"Most people never get the chance to be heroes. Truck drivers don’t. Financial advisers don’t. Executive assistants don’t. They have to find meaning just from being regular people..."
This is where I think are missing something, Noah. You are thinking too much about the particular -- mathematicians and the world stage -- as opposed to a painful generality.
My Dad, for example, was an anonymous worker for an ultimately failing corporation, Yet, consider this: When he was long retired and mostly housebound with serious ailments, my brother and I talked him into one last short visit to a nearby nature preserve. Where several people whispered among themselves before coming over and asking reverentially, "Sorry to intrude, but aren't you ______________"
You see, he was known as the authority on identifying birds. LOCAL authority. (And of course, only known among the modest percentage of people in the area who were into nature.)
But his remarkable knowledge of bird song and plumage provided him with status. And, like so many other particular abilities that provide status, technology has since rendered that ability irrelevant. Screens keep people inside, and, for those that still experience nature, there are apps to identify the birds. And plants. And most everything else.
People need status in the same way that they need love and belonging and security and stimulation. And they obtain it by getting a reputation for being good at something.
Given the global reach of our communications system, I understand your focus on a global example -- world class mathematicians' despair at the threat to their world class status. But exactly the same thing has long been happening as rapid technological advances trivialize abilities that previously offered status -- hard earned status -- on local and family levels.
Diagnosis of engine problems by sound, smell, and feel. Beautiful handwriting and perfect spelling. Reading of the night sky. Cooking by feel. Knowledge of roads, landmarks, shortcuts. In these and myriad other cases, skills that were scarce and thus offered status were replaced by something that made the scarcity disappear.
For me, it says it all to note that far younger people than myself are already bemoaning that internet-related skills that arose in significance after my retirement are now being eclipsed by further technological progress.
Don't misunderstand, I am not saying that we should or can hold up technological advances on this account. Do that, and other civilizations will dance on our graves. But by the same token, saying that people "have to find meaning just from being regular people" is a statement blind to actual human nature, akin to saying "obese people will have to find satisfaction from eating celery."
Rather, the agony of these mathematicians ought to be taken as offering insight as to the widespread despair in our society, despite most people living in unprecedented material comfort and security.
I really like your birdwatching example because it shifts the discussion away from world-famous mathematicians toward ordinary human experience.
But I wonder if there's another way to look at it. When AI surpassed Go champions, many people thought it would diminish human intelligence. Instead, it clarified something: Go mastery was always a very specialized ability shared by a tiny fraction of humanity. The same may soon be true for frontier mathematics and perhaps parts of programming.
Oddly enough, that makes me feel more optimistic, not less. AI isn't replacing humanity all at once. It's first replacing some of our rarest specialized skills, which makes its boundaries easier to see.
If we step back further, perhaps civilization has never primarily been a story about individual intelligence. It's a story about expanding collaboration. Language, writing, printing, universities, the scientific method, the internet... each dramatically increased the scale at which humans could coordinate. AI may simply be the next step in that long evolutionary process.
Which is why I sometimes joke that AI runs on LLMs (Large Language Models), while human civilization has always run on LCMs: Large-scale Collaborative Models.
From that perspective, whether AI is a "tool" or a "replacement" becomes a less interesting question. The more interesting one is whether it expands humanity's capacity to collaborate, or unintentionally weakens it.
Regular people are still heroes to their kids, spouses, community, friends, colleagues, and others. People have a need to feel like they matter, it's why social media and the algorithm is so powerful / dangerous. People feel like when they shout into the void they are getting validated instead of just ignored. People need to feel like they matter, and we are always looking for ways to get that feeling or achievements in general. Humans are strivers on the whole.
The fact that we are living in an unprecedented levels of comfort and people are still not happy or feeling like they matter enough is proof of the human condition.
Ordinary people do sometimes get the chance to be heroes. Not world famous heroes, but someone's hero. A truck driver might find someone on the side of the road in need of help, and be their hero. A financial advisor might save somebody's life savings, and be their hero. An executive assistant might detect an embezzlement scheme and be their company's hero. A mom or dad could save something really important to their kid from disaster, and be their hero.
These moments are often completely unexpected. You never know who might get the chance to be a hero today.
Then pride yourself on being highly adaptable, self-reliant, flexible, and a jack of all trades master of none who could learn almost *any* skill given enough time and effort. Be a raccoon/fox - not a panda. This has worked wonders for me, so far made me immune to everything life and tech has thrown at me, and has largely made *me* the judge of my own quality so that I need very little to no input from anyone else. At the point that literally every fox is redundant, we are probably looking at the world of super abundance at which point "Go forth and do everything else until the end of all ages. - https://www.youtube.com/watch?v=Bbwp4PbWYzw" I personally doubt we will ever get there, but if we do, how is this bad?
The world cannot be compelled to deliver status to you any more than you can force people to love you.
The worst side effect of this is that it makes me tremendously value my own time because I'm extremely certain I could be doing something more worthwhile with it than whatever thing other people are asking me to do with it instead. But, however you shake it, ennui and existential dread is *not* a problem I have. I am frustrated by how little time I get to live in my own head and with my own pursuits - not how "seen" I am.
I don't see why people like your father don't still get to be local heroes because of LLMs. Skills like those you describe are still impressive to humans. What about if there's no signal in a rural area and you want to identify a bird? A friend of mine has an encyclopedic knowledge of geograpghy which encompasses flags, capitals, country areas and silhouettes and more. Despite the fact I could look up everything he knows and more on the internet or ask an LLM, it doesn't make his achievement as a human any less impressive.
It's much as others (and Noah himself) have said, we still have athletes and chess players. The story is much less one of doom and gloom for the ordinary person, rather a chance to find deep meaning in doing impressive things for their own sake as well as the small and simple things in our lives.
There is also the fact that allowing ones status or reputation to determine ones emotional state is a doomed endeavour, it's externalising the locus of control. Whilst it may be human nature to receive feel good neurotransmitters when our perceived status goes up, it doesn't mean it's what we should focus on.
A similar analogy to your bird story is the one about mushroom identification. Fungi are still relatively misunderstood compared to other parts of nature, so much so that we still rely heavily on specialist knowledge and have to be incredibly careful when attempting to eat a foraged mushroom. Since ChatGPT's arrival people have been generating slop to sell as foraging guides, which often have incorrect information in them. These errors are potentially deadly. The only way to combat this is with the humans that really *know* the truth, whose ancestors often paid for that knowledge with their lives! Much like the understanding of mathematical proofs provided by AI, we need people who can do this. LLMs as they are do not understand what is true, just what is probalistically most likely from their dataset.
> while that won’t be as *heroic* of a job as what math research used to be, it’ll still be a *prestigious* one, because most humans will still be unable to do it.
> Just as there are still sprinters even though humans can’t outrun cars, there will still be mathletes.
The status you focus on, as I understand, is a positional good. It does not come from "scarcity" which technology can make disappear, but from ranking, which is always there. Tool-Assisted-Speedruns did not make human speedrun categories disappear. Civil GPS navigation usage increased along with non-GPS Orienteering activity participation. I fail to see how apps which can identify birds would hurt the status of a local bird authority. Sure some idiots may challenge him with the apps. But the apps can also enable more people to venture into the nature and appreciate his authority.
“We motivate ourselves with our own sense of heroism, and to be reminded that we’re cogs in a machine greater than ourselves makes life seem a little less meaningful.”
It’s similar to how many religious people of yore thought that by seeking to understand the universe in scientific terms would strip all the wonder, meaning, and beauty from it…and, uh, nope. The universe described by science is awe inspiring, gorgeous, and fucking nuts!
I guess I’m saying that having better tools to go farther down the rabbit hole has always made the world more interesting and inspiring.
I'm a math Ph.D. (no longer doing research) who's pretty down about what AI might mean for the trajectory of the field, and I think this piece doesn't put its finger on why.
The fact that I'm not going to be a "hero" is old news to me; I've known it for longer than ChatGPT has existed. But this never made me think my interest in learning and teaching math is a waste of time, and I'm still grateful that I got to spend five years in grad school learning full time from my peers and my professors.
The future I worry about is one where there's nothing for humans to contribute, where paying a math professor when you have a computer would be like paying a weightlifter to move boxes in a warehouse when you have a forklift. I'm not as sanguine as you that the social infrastructure around human mathematicians would survive.
Why would anyone spend five years in grad school learning a skill that a computer can do better? Why would they be paid to? Right now, no one gets paid to train for five years at being a human calculator, to use your example. If they did, why would they learn from another human being rather than just ask the LLM's? What reason would we even have to ever talk to each other about math at all?
One of the things I love the most about math is getting to do it with other people. I love learning from people who are deeper into a topic than I am, working on a problem with a friend, and sharing what I've learned with people who are excited to know about it. What I dread isn't that I don't get to be a hero, it's that I can envision the end of mathematics *as a thing that humans do together*.
You should join some fandoms/hobbies to see some of the utterly pointless and unpaid but demanding things uber nerds will do: everything from building elaborate cosplaying costumes to inventing entire fantasy languages. There's an entire genre of video games that are just about solving puzzles. My dad took up stalk hunting with 100% self made bow and arrows using caveman techniques. He's now super into making homemade wine and moonshine and has gotten very good at it.
Rigor + camaraderie is not extinct and never will be. People still do fancy calligraphy, write form poetry, restore and drive around Model Ts, and memorize the entire Bible. I see no reason people who love math will just stop doing math.
Getting paid for nerd rigor + camaraderie is a very rare luxury. Most of us nerds do boring normal jobs that aren't that demanding or interesting and get our rigor/camaraderie on the side.
I'm more familiar with those worlds than you might have guessed! I'm a co-creator, with some friends from grad school, of one of those video games that are just about solving puzzles. I love groups of nerds taking something completely pointless very seriously and forming communities around it, and like you say a lot of them do some pretty amazing things. I have no doubt that if mathematics doesn't survive as a career, some group of obsessed nerds will carry it forward in some form, and that definitely is some comfort. As our future replacements like to say, you're absolutely right, and I appreciate the pushback.
But I'm also aware of how much would be lost. I've been working for the last several years as a private tutor, specializing in teaching adults proof-based math (more info at https://nicf.net/tutoring/ if anyone's interested!). This is my favorite job I've ever had by far, and I love seeing how excited my students can get about this material and how much progress they can make. But most of them are also balancing learning math against a full-time job, and as a result they can't realistically learn this stuff at the pace a full-time student can. This isn't because they're lazy or bad at math --- quite the opposite! --- they just have other commitments.
There's a lot of beautiful mathematics that's accessible to someone without a whole lot of training, but there's also a lot that you can't deeply appreciate without putting in several years of work. So far, none of my students have gotten to anything in that second category, though a lot of them have made significant progress. I'm sure a math hobbyist community would contain some people excited to put in the work to preserve some of this stuff --- preserve it, that is, as living knowledge held by human minds --- but a lot of it would die.
You're also absolutely right that it's a rare privilege for someone's nerdy obsession to get to be a career. What I'm describing is far from the most important AI-related issue in the world; it's not even the most important issue in my life personally. And I don't think society owes me or other mathematicians anything. We're certainly not owed a perpetual sinecure where we get paid just to read math books and talk to each other about them without producing anything.
The only thing I was trying to communicate here is that something I care very deeply about seems to be disappearing from the world, I'm sad to see it go, and that sadness isn't based in losing the chance to be a hero. I'm not asking anyone else to do anything except let me grieve its loss.
Your essay hit upon a few different ideas that have become clear to me in the last year.
First, Gödel showed that there are deep limits to pure mathematics ability to make predictions about the real world. More than a century ago, logician Bertrand Russel was seen as the frontier model, able to understand the deepest workings of the Universe sitting in an armchair with a pencil. Gödel showed that was absurd.... mathematics is essential and powerful, but the world can only be understood through empiricism. And it has taken a century of painstaking and expensive observations and experiments to bring us to where we are today, not an army of mathematicians.
By the same token, those who assume that an AI superintelligence will sweep away all science and give us a new frontier... um, nope. That superintelligence (I like hive-mind better) will be limited by the empirical data it has available. Math is different, unincumbered by empiricism. So in math AI will be able to push the frontier in new directions and further than we previously imagined. And that IS important, ultimately to where science chooses to go.
This is IMO what is implied when you say 'AI needs us for edge compute'. And it will for awhile longer.
Second, the hive-mind business. I have been using LLMs in my physical science research. While my colleagues have complained about hallucinated references, I have been gobsmacked by LLMs power of SYNTHESIS. I can have a a vague idea, describe it to an LLM, and it will find a paper in my field that developed that idea. Great. But I can then ask it if that idea exists in OTHER disciplines. Often, it then rattles off a list of how the SAME idea has been reinvented in half a dozen separate fields, completely independently, and described with different jargon!
The obviousl implication, is that the science we have now, so much bigger than individual scientists, is badly balkanized and siloed into separate subfields and reinventing small wheels. And AI, by virtue of training on the whole corpus, trivially sees the connections and synthesizes them into one whole!
So for the science outside mathematics, I expect a burst of insights coming from that LLM driven synthesis of science into one beautiful theoretical whole.
Third, I believe the idea that advances in math precede advances in science, by leading us to ask new questions, and giving us tools to build better models. And the teams of applied math folks that build these wonderous commercial-scale LLMs... they have discovered a LOT of new applied math along the way. And I think that, separate from AI, will spin off a lot of new undeerstanding in how learning processes, evolution and optimization work. And that will revolutionize and deepen our understanding of both biology, biophysics and cognitive science in ways that were impossible before.
Why learn a language? Why learn to write and read? Why study history or study anything really. The path we are going down with AI is not looking good for the next generation. The latest generation is already glued to their phones, social content, gaming and no real path or future looking forward. We are told by Musk et al we may not have to work anymore but that transition will be long and painful for most people. Humans need exploration and learning and that requires goals and chances to become a hero. AI is taking all of that away.
I think you are too dismissive of gaming. It's provided me with all the exploration and goals and learning and chances to become a hero that I've needed for decades. There is already a game out there for everyone. With AI, there will soon be more than ever!
This is a very perceptive question. Even an AI that can answer any question (which is far beyond what we have today, and is likely IMHO to remain so) can't provide meaning in life or learning. It can't do critical thinking for you, which is necessary to understand the world around you.
Unfortunately, there will be people who take so many shortcuts that they never learn the skills to understand outputs of AI in context of the world around them -- you see this in the large number of people who use AI to write papers for them at schools for which they're paying an arm and a leg to attend.
I still think these are simply tools to help search large solution spaces, and so may make individuals 50-100% (not 100X) more productive, not things that will destroy all meaning in life.
Great point, life doesn't give us meaning, we give life meaning... Even if AI can do a lot for us, it can't feel that emptiness inside of us, give us purpose or make us feel needed.
History, English, language departments in general, Classics, Philosophy,
Basically, the argument he is making, without using the term, is that Mathematics will become de facto another one of the liberal arts, but we shouldn't worry because it's cheap.
Being cheap hasn't saved any of the other liberal arts.
"Isaac Newton invented calculus and classical mechanics all by himself. "
Yes, but as he said, on the shoulders of giants, and Leibniz was only slightly behind him on calculus, and classical mechanics was largely formed before Newton wrote his laws.
Agreed on the calculus point. On the classical mechanics? Well, it's complicated. What Newton did in the Principia was an earth(heaven?)shaking synthesis and breakthrough, and one of the greatest (if not the greatest?) intellectual achievements in history. But, per his shoulder of giants aphorism, he was absolutely dependent on what came before. He executed a brilliant combination of Kepler's laws on the orbits of the planets (well, Mars at least) and Galileo's terrestrial physics and the quantification of motion. But without those Newton would have had so much little work with.
And even Newton's accomplishments, as heroic as they were, reflects Noah's point about the collective endeavor of science. Others provided critical building blocks; Newton turned them into a glorious cathedral.
But part of me wonders about the what-if? Kepler discovered his laws because of his obsessive torturing of the data left him by Brahe. But that depended on Brahe collecting history's most precise data, an obsession of his. And (given all the legal wrangling), Kepler was fortunate to have access to the data. And, again, to be so obsessive that he didn't let a mere eight minutes of arc in the orbit of Mars keep him from throwing away his beloved theory of the perfect solids and instead grudgingly accept elliptical orbits (and thus onward to Newton).
Take away Brahe. Take away Kepler's access to the data. Take away just a bit of Kepler's fanatical dedication to precision in explaining orbits and the building block that Newton placed his structure on disappears. And had that happened, who would remember Newton apart from some nice work on optics?
That young mathematician who was distraught over the possibility of AI doing all math better than humans, making human mathematicians unnecessary, I am sorry for how he feels, but there are vastly more non- professional mathematicians in the world than professional mathematicians, and all of them will eventually be profoundly better off with how much this will advance science and medicine and standards of living. I like math too, but not everyone can do their favorite hobby for a living.
I would also point to chess. Interestingly, when computers became vastly better than humans at chess, this did not seem to hurt the popularity of chess much, and this is something I know about, as I still, at 63, proudly display the trophies from winning my age group several years in the Michigan Junior Championships. As far as the analogy to literary authors, this is different. There is a pretty limited number of ways you can do a proof, and an AI may be able to find them all, but all the ways you could write a 400 page novel, or an 18 book series, like The Dresden Files, basically unlimited. A human can still do novel novels.
"Its ability to understand complex ideas is not limited by the ability of a single human brain to apprehend, intuit, or communicate those ideas." Incorrect. LLMs "understand" exactly nothing and there is nothing in their archtitecture that puts them on the path to doing so. The lack of an LLM's ability to perform abductive reasoning is why mathematicians are still every bit as important as they ever were. Giving a word processor credit for the original work of an author would be equivalent to giving the AIs credit for solving the theories developed by mathematicians.
Mathemticians are at the very pinnacle of human thought. They will be among the last to be replaced by AI and that will require that machines actually learn to think, not just appear to think.
I am a former mathematician and I meet maths students during regular Spring and Fall Schools of Algebra that my department holds.
The community is neither blasé nor as dismissive as you. For the usual standards of a specialization that usually insists on exact definitions, few waste their time on picking apart the meaning of "understand", not least because we don't really understand how our human cognition works and if it is indeed somehow superior to what LLMs do or not.
What matters to them is that this ... entity ... produces top-level mathematical results. The comparison to word processors is misleading. You cannot leave Libre Office running overnight and return to it with an expectation that there will be Hemingway-level prose on the screen.
The level of uncertainty among the young is now unprecedented - no one even tries to guess how the field will look five or ten years from now, but the general rule in the academia is that the old guard tries to protect its jobs and positions first and foremost, so any massive change will likely come at the cost of the new entrants.
The fact that the mathematics community is "neither blasé nor as dismissive" as me is only notable as a demonstration that the AI industry has stampeded it into hand wringing along with the rest of society.
Not understanding how the human brain manifests understanding has no bearing on our ability to recognize that that the functioning of LLMs does not manifest understanding. They are trained to recognize patterns in large data sets. Their ability to see things humans do not or cannot does not make them intelligent. Simply useful.
You took the wrong idea from my word processor analogy. A word process is a tool used by writers to create prose originating in the writer's brain. The LLMs are a tool used by mathematicians to prove theories originating in the mathematician's brain. They are not capable of creating the theories.
Of course the young are suffering unwarranted uncertainity because the entire world refuses to be rational about what AI is and what it is not. And is not going to be. We are simply not on a path towards actual intelligence with the current technology. Society would be better served by realistic discussions of how to best leverage these tools rather than convincing young people that there is no place for them in the world to come. In fact, it is the opposite. They have the mental plasticity to see the benefits where the old guard only sees change which will obsolete them long before they hit retirement.
Indeed, but I don't understand why you take pride in being condescending. It is an awful human trait.
"that the AI industry has stampeded it into hand wringing along with the rest of society."
If a tool solves the problem your thesis has been attacking for two years overnight, you don't have to be "stampeded" like an unthinking buffalo into weighing the ramifications thereof for future research and future you as a researcher.
"They are not capable of creating the theories."
Would you be willing to make a bet on this claim staying true by, say, 2030?
I am not even sure if this is true today. Maybe people just don't prompt them for new theories. Proofs and counterexamples are more flashy.
My comment was about your condescension, not mine. Mine originates in years of listening to people who understand nothing of how this technology works lecture those of who do on what is and is not going to happen. It is tedious.
Yes, I would be willing to make a bet on the claim staying true by 2030. People are simply not grasping the leap in complexity that will be required for true intelligence to arise from machines. I do happen to believe that we will get there eventually. We're just not there now and we should stop scaring the kids. Life is difficult enough without crushing fear that humanity is about to become obsolete.
I'll bring out my usual response to this kind of claim: What's the *least* impressive cognitive task that you believe LLMs will never be able to do because of this fundamental limitation?
They can't do anything that requires abductive reasoning. And mathematics is at the forefront of work that requires it. LLMs cannot manifest an idea that has not already appearing at its inputs. It can appear to because it may recognize a pattern in the input data that has gone unnoted, but that is not the same as creating a new idea.
The Wikipedia page (https://en.wikipedia.org/wiki/Abductive_reasoning) gives as examples a number of things that LLMs can already do. If you have a different definition in mind, please name a task that falls under it.
Just ask one if it can do abductive reasoning. You will see they cannot. They can only approximate it which can be left as an exercise to the reader to decide if that is a civilization upending gap or not.
I'm not going to offer a response other than to say that mine, Perplexity, offers a nuanced answer that is not definitive and references multiple papers on arxiv. We can pass on the your source vs mine discussion...
I really enjoyed the provocation around how heroism has to change, how we perhaps need a shift away from solely focusing on individual achievement
A lot of people are arguing that relationships will be the new binding constraint if individual knowledge is cheap and easy to come by. I think that lens is still highly individualistic - I think the binding constraint will be more about the output of complex collaborative efforts
Perhaps we are seeing the end of the creative potential of individualism. I worry though about the psychological effects - what comes to mind is the discussion around what the "enclosure of the frontier" meant psychologically for Americans, and how the economic reality of a continued ability to claim homestead land didn't really do enough to counteract the feelings that the US was losing something in the process.
Which is also why I like the focus here on heroism specifically - the stories we tell ourselves about what's happening at the "frontier" are quite important
I'm an active research mathematician and have been following the progress for a while, both in general and in my particular area. (Only for a few years really, but that goes all the way back to the pre-ChatGPT era!) The "Heroes" framing is a nice way of packaging one of several challenges academic math faces now -- and pretty much everyone else will soon. Whether or not us math PhDs always like to admit it, a shot at status and prestige is a real part of the incentive structure that gets lots of us to spend our 20s in grad school working for meagre stipends relative to what we could've earned, with only a small chance at continuing in faculty jobs afterwards. Being able to work on what interests you counts for a lot too, and as Nic Ford commented earlier, plenty of folks enjoy that opportunity regardless of what happens after. (BTW, you wrote a very nice thesis Nic!) But a chance to be the best at what you do -- even if it's a tiny niche that only a handful of others appreciate -- is what distinguishes the vocation from mere recreation.
That said, there's a major gap between talk this week about "AI is better at math" and the actual experience of human mathematicians. The true output of mathematics is not theorems or proofs, but *understanding*. Theorem statements and formal proofs are ways of packaging and transmitting that understanding. (To be fair, this is a mainstream view among mathematicians, but not completely uncontroversial... there are some who say human understanding is overrated.) By far the best articulation of this view I've seen, especially as it bears on the current moment, is David Bessis's essay The Fall of the Theorem Economy. He draws a distinction between "secret math" (what goes on in our minds) and "formal math" (what gets written down). If "secret math" is the real thing, as many of us believe in our bones, saying AI is going to be better at math is a little like saying it's going to be better at listening to music. A lot of the complication and confusion comes from the fact that the societal value of math is not just its aesthetics, but also its applications. (Some would deny that mathematical aesthetics has any societal value, but please indulge me a bit!) There's lots more to say about this; for now I strongly recommend that essay to anyone interested in what we working mathematicians are really doing with our time.
It seems pretty likely that the meaning of the Fields Medal will be completely different next time it's awarded, four years from now. There might still be some room for heroic feats of human understanding and explanation in the meantime. But keeping the culture alive is going to require more of us mathematicians speaking up about what we actually value in our science/art, and communicating that more broadly than we're used to doing.
Thanks so much for the kind words, David! It really means a lot to me to hear that.
I agree with every word of this. Status and prestige were a big motivator for me early in my career. I had fantasies of greatness through most of grad school. Looking back, my personal benchmarks for what would "count" as a successful career were ridiculous, and I held myself to standards I would never have imposed on anyone else. Watching those unrealistic hopes get dashed was almost certainly part of what made me decide to leave research.
As you say, this is pretty common, and the culture of the field unfortunately does a lot to encourage it. I will say, though, that I've loved math for literally as long as I can remember, way longer than I've known that there were any prizes to be won, and I still love it now even after pretty definitively giving up on winning them. This is part of what tweaks me a bit when I see a certain kind of response to things like the OpenAI news: "Serves you right, you're just mad because you used to get to brag about how smart you are for being good at math and you won't get to anymore." Some of us actually care about the thing itself, I promise!
I'll also second the recommendation of Bessis's article. He did a better job articulating why I find mathematics worthwhile than anything I've ever read, and your listening-to-music analogy also resonates for me. If we do end up in a world where humans are useless at "formal math", though, I'm not sure how we justify asking society to pay us to engage in "secret math" inside our own heads. I don't even necessarily think it *would* be justifiable, as sad as that would make me.
Nice to see the AI optimism. I get the sense though that solving these obscure math problems won't have a material impact on my life or yours. Why not point AI at something more practical, like fixing bullet point handling in Microsoft Word or addressing the countless bugs in Windows 11 or making Spotify's user interface more intuitive and functional?
Coding was supposed to be AI's superpower, but as far as I can tell, it's just generating millions upon millions of lines of slop. I had difficulty yesterday finding a usable, simple Note taking app for my phone, because the app store is absolutely polluted with mountains of vibe-coded garbage apps that crowd out the ones that actually work. Windows updates have gotten so bad that I've stopped automatically installing them.
Software devs I've talked to are considering leaving the field entirely -- not because they're no longer perceived as "heroes," but because the whole design process, which once involved some level of mastery and understanding, now is nothing more than pulling a slot machine lever, committing the non-deterministic slop to the repo, and hoping for the best.
I dunno, I guess I just don't feel the love that you do for this tech. Not saying you won't be proven right in the long-term. But for now, I'm just not feeling it.
> But that’s not so bad, really. Most people never get the chance to be heroes. Truck drivers don’t. Financial advisers don’t. Executive assistants don’t. They have to find meaning just from being regular people — from taking care of their kids, having friends, having hobbies, joining civic organizations, getting involved in politics, and so on. It’s not such a terrible fate.
Well, but it *is* a terrible fate. There are a lot of people doing various sorts of cognitive work (note that bloggers are included here!) where they get meaning from the work they do. But some large fraction of people do work solely to earn money; the job has no meaning for them, it only gets money that enables them to do meaningful things. I would guess that almost all professional mathematicians get meaning from their work (otherwise they'd do something better-paying), so you're threatening all of them with the loss of their source of meaning.
> Do most people want a meaningful job even if it means taking a pay cut? Not really. Across multiple surveys, a study found that most people prefer higher pay in a less meaningful job. The surveys found that people expected that a higher-paying job would enable more happiness and meaning outside of work. Indeed, their preference for a higher-paying job was weakened if they were told to assume the lower-paying-but-more-meaningful job "would enable you to have a happy, meaningful life outside of work." -- Ward, Sarah, "Choosing Money Over Meaningful Work: Examining Relative Job Preferences for High Compensation Versus Meaningful Work"
A hero for me is Gregor Johann Mendel. I attended a conference in the Czech Republic honoring the bicentennial of Mendel's birth a few years ago. I asked if Mendel had access to a slide rule. The modern slide rule was invented in France in 1859, and Mendel was doing his genetic research on peas at that time...but slide rules may have been too expensive for Mendel's monastery to purchase one. (Mendel's family were farming smallholders, so they couldn't have bought one, either.) My takeaway: Very likely Mendel used a pencil and paper to do his statistical analysis that led to his discovery of what we now know as genetics. Amazing.
Wonderful essay! Classics scholar Joel Christensen sees heroes as mirrors of their civilizations. When a civilization changes, its heroes change. Who will be our heroes in the age of AI?
"Most people never get the chance to be heroes. Truck drivers don’t. Financial advisers don’t. Executive assistants don’t. They have to find meaning just from being regular people..."
This is where I think are missing something, Noah. You are thinking too much about the particular -- mathematicians and the world stage -- as opposed to a painful generality.
My Dad, for example, was an anonymous worker for an ultimately failing corporation, Yet, consider this: When he was long retired and mostly housebound with serious ailments, my brother and I talked him into one last short visit to a nearby nature preserve. Where several people whispered among themselves before coming over and asking reverentially, "Sorry to intrude, but aren't you ______________"
You see, he was known as the authority on identifying birds. LOCAL authority. (And of course, only known among the modest percentage of people in the area who were into nature.)
But his remarkable knowledge of bird song and plumage provided him with status. And, like so many other particular abilities that provide status, technology has since rendered that ability irrelevant. Screens keep people inside, and, for those that still experience nature, there are apps to identify the birds. And plants. And most everything else.
People need status in the same way that they need love and belonging and security and stimulation. And they obtain it by getting a reputation for being good at something.
Given the global reach of our communications system, I understand your focus on a global example -- world class mathematicians' despair at the threat to their world class status. But exactly the same thing has long been happening as rapid technological advances trivialize abilities that previously offered status -- hard earned status -- on local and family levels.
Diagnosis of engine problems by sound, smell, and feel. Beautiful handwriting and perfect spelling. Reading of the night sky. Cooking by feel. Knowledge of roads, landmarks, shortcuts. In these and myriad other cases, skills that were scarce and thus offered status were replaced by something that made the scarcity disappear.
For me, it says it all to note that far younger people than myself are already bemoaning that internet-related skills that arose in significance after my retirement are now being eclipsed by further technological progress.
Don't misunderstand, I am not saying that we should or can hold up technological advances on this account. Do that, and other civilizations will dance on our graves. But by the same token, saying that people "have to find meaning just from being regular people" is a statement blind to actual human nature, akin to saying "obese people will have to find satisfaction from eating celery."
Rather, the agony of these mathematicians ought to be taken as offering insight as to the widespread despair in our society, despite most people living in unprecedented material comfort and security.
Let me think about that...
I really like your birdwatching example because it shifts the discussion away from world-famous mathematicians toward ordinary human experience.
But I wonder if there's another way to look at it. When AI surpassed Go champions, many people thought it would diminish human intelligence. Instead, it clarified something: Go mastery was always a very specialized ability shared by a tiny fraction of humanity. The same may soon be true for frontier mathematics and perhaps parts of programming.
Oddly enough, that makes me feel more optimistic, not less. AI isn't replacing humanity all at once. It's first replacing some of our rarest specialized skills, which makes its boundaries easier to see.
If we step back further, perhaps civilization has never primarily been a story about individual intelligence. It's a story about expanding collaboration. Language, writing, printing, universities, the scientific method, the internet... each dramatically increased the scale at which humans could coordinate. AI may simply be the next step in that long evolutionary process.
Which is why I sometimes joke that AI runs on LLMs (Large Language Models), while human civilization has always run on LCMs: Large-scale Collaborative Models.
From that perspective, whether AI is a "tool" or a "replacement" becomes a less interesting question. The more interesting one is whether it expands humanity's capacity to collaborate, or unintentionally weakens it.
Underrated point you are bringing up imo.
Regular people are still heroes to their kids, spouses, community, friends, colleagues, and others. People have a need to feel like they matter, it's why social media and the algorithm is so powerful / dangerous. People feel like when they shout into the void they are getting validated instead of just ignored. People need to feel like they matter, and we are always looking for ways to get that feeling or achievements in general. Humans are strivers on the whole.
The fact that we are living in an unprecedented levels of comfort and people are still not happy or feeling like they matter enough is proof of the human condition.
Ordinary people do sometimes get the chance to be heroes. Not world famous heroes, but someone's hero. A truck driver might find someone on the side of the road in need of help, and be their hero. A financial advisor might save somebody's life savings, and be their hero. An executive assistant might detect an embezzlement scheme and be their company's hero. A mom or dad could save something really important to their kid from disaster, and be their hero.
These moments are often completely unexpected. You never know who might get the chance to be a hero today.
Then pride yourself on being highly adaptable, self-reliant, flexible, and a jack of all trades master of none who could learn almost *any* skill given enough time and effort. Be a raccoon/fox - not a panda. This has worked wonders for me, so far made me immune to everything life and tech has thrown at me, and has largely made *me* the judge of my own quality so that I need very little to no input from anyone else. At the point that literally every fox is redundant, we are probably looking at the world of super abundance at which point "Go forth and do everything else until the end of all ages. - https://www.youtube.com/watch?v=Bbwp4PbWYzw" I personally doubt we will ever get there, but if we do, how is this bad?
The world cannot be compelled to deliver status to you any more than you can force people to love you.
The worst side effect of this is that it makes me tremendously value my own time because I'm extremely certain I could be doing something more worthwhile with it than whatever thing other people are asking me to do with it instead. But, however you shake it, ennui and existential dread is *not* a problem I have. I am frustrated by how little time I get to live in my own head and with my own pursuits - not how "seen" I am.
I don't see why people like your father don't still get to be local heroes because of LLMs. Skills like those you describe are still impressive to humans. What about if there's no signal in a rural area and you want to identify a bird? A friend of mine has an encyclopedic knowledge of geograpghy which encompasses flags, capitals, country areas and silhouettes and more. Despite the fact I could look up everything he knows and more on the internet or ask an LLM, it doesn't make his achievement as a human any less impressive.
It's much as others (and Noah himself) have said, we still have athletes and chess players. The story is much less one of doom and gloom for the ordinary person, rather a chance to find deep meaning in doing impressive things for their own sake as well as the small and simple things in our lives.
There is also the fact that allowing ones status or reputation to determine ones emotional state is a doomed endeavour, it's externalising the locus of control. Whilst it may be human nature to receive feel good neurotransmitters when our perceived status goes up, it doesn't mean it's what we should focus on.
A similar analogy to your bird story is the one about mushroom identification. Fungi are still relatively misunderstood compared to other parts of nature, so much so that we still rely heavily on specialist knowledge and have to be incredibly careful when attempting to eat a foraged mushroom. Since ChatGPT's arrival people have been generating slop to sell as foraging guides, which often have incorrect information in them. These errors are potentially deadly. The only way to combat this is with the humans that really *know* the truth, whose ancestors often paid for that knowledge with their lives! Much like the understanding of mathematical proofs provided by AI, we need people who can do this. LLMs as they are do not understand what is true, just what is probalistically most likely from their dataset.
> while that won’t be as *heroic* of a job as what math research used to be, it’ll still be a *prestigious* one, because most humans will still be unable to do it.
> Just as there are still sprinters even though humans can’t outrun cars, there will still be mathletes.
The status you focus on, as I understand, is a positional good. It does not come from "scarcity" which technology can make disappear, but from ranking, which is always there. Tool-Assisted-Speedruns did not make human speedrun categories disappear. Civil GPS navigation usage increased along with non-GPS Orienteering activity participation. I fail to see how apps which can identify birds would hurt the status of a local bird authority. Sure some idiots may challenge him with the apps. But the apps can also enable more people to venture into the nature and appreciate his authority.
“We motivate ourselves with our own sense of heroism, and to be reminded that we’re cogs in a machine greater than ourselves makes life seem a little less meaningful.”
It’s similar to how many religious people of yore thought that by seeking to understand the universe in scientific terms would strip all the wonder, meaning, and beauty from it…and, uh, nope. The universe described by science is awe inspiring, gorgeous, and fucking nuts!
I guess I’m saying that having better tools to go farther down the rabbit hole has always made the world more interesting and inspiring.
I'm a math Ph.D. (no longer doing research) who's pretty down about what AI might mean for the trajectory of the field, and I think this piece doesn't put its finger on why.
The fact that I'm not going to be a "hero" is old news to me; I've known it for longer than ChatGPT has existed. But this never made me think my interest in learning and teaching math is a waste of time, and I'm still grateful that I got to spend five years in grad school learning full time from my peers and my professors.
The future I worry about is one where there's nothing for humans to contribute, where paying a math professor when you have a computer would be like paying a weightlifter to move boxes in a warehouse when you have a forklift. I'm not as sanguine as you that the social infrastructure around human mathematicians would survive.
Why would anyone spend five years in grad school learning a skill that a computer can do better? Why would they be paid to? Right now, no one gets paid to train for five years at being a human calculator, to use your example. If they did, why would they learn from another human being rather than just ask the LLM's? What reason would we even have to ever talk to each other about math at all?
One of the things I love the most about math is getting to do it with other people. I love learning from people who are deeper into a topic than I am, working on a problem with a friend, and sharing what I've learned with people who are excited to know about it. What I dread isn't that I don't get to be a hero, it's that I can envision the end of mathematics *as a thing that humans do together*.
why are there professional chess players?
Same reason we have professional athletes.
You should join some fandoms/hobbies to see some of the utterly pointless and unpaid but demanding things uber nerds will do: everything from building elaborate cosplaying costumes to inventing entire fantasy languages. There's an entire genre of video games that are just about solving puzzles. My dad took up stalk hunting with 100% self made bow and arrows using caveman techniques. He's now super into making homemade wine and moonshine and has gotten very good at it.
Rigor + camaraderie is not extinct and never will be. People still do fancy calligraphy, write form poetry, restore and drive around Model Ts, and memorize the entire Bible. I see no reason people who love math will just stop doing math.
Getting paid for nerd rigor + camaraderie is a very rare luxury. Most of us nerds do boring normal jobs that aren't that demanding or interesting and get our rigor/camaraderie on the side.
I'm more familiar with those worlds than you might have guessed! I'm a co-creator, with some friends from grad school, of one of those video games that are just about solving puzzles. I love groups of nerds taking something completely pointless very seriously and forming communities around it, and like you say a lot of them do some pretty amazing things. I have no doubt that if mathematics doesn't survive as a career, some group of obsessed nerds will carry it forward in some form, and that definitely is some comfort. As our future replacements like to say, you're absolutely right, and I appreciate the pushback.
But I'm also aware of how much would be lost. I've been working for the last several years as a private tutor, specializing in teaching adults proof-based math (more info at https://nicf.net/tutoring/ if anyone's interested!). This is my favorite job I've ever had by far, and I love seeing how excited my students can get about this material and how much progress they can make. But most of them are also balancing learning math against a full-time job, and as a result they can't realistically learn this stuff at the pace a full-time student can. This isn't because they're lazy or bad at math --- quite the opposite! --- they just have other commitments.
There's a lot of beautiful mathematics that's accessible to someone without a whole lot of training, but there's also a lot that you can't deeply appreciate without putting in several years of work. So far, none of my students have gotten to anything in that second category, though a lot of them have made significant progress. I'm sure a math hobbyist community would contain some people excited to put in the work to preserve some of this stuff --- preserve it, that is, as living knowledge held by human minds --- but a lot of it would die.
You're also absolutely right that it's a rare privilege for someone's nerdy obsession to get to be a career. What I'm describing is far from the most important AI-related issue in the world; it's not even the most important issue in my life personally. And I don't think society owes me or other mathematicians anything. We're certainly not owed a perpetual sinecure where we get paid just to read math books and talk to each other about them without producing anything.
The only thing I was trying to communicate here is that something I care very deeply about seems to be disappearing from the world, I'm sad to see it go, and that sadness isn't based in losing the chance to be a hero. I'm not asking anyone else to do anything except let me grieve its loss.
Your essay hit upon a few different ideas that have become clear to me in the last year.
First, Gödel showed that there are deep limits to pure mathematics ability to make predictions about the real world. More than a century ago, logician Bertrand Russel was seen as the frontier model, able to understand the deepest workings of the Universe sitting in an armchair with a pencil. Gödel showed that was absurd.... mathematics is essential and powerful, but the world can only be understood through empiricism. And it has taken a century of painstaking and expensive observations and experiments to bring us to where we are today, not an army of mathematicians.
By the same token, those who assume that an AI superintelligence will sweep away all science and give us a new frontier... um, nope. That superintelligence (I like hive-mind better) will be limited by the empirical data it has available. Math is different, unincumbered by empiricism. So in math AI will be able to push the frontier in new directions and further than we previously imagined. And that IS important, ultimately to where science chooses to go.
This is IMO what is implied when you say 'AI needs us for edge compute'. And it will for awhile longer.
Second, the hive-mind business. I have been using LLMs in my physical science research. While my colleagues have complained about hallucinated references, I have been gobsmacked by LLMs power of SYNTHESIS. I can have a a vague idea, describe it to an LLM, and it will find a paper in my field that developed that idea. Great. But I can then ask it if that idea exists in OTHER disciplines. Often, it then rattles off a list of how the SAME idea has been reinvented in half a dozen separate fields, completely independently, and described with different jargon!
The obviousl implication, is that the science we have now, so much bigger than individual scientists, is badly balkanized and siloed into separate subfields and reinventing small wheels. And AI, by virtue of training on the whole corpus, trivially sees the connections and synthesizes them into one whole!
So for the science outside mathematics, I expect a burst of insights coming from that LLM driven synthesis of science into one beautiful theoretical whole.
Third, I believe the idea that advances in math precede advances in science, by leading us to ask new questions, and giving us tools to build better models. And the teams of applied math folks that build these wonderous commercial-scale LLMs... they have discovered a LOT of new applied math along the way. And I think that, separate from AI, will spin off a lot of new undeerstanding in how learning processes, evolution and optimization work. And that will revolutionize and deepen our understanding of both biology, biophysics and cognitive science in ways that were impossible before.
Why learn a language? Why learn to write and read? Why study history or study anything really. The path we are going down with AI is not looking good for the next generation. The latest generation is already glued to their phones, social content, gaming and no real path or future looking forward. We are told by Musk et al we may not have to work anymore but that transition will be long and painful for most people. Humans need exploration and learning and that requires goals and chances to become a hero. AI is taking all of that away.
I think you are too dismissive of gaming. It's provided me with all the exploration and goals and learning and chances to become a hero that I've needed for decades. There is already a game out there for everyone. With AI, there will soon be more than ever!
This is a very perceptive question. Even an AI that can answer any question (which is far beyond what we have today, and is likely IMHO to remain so) can't provide meaning in life or learning. It can't do critical thinking for you, which is necessary to understand the world around you.
Unfortunately, there will be people who take so many shortcuts that they never learn the skills to understand outputs of AI in context of the world around them -- you see this in the large number of people who use AI to write papers for them at schools for which they're paying an arm and a leg to attend.
I still think these are simply tools to help search large solution spaces, and so may make individuals 50-100% (not 100X) more productive, not things that will destroy all meaning in life.
Dude, being in the corporate world for these decades, there are plenty of people faking it all these time before there were AI
Great point, life doesn't give us meaning, we give life meaning... Even if AI can do a lot for us, it can't feel that emptiness inside of us, give us purpose or make us feel needed.
The sheer naivete of saying that mathematics as a profession will be fine because it only costs 5-6 billion dollars is wild.
Lots of academic fields cost far less and are nevertheless being destroyed anyway.
Which ones?
History, English, language departments in general, Classics, Philosophy,
Basically, the argument he is making, without using the term, is that Mathematics will become de facto another one of the liberal arts, but we shouldn't worry because it's cheap.
Being cheap hasn't saved any of the other liberal arts.
"Isaac Newton invented calculus and classical mechanics all by himself. "
Yes, but as he said, on the shoulders of giants, and Leibniz was only slightly behind him on calculus, and classical mechanics was largely formed before Newton wrote his laws.
Agreed on the calculus point. On the classical mechanics? Well, it's complicated. What Newton did in the Principia was an earth(heaven?)shaking synthesis and breakthrough, and one of the greatest (if not the greatest?) intellectual achievements in history. But, per his shoulder of giants aphorism, he was absolutely dependent on what came before. He executed a brilliant combination of Kepler's laws on the orbits of the planets (well, Mars at least) and Galileo's terrestrial physics and the quantification of motion. But without those Newton would have had so much little work with.
And even Newton's accomplishments, as heroic as they were, reflects Noah's point about the collective endeavor of science. Others provided critical building blocks; Newton turned them into a glorious cathedral.
But part of me wonders about the what-if? Kepler discovered his laws because of his obsessive torturing of the data left him by Brahe. But that depended on Brahe collecting history's most precise data, an obsession of his. And (given all the legal wrangling), Kepler was fortunate to have access to the data. And, again, to be so obsessive that he didn't let a mere eight minutes of arc in the orbit of Mars keep him from throwing away his beloved theory of the perfect solids and instead grudgingly accept elliptical orbits (and thus onward to Newton).
Take away Brahe. Take away Kepler's access to the data. Take away just a bit of Kepler's fanatical dedication to precision in explaining orbits and the building block that Newton placed his structure on disappears. And had that happened, who would remember Newton apart from some nice work on optics?
That young mathematician who was distraught over the possibility of AI doing all math better than humans, making human mathematicians unnecessary, I am sorry for how he feels, but there are vastly more non- professional mathematicians in the world than professional mathematicians, and all of them will eventually be profoundly better off with how much this will advance science and medicine and standards of living. I like math too, but not everyone can do their favorite hobby for a living.
I would also point to chess. Interestingly, when computers became vastly better than humans at chess, this did not seem to hurt the popularity of chess much, and this is something I know about, as I still, at 63, proudly display the trophies from winning my age group several years in the Michigan Junior Championships. As far as the analogy to literary authors, this is different. There is a pretty limited number of ways you can do a proof, and an AI may be able to find them all, but all the ways you could write a 400 page novel, or an 18 book series, like The Dresden Files, basically unlimited. A human can still do novel novels.
"Its ability to understand complex ideas is not limited by the ability of a single human brain to apprehend, intuit, or communicate those ideas." Incorrect. LLMs "understand" exactly nothing and there is nothing in their archtitecture that puts them on the path to doing so. The lack of an LLM's ability to perform abductive reasoning is why mathematicians are still every bit as important as they ever were. Giving a word processor credit for the original work of an author would be equivalent to giving the AIs credit for solving the theories developed by mathematicians.
Mathemticians are at the very pinnacle of human thought. They will be among the last to be replaced by AI and that will require that machines actually learn to think, not just appear to think.
I am a former mathematician and I meet maths students during regular Spring and Fall Schools of Algebra that my department holds.
The community is neither blasé nor as dismissive as you. For the usual standards of a specialization that usually insists on exact definitions, few waste their time on picking apart the meaning of "understand", not least because we don't really understand how our human cognition works and if it is indeed somehow superior to what LLMs do or not.
What matters to them is that this ... entity ... produces top-level mathematical results. The comparison to word processors is misleading. You cannot leave Libre Office running overnight and return to it with an expectation that there will be Hemingway-level prose on the screen.
The level of uncertainty among the young is now unprecedented - no one even tries to guess how the field will look five or ten years from now, but the general rule in the academia is that the old guard tries to protect its jobs and positions first and foremost, so any massive change will likely come at the cost of the new entrants.
So much condescension, so little time...
The fact that the mathematics community is "neither blasé nor as dismissive" as me is only notable as a demonstration that the AI industry has stampeded it into hand wringing along with the rest of society.
Not understanding how the human brain manifests understanding has no bearing on our ability to recognize that that the functioning of LLMs does not manifest understanding. They are trained to recognize patterns in large data sets. Their ability to see things humans do not or cannot does not make them intelligent. Simply useful.
You took the wrong idea from my word processor analogy. A word process is a tool used by writers to create prose originating in the writer's brain. The LLMs are a tool used by mathematicians to prove theories originating in the mathematician's brain. They are not capable of creating the theories.
Of course the young are suffering unwarranted uncertainity because the entire world refuses to be rational about what AI is and what it is not. And is not going to be. We are simply not on a path towards actual intelligence with the current technology. Society would be better served by realistic discussions of how to best leverage these tools rather than convincing young people that there is no place for them in the world to come. In fact, it is the opposite. They have the mental plasticity to see the benefits where the old guard only sees change which will obsolete them long before they hit retirement.
"So much condescension"
Indeed, but I don't understand why you take pride in being condescending. It is an awful human trait.
"that the AI industry has stampeded it into hand wringing along with the rest of society."
If a tool solves the problem your thesis has been attacking for two years overnight, you don't have to be "stampeded" like an unthinking buffalo into weighing the ramifications thereof for future research and future you as a researcher.
"They are not capable of creating the theories."
Would you be willing to make a bet on this claim staying true by, say, 2030?
I am not even sure if this is true today. Maybe people just don't prompt them for new theories. Proofs and counterexamples are more flashy.
My comment was about your condescension, not mine. Mine originates in years of listening to people who understand nothing of how this technology works lecture those of who do on what is and is not going to happen. It is tedious.
Yes, I would be willing to make a bet on the claim staying true by 2030. People are simply not grasping the leap in complexity that will be required for true intelligence to arise from machines. I do happen to believe that we will get there eventually. We're just not there now and we should stop scaring the kids. Life is difficult enough without crushing fear that humanity is about to become obsolete.
I'll bring out my usual response to this kind of claim: What's the *least* impressive cognitive task that you believe LLMs will never be able to do because of this fundamental limitation?
They can't do anything that requires abductive reasoning. And mathematics is at the forefront of work that requires it. LLMs cannot manifest an idea that has not already appearing at its inputs. It can appear to because it may recognize a pattern in the input data that has gone unnoted, but that is not the same as creating a new idea.
The Wikipedia page (https://en.wikipedia.org/wiki/Abductive_reasoning) gives as examples a number of things that LLMs can already do. If you have a different definition in mind, please name a task that falls under it.
Just ask one if it can do abductive reasoning. You will see they cannot. They can only approximate it which can be left as an exercise to the reader to decide if that is a civilization upending gap or not.
My AI assures me they can do abductive reasoning and provides examples.
I'm not going to offer a response other than to say that mine, Perplexity, offers a nuanced answer that is not definitive and references multiple papers on arxiv. We can pass on the your source vs mine discussion...
Lovely post. One correction: Wiles was less than a decade before Perelman, not a generation before.
Andrew Wiles completed his proof of Fermat's Last Theorem in 1994. Grigori Perelman proved the Poincaré conjecture in 2002–2003.
It's also interesting that Perelman himself very much disagreed with the idea Noah expresses here, that his own contribution carried a special status.
I really enjoyed the provocation around how heroism has to change, how we perhaps need a shift away from solely focusing on individual achievement
A lot of people are arguing that relationships will be the new binding constraint if individual knowledge is cheap and easy to come by. I think that lens is still highly individualistic - I think the binding constraint will be more about the output of complex collaborative efforts
Perhaps we are seeing the end of the creative potential of individualism. I worry though about the psychological effects - what comes to mind is the discussion around what the "enclosure of the frontier" meant psychologically for Americans, and how the economic reality of a continued ability to claim homestead land didn't really do enough to counteract the feelings that the US was losing something in the process.
Which is also why I like the focus here on heroism specifically - the stories we tell ourselves about what's happening at the "frontier" are quite important
Perhaps the heroes will be a band of fighters who battle to stop Skynet before it's too late..
I'm an active research mathematician and have been following the progress for a while, both in general and in my particular area. (Only for a few years really, but that goes all the way back to the pre-ChatGPT era!) The "Heroes" framing is a nice way of packaging one of several challenges academic math faces now -- and pretty much everyone else will soon. Whether or not us math PhDs always like to admit it, a shot at status and prestige is a real part of the incentive structure that gets lots of us to spend our 20s in grad school working for meagre stipends relative to what we could've earned, with only a small chance at continuing in faculty jobs afterwards. Being able to work on what interests you counts for a lot too, and as Nic Ford commented earlier, plenty of folks enjoy that opportunity regardless of what happens after. (BTW, you wrote a very nice thesis Nic!) But a chance to be the best at what you do -- even if it's a tiny niche that only a handful of others appreciate -- is what distinguishes the vocation from mere recreation.
That said, there's a major gap between talk this week about "AI is better at math" and the actual experience of human mathematicians. The true output of mathematics is not theorems or proofs, but *understanding*. Theorem statements and formal proofs are ways of packaging and transmitting that understanding. (To be fair, this is a mainstream view among mathematicians, but not completely uncontroversial... there are some who say human understanding is overrated.) By far the best articulation of this view I've seen, especially as it bears on the current moment, is David Bessis's essay The Fall of the Theorem Economy. He draws a distinction between "secret math" (what goes on in our minds) and "formal math" (what gets written down). If "secret math" is the real thing, as many of us believe in our bones, saying AI is going to be better at math is a little like saying it's going to be better at listening to music. A lot of the complication and confusion comes from the fact that the societal value of math is not just its aesthetics, but also its applications. (Some would deny that mathematical aesthetics has any societal value, but please indulge me a bit!) There's lots more to say about this; for now I strongly recommend that essay to anyone interested in what we working mathematicians are really doing with our time.
It seems pretty likely that the meaning of the Fields Medal will be completely different next time it's awarded, four years from now. There might still be some room for heroic feats of human understanding and explanation in the meantime. But keeping the culture alive is going to require more of us mathematicians speaking up about what we actually value in our science/art, and communicating that more broadly than we're used to doing.
Thanks so much for the kind words, David! It really means a lot to me to hear that.
I agree with every word of this. Status and prestige were a big motivator for me early in my career. I had fantasies of greatness through most of grad school. Looking back, my personal benchmarks for what would "count" as a successful career were ridiculous, and I held myself to standards I would never have imposed on anyone else. Watching those unrealistic hopes get dashed was almost certainly part of what made me decide to leave research.
As you say, this is pretty common, and the culture of the field unfortunately does a lot to encourage it. I will say, though, that I've loved math for literally as long as I can remember, way longer than I've known that there were any prizes to be won, and I still love it now even after pretty definitively giving up on winning them. This is part of what tweaks me a bit when I see a certain kind of response to things like the OpenAI news: "Serves you right, you're just mad because you used to get to brag about how smart you are for being good at math and you won't get to anymore." Some of us actually care about the thing itself, I promise!
I'll also second the recommendation of Bessis's article. He did a better job articulating why I find mathematics worthwhile than anything I've ever read, and your listening-to-music analogy also resonates for me. If we do end up in a world where humans are useless at "formal math", though, I'm not sure how we justify asking society to pay us to engage in "secret math" inside our own heads. I don't even necessarily think it *would* be justifiable, as sad as that would make me.
Nice to see the AI optimism. I get the sense though that solving these obscure math problems won't have a material impact on my life or yours. Why not point AI at something more practical, like fixing bullet point handling in Microsoft Word or addressing the countless bugs in Windows 11 or making Spotify's user interface more intuitive and functional?
Coding was supposed to be AI's superpower, but as far as I can tell, it's just generating millions upon millions of lines of slop. I had difficulty yesterday finding a usable, simple Note taking app for my phone, because the app store is absolutely polluted with mountains of vibe-coded garbage apps that crowd out the ones that actually work. Windows updates have gotten so bad that I've stopped automatically installing them.
Software devs I've talked to are considering leaving the field entirely -- not because they're no longer perceived as "heroes," but because the whole design process, which once involved some level of mastery and understanding, now is nothing more than pulling a slot machine lever, committing the non-deterministic slop to the repo, and hoping for the best.
I dunno, I guess I just don't feel the love that you do for this tech. Not saying you won't be proven right in the long-term. But for now, I'm just not feeling it.
> But that’s not so bad, really. Most people never get the chance to be heroes. Truck drivers don’t. Financial advisers don’t. Executive assistants don’t. They have to find meaning just from being regular people — from taking care of their kids, having friends, having hobbies, joining civic organizations, getting involved in politics, and so on. It’s not such a terrible fate.
Well, but it *is* a terrible fate. There are a lot of people doing various sorts of cognitive work (note that bloggers are included here!) where they get meaning from the work they do. But some large fraction of people do work solely to earn money; the job has no meaning for them, it only gets money that enables them to do meaningful things. I would guess that almost all professional mathematicians get meaning from their work (otherwise they'd do something better-paying), so you're threatening all of them with the loss of their source of meaning.
> Do most people want a meaningful job even if it means taking a pay cut? Not really. Across multiple surveys, a study found that most people prefer higher pay in a less meaningful job. The surveys found that people expected that a higher-paying job would enable more happiness and meaning outside of work. Indeed, their preference for a higher-paying job was weakened if they were told to assume the lower-paying-but-more-meaningful job "would enable you to have a happy, meaningful life outside of work." -- Ward, Sarah, "Choosing Money Over Meaningful Work: Examining Relative Job Preferences for High Compensation Versus Meaningful Work"
A hero for me is Gregor Johann Mendel. I attended a conference in the Czech Republic honoring the bicentennial of Mendel's birth a few years ago. I asked if Mendel had access to a slide rule. The modern slide rule was invented in France in 1859, and Mendel was doing his genetic research on peas at that time...but slide rules may have been too expensive for Mendel's monastery to purchase one. (Mendel's family were farming smallholders, so they couldn't have bought one, either.) My takeaway: Very likely Mendel used a pencil and paper to do his statistical analysis that led to his discovery of what we now know as genetics. Amazing.
Wonderful essay! Classics scholar Joel Christensen sees heroes as mirrors of their civilizations. When a civilization changes, its heroes change. Who will be our heroes in the age of AI?