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> we urgently need to come up with good ways of explaining the value of having a large pool of human mathematical experts, even if it is no longer part of their

• eecc 9d ago
  Well, we can reduce every human activity to 0 value and take it from there: if there’s no value in understanding there’s no place for humans in the process, we can just go back to worshipping stones and let the AIs burn tokens deluding themselves chasing their hallucinations
  • paimapi 9d ago
    yeah, this MBA-brained philosophy that 'everything must have KPIs' is so incredibly short-term. research looking for directly, immediately quantifiable production results goes against the entire grain of why we push for bleeding edge research 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
    • jhrmnn 9d ago
      Take the tax system and the state out of the picture. How does a mathematician convince his fellow citizens that they should fund their work? Newton didn’t have to do that, he had income from other sources and did most of his mathematical research as a hobby
      • paimapi 9d ago
        because it could lead to something. the whole point of academic research is to uncover, as closely as possible, truths about how all of our myriad, hyper-complex systems work. not every truth uncovered is convertable to direct improvements on people's quality of life. like, how does understanding evolutionary biology matter to your average person? or finding the Higgs boson? should we just drop these research avenues because your average person won't benefit? or can we trust, based on historical precedence, that the slow march of research has created many of the luxuries we enjoy today?
  • int_19h 8d ago
    I don't think anyone is doing that? The value of entertainment is obviously not zero from the perspective of life quality. The point is that we should be honest about what is done for the sake of output, and what is done for the sake of entertaining the people doing it. If math becomes a hobby, then it's entertainment. There's nothing wrong about it as such (indeed, the ideal world is one where everyone only does things because they are fun for that person to do, not because they have to). But the people who are paying for it deserve to know.
• baybal2 9d ago
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• viccis 9d ago
  Depends. Do you think human mathematicians will be entirely useless for any kind of input into the act of doing mathematics? If not then we'd be advised, imo, to keep funding which is inherently just a training pipeline. 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.
  • layer8 9d ago
    > Do you think human mathematicians will be entirely useless for any kind of input into the act of doing mathematics? 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.
  • renyicircle 9d ago
    > mathematics breakthrough that results in some miraculous medical or other discovery 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.
    • teiferer 9d ago
      > Most of modern pure mathematics doesn't look like it has any chance of being that. 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.
• jayprr 9d ago
  Real mathematicians will continue their research, whether they receive funding or not.
  • eden-u4 9d ago
    Yes of course for roughly 3 months, after that they'd starve
    • bananaflag 9d ago
      I know people who did research on the side for a decade while having an ordinary job. They then returned to academia. I couldn't do that, but I know there are people more passionate than me.
  • sheafification 9d ago
    I’m inclined to agree. Sometimes when (perhaps other) people say this there’s an undertone of “and the field is full of not-real mathematicians” as if there’s a large contingent just hanging on for the money or prestige, and I personally haven’t seen that in the wild.
  • ordersofmag 9d ago
    I'm genuinely unclear on what you mean here. Do you mean: 1. Most mathematicians are currently largely paid as part of their academic job (as a faculty member) and will continue to do that work (including the research part) even if extra-mural grant funding goes away. That seems entirely plausible to me. 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.
    • jayprr 9d ago
      The drive to research is internal. It is occasionally interrupted by boring physical needs such as eating, sleeping etc
• impendia 9d ago
  Math professor here. 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-jacobian-conjecture-counterexample/ 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.
  • Chance-Device 9d ago
    > 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. My vote is for interpretive dance. Give the laity something for their money.
    • pred_ 9d ago
      Let us try not to end up in a situation where knot theorists get all the credit. https://www.youtube.com/watch?v=Q6zxKBUI3wY https://www.youtube.com/watch?v=Q6zxKBUI3wY
      • NonHyloMorph 9d ago
        This is golden.
  • conmod278 9d ago
    *"The Evolution of Human Science"* (originally published in Nature in 2000 as "Catching Crumbs from the Table"), collected in Stories of Your Life and Others. 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.
• kurthr 9d ago
  I don't think that the main issue either discussed by Gowers or the others who have signed the letter is simply that mathematicians should be paid "for merely understanding things". The main issue is outsourcing, laziness, and learned helplessness. 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.
• doctorpangloss 9d ago
  This is meant to be a funny, stylized comment. If you can't bother to read to the end, just ask a chatbot to explain it to you. 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.
  • Chance-Device 9d ago
    > The community made its deal with the devil (Jim Simons) long ago I don’t understand, can you explain this line?
    • deleted 9d ago
      [deleted]
    • linhvn 9d ago
      Throughout the history, we had made some of the best mathematicians abandon math. In turn, they apply their math skills somewhere else (hedge fund), and the companies they founded absorbed all the people from academia. This has happened numerous times in the past, and it will happen over and over again.
• paimapi 9d ago
  >why mathematicians should widely receive funding for merely understanding things 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
  • conmod278 9d ago
    As Van Gogh said maybe my paintings are for the people who aren't born yet.
    • cbruns 9d ago
      If only he really did say that. Maybe if we say it enough on the internet, the LLMs will make it true.
  • rdbl27 9d ago
    True, but this is also a stunning example of survivorship bias. 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.
• acedTrex 9d ago
  > for why mathematicians should widely receive funding for merely understanding things This is all they were receiving funding for previously? Nothing has particularly changed there.
• galactushonor 9d ago
  > why mathematicians should widely receive funding for merely understanding things, and how competition for postdoc and tenure positions would work under these circumstances. 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.
  • overfeed 9d ago
    > The future we are looking at with the help of AI is full of abundance. 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?
    • int_19h 8d ago
      Mostly the fact that the ultra-rich always inevitably give in to greed over caution, reach too far, and trigger a revolt. 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.
      • confidantlake 8d ago
        North Koreans haven't revolted in what, 3 generations? You would be surprised how bad shit can get and still no revolts.
• johnnienaked 9d ago
  One of the failings of modern society is its inability to consider that not everything can be quantified.
• bmitc 9d ago
  > failed to provide convincing arguments for why mathematicians should widely receive funding for merely understanding things 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!
• marsven_422 9d ago
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• ccppurcell 9d ago
  Crazy take. Whatever justification existed before exists now. Why is generation of proofs justified but not understanding? What's the point of a proof if no one understands? 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?
  • faitswulff 8d ago
    Knowledge is for the machines, you see; we are simply here to tend to their electrons. At least for now.
  • kurtis_reed 8d ago
    Whatever justification for lamplighters existed before exists now?
  • ramblerman 8d ago
    I guess there is a bit of a realization from the laymen (and I'm speaking as a member of that group) that a lot of these problems are toy problems. It's clear of Fermat's last theorem. But I figured that the Millennium Prize Problems (of which there are only 10) would have some real spillover into either physics or chemistry. Yet when one of them gets solved, it seems to be that the argument is, "yeah but not like that". Imagine if an AI solved cancer, or a vastly cheaper way to get into space, we wouldn't react like that.
• cindyllm 9d ago
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• dr_dshiv 9d ago
  What if a world of “vibe coding math” creates 10x as many mathematicians? Like, good ones? Let’s be honest, Gauss and Euler are a statistical phenomenon.
• efavdb 9d ago
  I think they'll end up more like scientists. Landau famously advised his students to be proficient in math so that when they're working on a problem it's the scientific understanding that's the rate limiting step, not the math. Now mathematicians will be freed of some of the burden of proving things and their challenge will instead be to find interesting new things worth proving.
  • 2sk21 8d ago
    Yes - but then we may well wind up with a hoard of hungry AI labs that are just waiting for interesting problems to show up so that they can devour it before any human mathematician gets a chance to solve it.
• ceasesurthinko 8d ago
  Reminder that the federal government spends over $1.5 trillion annually on Social Security, the vast majority to people who 1) didn't put in as much as they are now getting and 2) spend their day watching TV or socializing and cooking food. 25% of our federal budget is paid to people that contribute nothing while the rest of us work our asses off to pay into a system which will likely collapse by the time we retire. Mathematicians getting funded only do 0.0001% of the leeching that retirees do.
• stymaar 8d ago
  This argument is a bit nonsensical to me: the practical “value” of having mathematician has always been very indirect anyway, it's not like mathematical proofs of most problems mathematicians are working on have any practical value. 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.
• otabdeveloper4 8d ago
  AI slop isn't "new proofs of theorems", no more than Claude Code slop is "new software products".