some island. They had an income stream that was taken away from somewhere else and given to them so that they could afford working on their pet projects.
The fact that it's not publicly funded doesn't change the fact that there's still resource allocation happening.
This is an anachronism, you're projecting modern social organization to an era that worked very differently.
For the kind of research where benefits accrue to the inventor (or her employer) and others can be excluded so that the benefits don't 'spill over', then private companies can fund it.
For the kind of research that spills over, you can just let the tax payers of that other country foot the bill. Eg the US can free-ride on Chinese research, and if having mathematicians in the population is good, the US can offer green cards to whatever has a math degree from a good enough university.
There might be some intermediate research that has just enough spill over that a company won't do it, but a country might, should be a rare creature. And differently sized countries should have different sweet spots: some companies are bigger than some countries after all. But I don't think we see different countries select the research (mathematical or otherwise) with an eye towards exactly tailoring spill over.
>useful filter
There's also "useful friction" as _almost_ imagined by Tao here
https://youtu.be/svl_1upFpQo?t=25m11s
We can't know in advance, but something like the "weird cadence" that arises when 2 skilled humans try to do a threesome with an AI..
could be reified into a local measure (eutripsis) of how likely advances (conceptual or otherwise) are in the midterm
1. You may not agree, but some people will argue that knowledge is worth accumulating in itself. We fund astronomy well beyond the solar system despite there being no real prospect of practical applications.
2. The value of calculus justifies the cost of all the curiosities. The economic benefits of funding lots of "curiosities" was well worth the few that were useful.
There are a lot of immediate practical benefits to learning more about the physics and chemistry of the universe beyond our solar system.
can you imagine chucking all of computer science away because Babbage's thinking machines and Lovelace's programming cards didn't really result in meaningful capital gains here in FY26Q3? or, a more realistic example - imagine biology and genetics today if Mendel's discoveries had been published in a more widely read journal, if he hadn't been outright dismissed for his mathematical approach. or Semmelweis' advocacy of antispetic procedures that flew in the face of the then humors-based understanding of medicine in the 1800s - how many lives would have been saved between then and when Germ Theory finally took off decades later?
it's ironic to me that it's often the same people who'll adopt the logic of banning reproductive rights on the off chance that someone very unprepared to have a child might birth someone who can cure cancer in spite of the probabilistic evidence of SES being highly correlated with educational attainment (eg that graph of the income bracket that the parents of all Nobel Prize winners start with). and yet when it comes to the actual nascent research and development required to pave the way for larger discoveries, that's seen as totally pointless and not worthy of funding. it's truly flabbergasting
In saying that, in the spirit of a good faith argument, is there value in temporarily deprioritising pure research in (current) times of funding drought?
Granted for the sake of argument. But our AI overlords are really good at accumulating that knowledge, and very patient in explaining it to us.
That is totally not true. I am sure you can hardly name even one of those "curiosities" that later turn out to be useful and not "free" (i.e. if not existed, wouldn't be invented on the spot as a tool for solving those particular problem that they end up solving).
Calculus (e.g. differentiation), for example, is mind-blowing when taking it seriously, and not only useful.
The idea of "speed at an infinitely short moment", for example, is philosophy!
It just so happens that certain kinds of mathematics are unreasonably effective in drawing parallels to the physical world, but as far as mathematicians are concerned those mathematics are neither better nor worse than those that do not correspond to anything tangible.
A sweeping generalization. I certainly know professional mathematicians who disagree.
Also: many consider “inter-connectedness”, not “tangible” to be a sign that a topic is interesting. That is, it touches branches of mathematics aside from its own.
Are you proposing that humanity should rely on AI to determine the fields of study that should be perused and those that should be defunded?
Why don't you first come up with an AI that can predict if the stock market will go up or down tomorrow, with 99.999% accuracy. Should be really simple as it only needs to answer what will happen tomorrow.
After that, come up with the AI that will predict how actions or non-actions today may affect outcomes 100 years into the future.
We already have examples of politicians relying on chatbots to understand problems. I wouldn't be at all surprised if, given a few more years, the above will be effectively the case without any deliberate effort.
Most of these aren’t even new inventions; read about the working conditions in the 19th century.
Define basic survival. Tantalum mine worker in the Congo who earns 22 cents per hour and raises his three children on that money, is he under "basic survival" level or below?
And to be clear, as a part of a society, are you ready to forgo your salary, except maybe 1 dollar per hour, to provide to other people? Why haven’t you done it yet?
The amount of money that current local economy can provide to everybody sustainably, given the appropriate arrangements in the system.
We have natural experiments of this: retirees, both early and otherwise. Do retirees during the first five years of their retirement "find productive work voluntarily" (your choice of words, not mine) in quantities that are comparable to what they did at work during the five years prior to their retirement? Not exceptional individuals, but on average.
I retired circa five years ago and spend my time doing stuff like walking the dog, drinking coffee and reading books, much like other retirees. My productivity is as close to zero as I can muster, and it is the rule, not the exception.
But also, in all honesty, if we can feed and shelter everyone on the planet with only a small proportion of the population engaged in productive labor, what's the problem with most people walking the dog, drinking coffee, and reading books?
Go on, please. Whatever argument you make, please account for early retirees as well.
> if we can feed and shelter everyone on the planet with only a small proportion of the population engaged in productive labor
But that is not the premise of the discussion at hand, though. My comment was written in this specific context:
>>> My argument is that most people only veg out because they are tired of a hectic work life, but if given the chance to coast for a long time they would find productive work voluntarily
On how to select what to fund in the future: find the brightest minds, fund whatever they want to do. That tends to work out in aggregate
It would have been worth what? Doing mathematical research at all? Nobody is suggesting we shut down mathematical research.
It doesn't justify a funding system that didn't exist / didn't fund those researchers. We need to come up with better reasons to fund such a thing.
The work that Newton and Leibniz did was in formalizing it and coming up with the notation that would end up being more widely accepted and applicable. It's very likely that the techniques would have been developed later to solve a practical problem.
It's not “survivorship bias”, it's merely the illustration that mathematics are a strong link problem: it's the strongest result that determines the impact of the field (not the weakest, like in weak-link problems).
You're effectively asking to predict the future hundreds of years in advance. Nobody and nothing can do that. With math, as with all science, you must be willing to accept that not everything will be a hit. There will be misses, and often the same person will generate both hits and misses, because it's fundamentally unpredictable what remains a miss and what doesn't over centuries. The best demonstration of this is that your own thinking here would've banned the invention of calculus: it didn't materially affect daily life for a solid century.
Really? Like what?
edit: this is either an unfalsifiable claim, because by "forgotten" you meant here is no extant knowledge or remaining record of it, or it's almost certainly nonsense and anything you could cite would be foundational to some area of modern mathematics, even if as a disproven counter theory.
Now, it's possible that Fermat thought he had a proof of his theorem, but that it would have turned out to be wrong. That happens sometimes. But he did not write it down on any document that has survived to this day, so we know that he had something that has been lost.
It's similar to history. We know that there are books, plays, etc. that used to exist, but that nobody knows today. Because other writings that have survived to this day quote from them. But beyond the quote, we don't know anything else about the play or the book or whatever.
Fermat's Last Theorem almost certainly isn't the only case of mathematical theories that we know were published somewhere but that we have no record of today. It's just the only one that I happen to know about, not being a mathematician myself. I'm sure there are some people on HN who know of others.
Ah yes, lets take the existing system that's already barely holding up and flood it with slop. What could go wrong?
> Since we lack the resources to fund every PhD with a crazy theory on what the next new subfield ought to be, how do we decide?
Do away with the perpetual uncertainty of the "will we or won't we continue to fund you" grant treadmill for practicing academics. Hold a yearly competition of academic prowess and intelligence open to any adult US citizen under retirement age. Award the winners a grant good for 40 years. If we allocated slots equal to 0.005% of the population each year (ie ~17k) that would represent 0.2% (ie 1 per 500) of the population in total at any given time.
Obviously I say that (mostly) in jest but clearly there are workable solutions if we approach things from a new angle instead of determinedly clinging to the status quo.
If it’s slop they can just safely ignore it and keep on doing business as usual
Survivorship bias is literally just how invention happens.
No one strikes gold on the first swing.
How can we hope to quantity the expenditure on math we've collectively forgotten? It's unknowable by definition. The only reasonable thing to do is to determine the value added after the expense paid. Even in a world where calculus is the only thing that we took away from the math of 1700s my guess is that this is still an economically beneficial calculation.
It's not "forgotten" in the technical sense that one _can_ still go dig into the dusty archives of any number of old university libraries, and review learned journals, diaries, commonplace books, personal correspondence, and so on from the 1700s that describe the mathematical work of the day in detail.
You can then systematically review that work, and test whether the claim that "nearly all mathematical output of the 18th century has been generally forgotten and never found any use."
I hypothesize that this experiment will show that nearly all of the mathematical output of the time long ago fell into oblivion. This is a falsifiable claim.
You redefine "forgot" to make it falsiable, but also neglect that you need to refute that some "forgotten" work didn't contribute to new work down the line.
As is almost all of human endeavor.
The direct use of that math to biuld better weapons. That math was/is essential to the development of modern artillery. The first tasks assigned most early computers were to calculate ballistic trajectories, and also tide tables which also have immense military applications. Math was and is a weapon.
This.
And ironically enough, the obsession for measurable successes at all cost is what drove 20th century communists regimes to their most catastrophic failures.
Thinking that mathematicians are now useless because they cannot continue publishing results that an AI couldn't is akin to Mao's claim that “bourgeois” intellectuals were worthless because they weren't busy driving agricultural yields up. We know where that ended…
If AI can bring forth mathematical discoveries much faster than academics, wouldn’t it behove society to use AI? It seems the me the tradeoff here is the benefit of all vs the ego of a few. I empathize with the struggle many math PhDs must be going through, and maybe I don’t fully understand the tradeoff as they see it, but I’m not convinced by the letter written by a few career, tenured academics.
That is a pretty weak point. Calculus from the very beginning was an applied math.
> how many of our modern technologies rely on the field having been birthed? that could only exist because of even further decades-worth of antecedent refinements, extrapolations, applications that had, at their time, no direct utilitarian cause?
Idk, about zero? I mean almost all of our modern technologies could exist perfectly fine even without previous decades-worth refinements and extrapolations of math theory. All the math tools that they would be needed would be created on the spot if they are required.
And Newton's calculus is rather an argument that is support that view: it is not like there was calculus, that had make describing of the world possible. No calculus was born as a tool to describe physical world from the very beginning.
Today, science funding comes out of the tax collected from everyone. The taxpayers want an explanation for how their money is spent. It could be, of course, vanity, just like it was before (taxpayer money is spent on sporting events, for example because people root for the athletes who represent them)... but, maybe there's a better way?
This is not the full story, but fits today's cartoon history caricature. In reality, there were also salaried employees who were teaching or working on developing practical applications, there were church fundings, the universities like Göttingen etc. Not all were particularly rich, Euler came from a modest background etc.
Different academic disciplines are very different, and most don't engage in the same kind of black-and-white problem solving that mathematicians do, where you either have solved a problem or you haven't.
But all insist that you engage in some sort of outwardly visible production in your field: books, articles, conference presentations, public lectures, exhibitions, performances, something.
We haven't yet figured out what that should be, but I presume that everyone would agree that this should continue. As one possible model, check out this blog post of Terry Tao's, where he gives his own perspective on the recently proved Jacobian conjecture.
https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the...
When computers can solve the underlying actual problem, this sort of work seems likely to rise in value, and be something which a greater number of mathematicians engage in.
Consider the "Jacobian conjecture counterexample": the work doesn't simply end once Terence Tao explains the computer-generated proof to a wider specialist audience.
1. I assume that the counterexample will give rise to a host of new questions, each of which will in turn need to be resolved. In the long run, the process of formulating questions might also be automated by AI - but likely not within the next few years to such an extent the growth of knowledge results in a decline in relevant questions.
2. Mathematicians will have a great deal to do in terms of meaningfully formalizing results within Mathlib - and hopefully Isabelle/HOL and other systems as well. From what I have read, the way current AI formalizes theorems makes them unsuitable for these libraries. I envision this as an undertaking not unlike the development of the Linux kernel. Throughout this formalization process, there should always be a human who has actually grasped the reasoning to ensure the AI hasn't simply exploited a flaw of the system.
3. Physics, chemistry, and many other sciences are currently benefiting from AI to a lesser extent. I anticipate significant changes at the interface between mathematics and other sciences as the body of mathematical knowledge expands dramatically. I cannot imagine this resulting in anything other than an increased workload, at least for the next few years.
Isn't it likely that mathematicians' workloads will initially rise rather than fall, provided they are willing to accept a shift in the nature of their tasks?
Your (1) is most certainly true.
As for your (2), most mathematicians I know have at most a passing interest in formalization, Mathlib, and Lean. My understanding, which is admittedly quite superficial, is that AI is actually getting quite good at translating human-readable mathematics. I could be mistaken about this, but even if there is a lot of human work to do, it sounds like a lot of anal-retentive oversight of work you didn't do yourself -- the sort of task that academics love to complain about!
Perhaps human interest in Lean will grow, but I don't anticipate it occupying the attention of more than a small slice of the community.
Your (3) is an interesting question. I work on the theoretical rather than applied side, but what you describe might very well be true for applied mathematicians.
Where I see models having a huge impact is in simulation code development.
One blocker for years now has been the adoption of GPUs. LLMs can fairly successfully and very quickly port to GPU and suggest/implement useful optimisations. Once it's verified, a code can go from anywhere between 2x to 1000x faster (mainly because CPU codes are so poorly optimised). Some science can reach much greater problem sizes, while some can run the same problems in hours rather than months and both can be revolutionary. Even more than that, LLMs seem to be finding fundamental performance bugs in both open and closed source core libraries so there's a bit of a whole-ecosystem uplift.
Can't comment on the more theoretical, less computational applied maths impacts!
My vote is for interpretive dance. Give the laity something for their money.
I would not presume this at all.
Every brick in the house you live in has been put there by a worker. The food you eat has been cultivated by a farmer. etc. etc.
You must explain what you give back to these people. It's fine if it's in a roundabout way, but it can't be nothing.
And the presumption isn't that there's something. The presumption is that there's nothing, and you must prove there's something.
Ha-ha. Sorry, but it is not "these people", who is paying to the mathematician. Government is doing it. So they must explain to the government what they cold give back to the government. Usually it is loyalty and the use of their social position to confirm the correctness of the government’s actions and political programs.
Goverment is extracting taxes from these people "for their own benefit" and giving it to the mathematician. When a farmer farms the food of the mathematician and sells it to the mathematician for money, he is simply earning back money that already used to be his.
Which is all well and good -- if it is actually in his own benefit.
Similarly, if all you ever read were OpenAI blog posts, you would get a very wrong impression of the usefulness of large language models of today in maths. For a working researcher, it's not a magic wand that you point at any given proposition and it tells you whether that proposition is true or not. It does appear to help if, while pointing your wand and utter the magical incantation “do it up bro”, you also make it convert $15 million into heat, but for most people, this kind of inverted Midas touch isn't quite accessible yet.
Instead, the reality seems to be closer to this, projecting a fair bit: a given mathematician will have a collection of propositions that they care about, and that they'll use as their own internal benchmark as new models come out. Very rarely will anything come out of it, but sometimes, in particular if you make sure to provide the wand with all relevant context, papers that could be relevant, proof strategies and lemma structures that you suspect are useful, something (which may or may not be plagiarism) will pop out, and that's really nifty. Moreover, it is not unimportant what the proposition and the relevant proof is like. And what does come out tends to be quite bizarre; proofs that use terminology that doesn't exist, seem overly pretentious, based on nonsense analogies where it's surprising that it even works at all, and the only comfort is that you can join it with an equally unreadable Lean blob. And where you would be _crazy_ to just publish those artifacts and think that you have contributed much of anything to maths.
But sometimes it works. It's still very unclear what kind of maths the models are good at, but it seems to certainly be an advantage if what you're looking for is a counterexample hidden in a pile of otherwise similar-looking non-counterexamples, if your proof is one that requires considering 36 different cases, each of which are so tedious that no researcher would have the patience to go through them by hand, or if the proof is an amalgamation of several existing structures, some of which are only documented in Georgian.
The gold rush, more than anything else, seems to be populating the convex hull of existing maths.
This can all change. The $15 million wand requirement today will be less tomorrow. Whether we ever get a move 37 is less clear, or whether we will eventually reach stagnation as all low-hanging fruit is picked, and the convex hull is populated; call this cope if you like. But maybe we do get move 37s all over the place, and it's fine that people think about what that future will look like.
Until then, and while we're still picking friut, let us rather have a think about what we can do to fix the incentive mismatch, to ensure that we increase the prestige of digestion over being the first to convince the LLM to do it up. Since that's the one thing everyone seems to agree, chances are it'll probably converge to something that doesn't have to be written in commandment form, but out of the guest posts hosted by Tao so far, the one by Antieau has some useful suggestions for standards (that aren't entirely unlike those from Leiden): https://terrytao.wordpress.com/2026/09/15/fast-math-slow-mat...
That's like where chess was when Deep Blue was built by IBM. Productivity improved. There was someone complaining on here recently that the seat-back entertainment system on some airline had a chess program set to "trounce all humans".
It's a very short piece written as a journal editorial. Metahumans have advanced so far beyond human comprehension that they do all the original science, communicating via digital neural transfer that humans can't access. Human scientists are left doing hermeneutics: interpreting metahuman publications and reverse-engineering their artifacts, trying to decode work they couldn't have produced themselves. The editorial asks whether human science still has a point, and lands on a modestly hopeful note: interpretation is still a legitimate form of inquiry, and understanding metahuman work still expands human knowledge even if it isn't original discovery.
It reads rather differently now than it did in 2000.
And anyway a mathematician's lifetime salary is basically nothing. I think total worldwide mathematics budget is less than a tenth of a percent of GDP. Meanwhile, openai cumulative loss stands at tens of billions?
Outsourcing understanding, teaching, and proving maths to LLMs is just as dumb as outsourcing food production, manufacturing, or entertainment to a foreign power. It's not that we haven't already done most of those things in the pursuit of temporary profit optimization, but each of them has obviously bad impacts on both the individuals in society who perform those tasks, and on risks to everyone when that outsourcing fails for any reason.
As described, using LLMs is like navigating with GPS. It's fine when you're using it to optimize a path due to traffic conditions, but it can be deadly if you're flying a plane and suddenly don't have it, or any training to deal with that situation. That is where we're headed. I don't really have a take on signing the letter in particular, because as mentioned it seems a bit pointless. At the same time it also seems a bit pointless to spend $10s of millions proving a conjecture a few months sooner than a group of mathematicians already were. I don't imagine they were going to make millions doing it. The definition of material waste.
Perhaps it serves a temporary marketing win for OpenAI, or a medium term improvement in LLM performance on some productive output, but longer term it certainly risks ceding whole swaths of human endeavor to a tool we may not always have. Just as falling demand for farmers, or skilled machinists, or writers, or artists is not an immediate crisis, in the long term there is no one left to transfer the knowledge to the next generation, if something goes wrong.
Let’s be honest, Gauss and Euler are a statistical phenomenon.
The reason why you want, as a society, to have a pool of human mathematicians sitting around solving problem nobody's asking but them, is to have this pool of people who understand math deeply enough to teach a digestible version to all your engineers and physicists (who are the one who actually use math for actually productive stuff sometimes) and to have them nearby to help if a physician or engineer has a question about the math they are using. And it's through these two means that over the long time a tiny fraction of mathematical progress ends up in the actual world. And it's fine because many thing can end up depending on a single piece of progress that happened 80 ago (for instance without the theory of numbers, there would be no modern cryptography, but at the same time most results of the theory of numbers will never be useful in any way).
And I don't think we have good reasons to believe an AI is going to be a good replacement for these two just because it knows how to solve well-studied hard problems.
More generally, I think the history of the Cultural Revolution should make us very reluctant to try accessing the “usefulness” of certain groups of intellectuals based on their measurable first-order output.
like, ask yourself, in Newton's time, was there much application for calculus? what about today? this is almost universally applicable to all research because even null findings are a map marker of where not-to-look
This is blinders on thinking. The future we are looking at with the help of AI is full of abundance. Money is not an issue in that world.
Why would you think that, when the gains of productivity increases haven't been distributed uniformly during the past several decades? What could disrupt the current trend towards more concentration?
And in this case it can go as far as "y'all can starve, we don't need you anymore". Which is perfectly true from a pure capitalist point of view, but also I can't think of a better way to get people to move on from Flock cameras to bigger things.
The only question is, how bad it will get before society snaps. And you can already see many prominent figures among the tech elites promoting UBI as a palliative - basically giving people just enough of the wealth that they won't revolt. And it would even work if they kept it up, but, again, greed always wins over prudence in the long term with these people.
This is all they were receiving funding for previously? Nothing has particularly changed there.
Most people do not use any math after school in their lives. All of their real problems are political. Kids spend significant time in school being told that math teaches them "problem solving" and then leave school and discover, since math solves no political problems, math doesn't solve problems at all. In other places around the world, where by many measures people are much more numerate than Americans, people are actually poorer and live under more authoritarian governments. In industry, math has been reduced to a shibboleth for a neurodivergent lack of ethics, which is why mathematics PhDs go into banking, and never politics - and we imagine politicians and lawyers to lack ethics, which is pure projection, nearly all of our best presidents and congressmen were lawyers. Even the academic environment that supports mathematicians and the STEM community generally - all of that concentrated neurodivergence and lack of people skills has led to less political power, which means less funding and less new students, which has been much more threatening to mathematics than automated proofs.
I love math, but my honest POV is, the value of theoretical math cannot get much lower. The crisis is insurmountable. The community made its deal with the devil (Jim Simons) long ago, it thought it was a STEM discipline like bio and it's really a philanthropic humanities discipline like opera. Math is having its opera moment. Someone would have to step up as the rich person who saves math, and unfortunately, all the best candidates are right now destroying it with chatbots.
I don’t understand, can you explain this line?
This has happened numerous times in the past, and it will happen over and over again.
Mathematicians receive almost no funding, as it is pennies coming from the already anemic NSF budget. I don't even know why it's a question as to why liberal arts needs more funding. They don't get any to begin with!
Mathematicians getting funded only do 0.0001% of the leeching that retirees do.
The person who might have made a mathematics breakthrough that results in some miraculous medical or other discovery will likely have decided it's not economically prudent to pursue a career (pure math academia) that the tech sages, in their all encompassing wisdom (exclusively over the next 1 to 2 financial quarters), have deemed worthless, and that instead he or she should just respond to that pesky Big Four recruiter who keeps dangling a cushy six figure internship.
Do you believe it is possible or have any recent examples? I feel like most of the stuff that could be applied to something like this has probably already been developed 100 years ago. This hope for some miracle math that cures cancer sounds like the thing they tell the government to keep the funding going. Most of modern pure mathematics doesn't look like it has any chance of being that. It's getting more specialized every day with more and more papers on obscure topics being published that 2 people in the world read.
I'd love to be corrected as I quite enjoy mathematics myself, though not professionally.
The stuff powering current tech (incl LLMs), the very foundational math, could have been described in exactly that way when it was new. Number theory, basis of most cryptography, was "pure math" not too long ago. It's only useful in hindsight.
Either way it seems like nobody is in a position to say "this branch of math will surely stay arcane abstract nonsense forever", so the argument for continuing specialized math research comes down to "we might lose out on some cool stuff if we stop", even if most of it will indeed remain useless for a long time.
(Besides, it's not more useless than playing the piano. But that's a whole other type of conversation. Though it shares resemblance if you think about it long enough.)
Sometimes one can be convinced that their mathematics will be useful, too. I've just recalled a rather motivating (though his life story is rather sad) quote by Grassmann, the inventor of modern linear algebra, whose mathematical work was not appreciated during his lifetime.
"I remain completely confident that the labour I have expended on the science presented here and which has demanded a significant part of my life as well as the most strenuous application of my powers, will not be lost. It is true that I am aware that the form which I have given the science is imperfect and must be imperfect. But I know and feel obliged to state (though I run the risk of seeming arrogant) that even if this work should again remain unused for another seventeen years or even longer, without entering into the actual development of science, still that time will come when it will be brought forth from the dust of oblivion and when ideas now dormant will bring forth fruit. I know that if I also fail to gather around me (as I have until now desired in vain) a circle of scholars, whom I could fructify with these ideas, and whom I could stimulate to develop and enrich them further, yet there will come a time when these ideas, perhaps in a new form, will arise anew and will enter into a living communication with contemporary developments. For truth is eternal and divine."
Not at all. My point is that the Fields medallists’ letter didn’t provide good arguments, not that there aren’t any. And therefore I’m agreeing with the Gowers quote above.
Yes, same as any other field. No one is immune
Or do you mean? 2. Real mathematicians will continue to devote a significant part of their life/energy to mathematics research as a hobby, even if no one is paying them (in any way) to do it? That seems more of a reach and makes me wonder if many currently folks current employed as mathematicians aren't 'Real mathematicians' from your point of view.
Discoveries for abstract theory, entertainment, and perhaps regurgitating media, or even basic education can be done with the help of LLMs, but you can't make anything. You can't test anything. You aren't living in the real world. You'll just be lulled into the false belief that everything is simple and fine and beautiful, just as you always wanted, and as airplanes fall from the sky.
Hey, maybe it could work on Cosmology, if you gave it access to the data?
You are absolutely right!
So, only the wealthy or sponsored?
I don't expect Sam Altman and his ilk to deliver such a world to us, but the problem is Altman, not the tech itself.
With the assistance of AI, we are entering a golden age of individual math research without the need of huge institutions
New best prompt:
Write me a really cool math proof that will make me lots of money fast!
Why not let it just spit out the next token on its own without interference, if you can barely fool yourself into believing you understand what it proves... or hallucinates.
But external funding, e.g. from the NSF, also supports conferences -- and I suspect that few people would be willing to attend if they had to pay out of pocket. Without this opportunity to talk to one another, the field would be much worse off.
I couldn't do that, but I know there are people more passionate than me.