[HN Gopher] Mathematical methods and human thought in the age of AI
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Mathematical methods and human thought in the age of AI
Author : zaikunzhang
Score : 186 points
Date : 2026-03-30 11:05 UTC (11 hours ago)
(HTM) web link (arxiv.org)
(TXT) w3m dump (arxiv.org)
| zaikunzhang wrote:
| See also
|
| https://www.youtube.com/watch?v=zJvuaRVc8Bg
| anotherpaulg wrote:
| Recorded 10 February 2026. Terence Tao of the University of
| California, Los Angeles, presents "Machine assistance and the
| future of research mathematics" at IPAM's AI for Science
| Kickoff.
| mchinen wrote:
| He also was on Dwarkesh's podcast last week
| (https://www.youtube.com/watch?v=Q8Fkpi18QXU ).
|
| I enjoyed the human->depth vs AI->breadth discussion and the
| waterline rising slowly to fill the 50 lowest hanging Erdos
| problems but struggling on the next few.
| bluecheese452 wrote:
| Enough Terence Tao spam.
| mchinen wrote:
| I haven't seen any negative sentiment toward Terence Tao
| before. Coming from outside the academic math sphere, genuinely
| curious if there's a real issue or if this comment is just spam
| itself.
| tines wrote:
| This comment is spam. When Tao says something we should take
| it seriously.
| myhf wrote:
| A big trend in AI spam is to take achievements in one field
| that could be called "AI" and use them as evidence of
| advancement in other fields that happen to be called "AI".
|
| https://en.wikipedia.org/wiki/Package-deal_fallacy
|
| Tao has been doing a lot of demonstrations of using LLMs for
| search and translation by experts who already know enough
| about a field to judge whether generated text is valid or
| meaningful. Those are valid demonstrations, but they don't
| justify the LLM-as-intelligent-agent narrative being pushed
| by most of the reporting on the topic, so the whole situation
| reeks of payola.
| nh23423fefe wrote:
| Tao is being paid to boost LLMs. That's your argument? This
| is what human creativity is capable of? Baseless
| conspiracies?
| gettingoverit wrote:
| It's actually a strange situation. Tao is the only high-
| profile mathematician who tries to resolve the
| reproducibility crisis in math by popularizing proof
| checkers, and who used LLMs in probably the most legitimate
| way: to produce formal undeniable proofs with them, that
| cannot really suffer from LLMs being wrong all the time.
|
| On the other hand, I still find content and arguments he
| produces to be quite weak, and honestly it's getting annoying
| to hear them that often. It's the case when he could really
| get some help of a ghost writer who is more experienced in
| popularization, otherwise this repetition might cause some
| serious harm instead.
| ancillary wrote:
| So much of HN is half-baked anecdotes about and by LLMs or
| philosophizing from VCs who talked to an LLM about Rene Girard
| for twenty minutes or pop sci articles that appear to be posted
| so that some bored developer can read the abstract and one
| experiment and dunk on it. Tao is uniquely positioned as a
| mathematician who has made enormous contributions to many areas
| and is old enough to contextualize it all against the past and
| young enough to be open to its possible futures. More Tao spam
| sounds good to me!
| gradstudent wrote:
| I skimmed the paper a couple of times, hoping to find the
| promised (from the abstract)
|
| > pathway to integrating AI into our most challenging and
| intellectually rigorous fields to the benefit of all humankind.
|
| There's very little insight here though. It seems mostly a
| retread of conversations we've been having in the academic
| community for a few years now. In particular, I was hoping to see
| some discussion of how we might restructure our educational
| institutions around this technology, when the machines rob
| students of the opportunity to develop critical thinking skills.
| Right now our best idea seems to be a retreat to oral and written
| examinations; an idea which doesn't scale and which ignores the
| supposed benefits of human+AI reasoning. The alternative
| suggestion I've seen is to teach prompt engineering, which seems
| (a) hard for foundational subjects and (b) again, seems to
| outsource much of the thinking to the AI, instead of extending
| the reach of human thought.
| BDPW wrote:
| Physical classrooms don't really scale either, is that really a
| fundamental problem?
| lo_zamoyski wrote:
| Indeed. Education isn't supposed to "scale". We've mucked
| around with education so much and subjected it to tech fad
| after tech fad that we hardly have anything resembling
| education.
|
| Because this has been going on so long, most people's
| reference point for what constitutes "education" is simply
| _off_ , mistaking "training" or something like that for it.
| But the purpose of education is intellectual formation, the
| ability to reason competently, and the comprehension of basic
| reality, which enables genuine intellectual freedom (there
| are moral presuppositions, too; immorality deranges the
| mind). This is what the _classical_ liberal arts were about.
|
| The _very bare minimum_ criterion (and it is a very bare
| minimum) for someone to be able to claim to be educated is
| not only knowledge of their field, but knowledge of the
| intellectual nature, foundations, and basis of their field in
| the greater intellectual scope. I would not hold someone with
| only that bare minimum in especially high esteem vis-a-vis
| education, but even that bar is higher than what education
| today provides.
| bonoboTP wrote:
| There are simply not enough teachers who can provide such
| an ideal, imagined education, at least not for the current
| rate of teacher salaries (and it's very far off). The
| educational strategy has to scale to real people, real
| teachers and real students as they are in the flesh, not
| some ivory tower pipe dream. We've had decades of this "we
| should teach _how_ to think, not _what_ to think ".
|
| Alternatively,if you don't care about scale, as in rolling
| out a system to the population at large, then yeah, this
| kind of advanced education exists, it's just very selective
| and is in advanced extracurricular or obtained through
| private tutors.
| lo_zamoyski wrote:
| This also assumes that universal education is a sensible
| aim. I think that's doubtful and that it contributes to
| these sorts of burdens and waters down the quality of
| education in the process.
|
| As a concrete example, for a few decades now, we're been
| pushing primary school students toward university
| education quite aggressively and broadly. It was quite
| common to scare students toward university by claiming
| that without a university degree, they would be flipping
| burgers at McDonalds. This, of course, is completely
| false and it is disgraceful that such dishonest and
| manipulative tactics were used. Today, because of rising
| university costs and the dubious value of most university
| education, we're seeing this idea challenged at the level
| of the university. Gen Z's interest in trades has
| increased by something like 1500%. I don't see this as a
| negative. In Germany, for instance, there is a more
| balanced distribution across trades and university.
|
| Now, I admit that the situation is a bit different in the
| case of primary education, but here, too, I think we do
| well to think in terms of reform rather than technology
| and patching up a pedagogically and administratively
| broken system. The American education system spends an
| inordinate amount of money on each student with little to
| show for it. If, for instance, those funds were allocated
| wisely, then a number of problems would likely go away or
| become smaller issues.
|
| Of course, what does "allocate wisely" mean? Education
| systems require a principled grasp of what education is
| _for_. If you don 't have a sound anthropological grasp
| of what it means to be human and how education is
| supposed to enable one's humanity and serve human
| persons, then you are in no position to run an education
| system or decide school curricula. I cannot stress this
| enough. Our education system today is very "pragmatist";
| we're constantly told we're being prepared for a career
| and a job market. That's not education: it's job
| training. Of course, schools are quite mediocre as
| training facilities, because they're sort of a halfway
| house between training and whatever residue of classical
| education still lingers. So that's one distinction:
| training vs. education. Now, if we simply accept this
| distinction, we should ask: how should one organize
| training on the one hand and education on the other to
| enable each to be successful within its own circumscribed
| domain? And what if we keep things as local and
| decentralized as possible? I guarantee you would not see
| the inept system we have today.
|
| So, with this...
|
| > There are simply not enough teachers who can provide
| such an ideal, imagined education
|
| ...I agree, but again, my view is that _at best_ we are
| buying time with these sorts of technological gimmicks.
| We 're also social animals. We cannot keep isolating
| ourselves behind technology under the pretext of
| "practicality".
| bonoboTP wrote:
| Yes, Germany has different educational tracks that are
| decided fairly early, at 10 or 12 years old (with some
| opportunity to change tracks). I don't think Americans
| like this idea.
|
| Still, 40% of young adults have a tertiary degree
| (https://www.oecd.org/en/publications/2025/09/education-
| at-a-...) while it's 47% in the US, so I wouldn't say
| it's a huge difference. And its not just a US thing,
| Denmark stands at 45%. So I wouldn't spin too big of a
| narrative around this.
|
| Education is a field where decade after decade they try
| some new fad which is basically the old fad re-dressed
| and never really learn much. That's because teachers and
| their methodologies don't really have that big of an
| effect. A stable non-chaotic learning environment and
| access to the learning material though any kind of
| presentation, and books gets you to pretty much as good
| as it gets. To have a real effect, you need private
| tutoring for the gifted or very small groups of talent
| nurturing, which goes far beyond the default curriculum.
| But again, these don't fit the current zeitgeist, so they
| will keep on pushing "critical thinking" and "how to
| think", no matter how much they fail.
| bonoboTP wrote:
| Yes. Tools like Khan Academy help lots of talented kids to
| progress in the curriculum beyond what's available in
| physical classrooms available to them.
| nutjob2 wrote:
| > when the machines rob students of the opportunity to develop
| critical thinking skills
|
| This is a fundamental misunderstanding of human nature.
| Machines don't rob people of critical thinking skills, people
| do. Mostly people do it to themselves, often inheriting it from
| their parents or social environment.
| ak_111 wrote:
| Wait it seems like doing unscalable things - like face-to-face
| teaching/examination - is exactly the sort of things that
| humanity can afford to do as it benefits from the surplus free
| time generated by AI efficiently doing the scalable things.
| woolion wrote:
| > We assert that artificial intelligence is a natural evolution
| of human tools developed throughout history to facilitate the
| creation, organization, and dissemination of ideas, and argue
| that it is paramount that the development and application of AI
| remain fundamentally human-centered.
|
| While this is a noble goal, it seems obvious that this isn't how
| it usually goes. For instance, "free market" is often used as a
| dogma against companies that are actively harmful to society, as
| "globalization" might be. An unstoppable force, so any form of
| opposition is "luddite behavior". Another one is easier transport
| and remote communication, that generally broke down the social
| fabric. Or social media wreaking havoc among teen's minds. From
| there, it's easy to see why the technological system might be
| seen as an inherent evil. In 1872's Erewhon, Butler already
| described the technological system as a force that human society
| could contain as soon as it tolerated it. There are already many
| companies persecuting their employees for not using AI enough,
| even when the employee's response is that the quality of its
| output is not good enough for the work at hand, rather than any
| ideological reason.
|
| I'm neither optimistic nor pessimistic about the changes that AI
| might bring, but hoping it to become "human-centered" seems
| almost as optimistic as hoping for "humane wars".
| cowpig wrote:
| > "free market" is often used as a dogma against companies that
| are actively harmful to society
|
| This is a predominantly America-specific piece of propaganda,
| and it's pretty recent.
|
| Adam Smith's ideas are primarily arguments against mercantilism
| (e.g. things like using tariffs to wield self-interested state
| power), something he showed to be against the common good. The
| "invisible hand" concept is used to show how self-interested
| action can, under conditions of *competitive markets*, lead to
| unintentional alignment with the common good.
|
| Obviously that's a significant departure from the way it's
| commonly used today, where Thiel's book has influenced so many
| entrepreneurs into believing Monopolies are Good.
|
| But the history of this is very Cold War-influenced, where
| "free markets" were politically positioned as alternatives to
| the USSR's "planned economy", and slowly pushed to depart
| further and further from Adam Smith's original argument about
| moral philosophy.
| abdullahkhalids wrote:
| Economic behavior is inherently game theoretic - agents take
| various actions and get some positive/negative reward as a
| result. Whether an agent's reward is positive or negative and
| of what magnitude, depends on the strategies employed by all
| agents. If some agents adopt new strategies, the reward
| calculus for everyone involved can completely change [1].
|
| Over the past few centuries, countless new economic
| structures and strategies have been discovered and practiced.
| The rewards for the same action today and in the past can be
| completely different due to this.
|
| So to me, if someone claimed more than a few decades ago that
| certain economic strategies and structures are good or bad,
| its simply not worth listening to them, unless someone
| reconfirms that the old finding still holds with the latest
| range of strategies. In that case, the credit and citation
| goes to that new someone, not the ghosts of the past.
|
| [1] A good interactive demo https://ncase.me/trust/
| Nevermark wrote:
| > if someone claimed more than a few decades ago that
| certain economic strategies and structures are good or bad
|
| As you point out, it is all game theory.
|
| But things that arrange for the game to be more beneficial
| to everyone, that align our interests more, deserve to be
| called "good", regardless of their inability to universally
| do so.
|
| The latter would be an impossible bar for anything.
|
| Where I find things frustrating, is when someone thinks
| because something is "good", it somehow becomes "enough".
| (Think, capitalized versions of different economic schools
| of thought.)
| runarberg wrote:
| > Economic behavior is inherently game theoretic.
|
| Game theory is just math. As with any math, the
| calculations can all work out, but that says nothing of how
| it reflects nature. All you can say is that if the axioms
| are all true, then this is the necessary outcome. Look for
| string theory as a cautionary tale here.
|
| Game theory assumes rational systems. But we have over 6
| decades of behavior science which contradicts that
| fundamental assumption. Economic behavior is not
| necessarily rational, and subsequently it is not inherently
| game theoretic. You will find plenty of dogmatic,
| idealistic, superstitious, counter productive, etc.
| behaviors in an economy. You need psychology, and not just
| math, to describe the economics which happens in the real
| world.
| abdullahkhalids wrote:
| Game theory definitely does not require rational agents.
| Game theory says there are agents with certain specified
| strategies. Whether a strategy is rational from the
| underlying theory of value the agent adopts is completely
| separate matter. For example, its very common to study
| agents who always do one action no matter what others do
| or what the reward function is. Hard to call such actors
| rational, but that does not stop as from studying them.
| runarberg wrote:
| When I said _rational_ I meant it in this way. That
| rational agents will perform in a way in which maximizes
| their utility (or reward function). In psychology we call
| this theory _homo economicus_ [1]. Regardless of theories
| of value, perceived rewards, and utilities, human beings
| have biases, prejudice, superstition, dogma, etc. etc. In
| real economies these non-strategic behaviors are
| consistently observed. This is why I say that economics
| are not just game theories, they are psychology,
| sociology, religion, as much as they are zero-sum games
| between actors.
|
| > Hard to call such actors rational, but that does not
| stop as from studying them.
|
| This is precisely why I object to your first post. _"Shut
| up and do the math"_ has not done the wonders which
| string theorists had hoped. Game theory is a perfectly
| fine way to mathematics, and to study certain strategies,
| but it tells us nothing about the nature of economies in
| the real world.
|
| https://en.wikipedia.org/wiki/Homo_economicus
| schmidtleonard wrote:
| > arguments against mercantilism
|
| It has been funny to watch the rise of "China is beating us"
| rhetoric against the steady backdrop of "mercantilism is
| obsolete/bad" dogma, because the elephant in the room is that
| China has been running a textbook mercantilist playbook.
| cowpig wrote:
| Looks to my uneducated eye like China has been enforcing
| competitive markets internally, with consistent economic
| policies. Meanwhile the US has stopped enforcing antitrust
| altogether and keeps violently changing its mind about
| economic policy every four years.
|
| And then externally Chinese policy is oriented around
| suppressing the value of its currency, which is basically a
| monopolist's tactic--artificially lowered prices in order
| to crowd out competition.
|
| I think that's mercantilist-ish, but kind of a modern
| version?
|
| It's definitely the opposite of what the US does, the
| currency is the world reserve and therefore drives the
| price of the dollar above what it would be without trade,
| which I guess makes exporting from the US much more
| difficult?
|
| Anyone who is an expert in global economics please correct
| me here :)
| naasking wrote:
| > Thiel's book has influenced so many entrepreneurs into
| believing Monopolies are Good.
|
| Haven't read his book, but the idea that monopolies are good
| isn't typically made in a vacuum, it's made relative to
| alternatives, most often "ham-fisted government
| intervention". It's easier to take down a badly behaving
| monopoly than to change government, so believing monopolies
| are better than the alternatives seems like a decent
| heuristic.
| vonneumannstan wrote:
| >Haven't read his book, but the idea that monopolies are
| good isn't typically made in a vacuum, it's made relative
| to alternatives, most often "ham-fisted government
| intervention". It's easier to take down a badly behaving
| monopoly than to change government, so believing monopolies
| are better than the alternatives seems like a decent
| heuristic.
|
| What? How is the first alternative poor government instead
| of multipolar competing companies? When was the last time a
| Monopoly was actually broken up in the US? ATT/Bell 50
| years ago? lol
| mrcincinnatus wrote:
| Good for whom, exactly?
| billiam wrote:
| This seems like a classic straw man argument. Plutocratic
| oligarchs have been making the argument that private
| monopolies are better than representative democracy at
| basically anything for decades.
| billiam wrote:
| This seems like a classic straw man argument. Plutocratic
| oligarchs have been making the argument that private
| monopolies are better than representative democracy at
| basically any societal function for decades without any
| actual data.
| layer8 wrote:
| How would a bad monopoly be likely to be taken down if not
| by government intervention?
| logicchains wrote:
| It eventually becomes so big and inefficient that it gets
| overtaken by new competitors.
| yoyohello13 wrote:
| A Monopoly implies an organization powerful enough to
| stop competition. Seems like this solution that relies on
| competitors is fatally flawed. If there are enough
| competitors to meaningfully compete then there isn't a
| monopoly.
| naasking wrote:
| You can only truly stop competition by government
| intervention.
| yoyohello13 wrote:
| When an organization gets big enough it is
| indistinguishable from government.
| layer8 wrote:
| A monopoly comes with serious moats, otherwise it
| wouldn't be one. It can stay big and inefficient for
| decades.
| Jensson wrote:
| Not if they hire good to go and literally kill the
| competition.
| naasking wrote:
| Open source vs. Microsoft is a great example.
| slopinthebag wrote:
| The government is a rare example of an extremely strong
| monopoly and not just a duopoly or a company holding
| significant marketshare. And yet people never seem to
| criticise it on those grounds despite it suffering from all
| of the same problems that corporate monopolies are accused
| of.
| tim333 wrote:
| In democracies people can vote in control of the government
| to benefit themselves, unlike private monopolies. Corrupt
| autocracies get much criticism.
| slopinthebag wrote:
| The amount of political control individuals have in a
| democracy is much less than people think. I get to vote
| every few years for a small preselected handful of
| representatives, none of whom represent me or my views,
| and that vote is usually meaningless anyways. In my
| political life _none_ of the parties I have voted for
| have won an election. So tell me how much control of the
| government do I have? How much do any of us have?
| Especially when the government itself often goes against
| the wishes of their voters anyways. The reason democracy
| is preferable to a dictatorship is because it prevents
| the government from doing things which are _widely_
| unpopular, like committing acts of genocide and political
| violence. But that 's it really.
|
| Remember, governments have a monopoly in areas of life
| that impact everybody constantly. Private monopolies do
| not, in every case you can simply ignore them and not
| purchase their products, and by doing so you exert more
| control over them than you do casting a meaningless vote
| every few years.
|
| The idea of democracy being will of the people is pure
| fantasy. It's useful to prevent governments from doing
| really bad things, that's it. It doesn't even matter who
| you vote for, broadly speaking. Just that you are able to
| exert that pressure.
| Izikiel43 wrote:
| Globalization was great for poor countries, not so much
| developed economies.
| js8 wrote:
| No it wasn't. Look at Joseph Stiglitz (Globalization and Its
| Discontents) and Ha-Joon Chang (Bad Samaritans, Kicking Away
| the Ladder) for counter-examples.
| nutjob2 wrote:
| This isn't correct. The deal is that the poor countries get
| development and increased employment, and the rich countries
| get lower prices. Generally speaking both types of countries
| get richer.
|
| That some workers lost their jobs is a symptom of any change.
| I don't know why people always get upset people losing their
| jobs. It's like death, if no one died relatively few people
| would be born. If you resist job losses you reduce overall
| employment and economic development.
| chromacity wrote:
| Are you serious? People get upset about losing jobs because
| they need jobs to pay their bills. Further, we often build
| our life identities around work; if you're a good car
| mechanic or a successful restaurant owner, you're proud of
| that. It's a part of you.
|
| Having to repeatedly restart your career is risky, painful,
| and demoralizing. I have no problem seeing why people don't
| like that and why it can lead to populist backlash or even
| violent revolutions (as it did in the past).
|
| By the way, to address your closing comment: people don't
| like dying either and tend to get upset when others die?
| km3r wrote:
| Society is better if we sacrifice one horse and buggy
| driver job for two engineering jobs. The drivers suffer
| from that, but the net win for society is so plainly
| obvious that it's a better investment to retrain the
| driver or just pay the off rather than support a job that
| dying anyways.
| palmotea wrote:
| > Society is better if we sacrifice one horse and buggy
| driver job for two engineering jobs.
|
| That's a "statistic" you're pulling out of your butt, and
| it's doing a lot of work. No one ever knows if something
| like that will actually happen.
|
| It could actually turn out that AI sacrifices 100
| engineering jobs for 10 low-level service or prostitution
| jobs and a crap-ton of wealth to those already rich.
|
| > The drivers suffer from that, but the net win for
| society is so plainly obvious that it's a better
| investment to retrain the driver or just pay the off
| rather than support a job that dying anyways.
|
| But what _actually_ happens is our free-market society
| doesn 't give a shit. No meaningful retraining happens,
| no meaningful effort goes into cushioning the blow for
| the "horse and buggy driver." Our society (or more
| accurately, the elites in charge) go tell those harmed to
| fuck off and deal with it.
| esafak wrote:
| > It could actually turn out that AI sacrifices 100
| engineering jobs for 10 low-level service or prostitution
| jobs and a crap-ton of wealth to those already rich.
|
| That's where wealth redistribution (Taxation) comes in.
| The USA is not good at progressive taxation, but everyone
| could be better off if it were implemented properly.
| Izikiel43 wrote:
| > The USA is not good at progressive taxation
|
| The top 10 percent of incomes pay 76% of all income
| taxes, the top 5% pays around 55% of all income tax.
|
| I would say it's pretty progressive.
| nutjob2 wrote:
| > But what actually happens is our free-market society
| doesn't give a shit.
|
| Maybe in the US, but in other countries those things
| actually happen. It's a political issue, not a moral
| issue with technology.
| shafoshaf wrote:
| I don't think the point is that the transition isn't
| difficult. It is that there is an overall benefit that
| outweighs the challenges of the transition.
|
| The sad part is that industrializing societies have not
| been very good at reconciling the benefits with the
| costs. The benefits first go to a select few and have
| seeped out to the masses slowly. Railroads in the US are
| a good example. The wealth accumulated by the
| Vanderbilts, Hills and Harrimans, did not get
| redistributed in any kind of equitable manner. However,
| everyday people did eventually gain a lot of benefit form
| of those railroads through economic expansion. (None of
| which address the loss of the native Americans, whose
| losses should also be part of the equation.)
| layer8 wrote:
| My impression is that the transition is such an open-
| ended process that you can't really call it that. It's
| unclear if and when the challenges will be overcome.
| nutjob2 wrote:
| You're missing my point. Job losses are a fact of life,
| just like death. Why should people get upset about the
| fact that someone might lose their job, or die? It's not
| amoral. These things happen constantly to millions of
| people, we'd we worn out. We happily send young healthy
| people to their death fighting in wars so we don't have
| to. I don't see people weeping because the armed forces
| exist.
|
| Or is this just some sort of PC bullshit, that we can't
| talk about this sort of progress without carefully
| lamenting job losses? If you're not useful doing a job,
| why should you be employed in it? That's the bottom line.
| intended wrote:
| Oh come now - globalizations was great at the regional level.
|
| It was not that great for sub groups within developed
| nations.
|
| The original thesis believed that people would be retrained
| into other equally well paying roles.
|
| Turns out people can't retrain into new domains, and led to
| under employment.
| esafak wrote:
| Why not, because they're too old to learn, or because the
| support infrastructure is not there? I believe most people
| are capable of continued learning, but they might need help
| (financial etc.) to make the transition.
| zitterbewegung wrote:
| Not even sure if AI was ever "human-centered" . DARPA funded a
| large amount of AI reseearch from even the 1960s. The DART tool
| used in the Gulf War made back all of their previous
| investments. [1]
|
| [1]
| https://en.wikipedia.org/wiki/Dynamic_Analysis_and_Replannin...
| sendes wrote:
| > We assert that artificial intelligence is a natural evolution
| of human tools.
|
| While nowhere in the paper this is actually asserted but the
| abstract, a whiggish narrative of a genuinely unprecedented
| technology --such that it can replace and supersede human
| "labour" altogether (one is reminded of The Evolution of Human
| Science by Ted Chiang)-- sounds naive at best, dangerous at
| worst.
| jebarker wrote:
| I don't see why "natural evolution of human tools" implies
| "such that it can replace and supersede human labor
| altogether". Can you clarify?
| sendes wrote:
| A common error in historical thinking tends to see human
| tools essentially as a positive linear plot between time and
| progress. But these tools until AI had the common property of
| being enhancing of human cognition, because they couldn't do
| the thinking _for you_. AI can do just that, and for all the
| benefit it brings, seeing it simply as the next step in the
| "natural evolution of human tools" is alarmingly disarming
| coming from frontier thinkers.
| nutjob2 wrote:
| * For certain speculative definitions of AI
| lovelearning wrote:
| > these tools until AI had the common property of being
| enhancing of human cognition, because they couldn't do the
| thinking for you
|
| I have a different take, centered around this idea: Not
| everyone was into thinking about everything all the time
| even before AI. I'd say most people most of the time
| outsourced actual thinking to someone else.
|
| 1) Reading non-fiction books:
|
| Not all books, even the non-fiction ones, necessarily
| require any thinking by the reader. A book that narrates
| history, for example, requires much less thinking than
| something like "The Road to Reality" or "Godel Escher
| Bach."
|
| Most of us outsourced the thinking and historical method to
| the authors of the history book and just passively consumed
| some facts or factoids. Some of us memorize and remember
| these factoids well, but that's not thinking, just
| knowledge storage.
|
| Philosophically, what's the difference between consuming
| books this way and reading an LLM's output?
|
| 2) Reading research papers:
|
| Most people don't read any research papers at all. No
| thinking there. Most people don't head to some forum to ask
| about latest research either. Also, researchers in most
| fields don't come out and do outreach regularly.
|
| Indeed, an LLM may actually be the only pathway for a lot
| of people to get at least _some_ knowledge and awareness
| about latest research.
|
| Those of us in scientific, engineering, humanities,
| healthcare fields may read some to many papers. But only a
| small subset reads very critically, looking for data
| errors, inconsistencies, etc. For most of us, the knowledge
| and techniques may be beyond our current understanding and
| possibly without any interest in understanding them in
| future either.
|
| Most of us are just interested in the observations or
| conclusions or applications. Those may involve some
| thinking but also may not involve any thinking, just blind
| acceptance of the paper's claims and possible applications.
|
| 3) Coding:
|
| Again, deep thinking is only done by a small set of
| programmers. Like the ones who write kernels, compilers,
| distributed algorithms, complex libraries.
|
| But most are just passive consumers who read some examples
| online or ask stackoverflow or reddit for direct answers.
| Some even outsource all their coding entirely to gig sites.
| Not much thinking there except pricing and scheduling.
| What's the difference between that and asking an LLM or
| copying an LLM's answers? At least, the LLMs patiently
| explain their code, unlike salty SO users!
|
| ----
|
| IMO, most people weren't doing much thinking even pre-AI.
|
| Post-AI, it's true that some people who did do some
| thinking may reduce it.
|
| But it's equally true that those people who weren't doing
| much thinking due to access or language barriers can
| actually start doing some thinking now with the help of AI.
| sendes wrote:
| > I'd say most people most of the time outsourced actual
| thinking to someone else.
|
| Someone else being human, until now. That may change.
| That's the whole point!
|
| But I concur with your general point on the upstream
| production of thinking and knowledge. Indeed, such elite
| thinkers are those in economic history referred to as the
| "upper-tail human capital". Terence Tao being one of them
| giving license to the kind of thinking that accepts AI as
| a simple tool that is not fundamentally breaking our
| relationship with technology is what exactly I am
| protesting.
|
| > But it's equally true that those people who weren't
| doing much thinking due to access or language barriers
| can actually start doing some thinking now with the help
| of AI.
|
| If only we keep thinking that thinking is a comparative
| advantage of our species, I suppose!
| Zigurd wrote:
| I'm glad I can still count on HN to come across the correct use
| of a lesser known definition of a word.
| nutjob2 wrote:
| > supersede human "labour" altogether
|
| For certain types of labor this has always been the case.
|
| The idea that AI will entirely replace all, or most, human
| labor makes no sense and is just AI hype.
|
| Like all technology before it AI will improve most people's
| lives.
| palmotea wrote:
| > Like all technology before it AI will improve most people's
| lives.
|
| 1. Let's be clear: what you're describing is faith.
|
| 2. And what are you smoking to assert " _all_ technology
| before ... AI [improved] most people 's lives"?
| nutjob2 wrote:
| > 1. Let's be clear: what you're describing is faith.
|
| And what I am countering is not? You can easily argue
| technology generally improves lives. Is it optimal? Beyond
| abuse? No. Does it have unintended consequences? Yes. Are
| we better of without it? No.
|
| > 2. And what are you smoking to assert "all technology
| before ... AI [improved] most people's lives"?
|
| OK social media is an unmitigated disaster, I'll give you
| that.
|
| But, for example, nukes have given us the longest period of
| relative peace in history.
| GodelNumbering wrote:
| > Today, unlike in the Luddites' time, we are already seeing
| skilled workers replaced not with lower-wage human labor, but
| with AI.
|
| To me this is the weakest claim of the article. This claim been
| thrown around endlessly without proof.
|
| https://fred.stlouisfed.org/series/IHLIDXUSTPSOFTDEVE
|
| Software Engineer job openings for instance is at 2 year high
| (still far lower than covid dislocations though), but arguably
| all Enterprise AI was built or deployed in the last two years. We
| should have seen a crash in the job openings if the AI job
| replacement claim was correct.
|
| This is something I've spend some time thinking about (personally
| written article, not AI slop):
| https://www.signalbloom.ai/posts/why-task-proficiency-doesnt...
| dude250711 wrote:
| It's not "the age of AI", it's just a Slop Decade.
|
| And the tools did not become "exponentially sophisticated", one
| thing it's logarithmic, another is that the improvements are
| questionable. But "pervasive" - yes, granted.
| vasco wrote:
| Is there a better illustration of the power of UX than the fact
| that a messaging chat interface was able to set free all of human
| knowledge from copyright, whereas a bittorrent client couldn't?
| gettingoverit wrote:
| In fact, the paper has an error in the argument that AI might
| find Fermat's theorem to be incorrect due to definition of
| natural numbers including a zero, because paper's version of a
| theorem explicitly says that the number should be greater than
| two, and zero cannot be greater than two.
|
| Surprisingly, this mistake proves the author's point that human
| can implicitly understand what was said, and that it still has
| value to it, even if it's incorrect.
| svat wrote:
| The short blog post announcing this paper:
| https://terrytao.wordpress.com/2026/03/29/mathematical-metho...
|
| In particular:
|
| > _This is an unabridged version of a solicited article for a
| forthcoming Blackwell Companion to the Philosophy of Mathematics.
| [...] took over a year to write - which means, at the current
| pace of development in the field, that some of it is already
| slightly out of date._
|
| ----
|
| Edit: The post at https://mathstodon.xyz/@tao/116319186983426174
| mentions also an (entirely unrelated) popular-math presentation
| titled "What does it mean to think like a mathematician?"
| https://terrytao.wordpress.com/wp-content/uploads/2026/03/ta...
| which is interesting too (despite the ChatGPT-generated
| illustrations and repeating stuff Tao has said before, on his
| blog etc.)
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