Mathematical methods and human thought in the age of AI (arxiv.org)

by zaikunzhang 93 comments 218 points
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93 comments

[−] woolion 46d ago

> 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 46d ago

> "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.

[−] slopinthebag 46d ago
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 46d ago
In democracies people can vote in control of the government to benefit themselves, unlike private monopolies. Corrupt autocracies get much criticism.
[−] slopinthebag 46d ago
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.

[−] jkhdigital 46d ago
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[−] schmidtleonard 46d ago

> 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 46d ago
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 :)

[−] mxkopy 46d ago
I mean they did execute a wealthy banker a couple years ago. So I think the mercantile class occupies a different place in society there than in America
[−] naasking 46d ago

> 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 46d ago

>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

[−] layer8 46d ago
How would a bad monopoly be likely to be taken down if not by government intervention?
[−] logicchains 46d ago
It eventually becomes so big and inefficient that it gets overtaken by new competitors.
[−] yoyohello13 46d ago
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.
[−] layer8 46d ago
A monopoly comes with serious moats, otherwise it wouldn’t be one. It can stay big and inefficient for decades.
[−] Jensson 46d ago
Not if they hire good to go and literally kill the competition.
[−] naasking 46d ago
Open source vs. Microsoft is a great example.
[−] mrcincinnatus 46d ago
Good for whom, exactly?
[−] billiam 46d ago
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.
[−] billiam 46d ago
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.
[−] abdullahkhalids 46d ago
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/

[−] zitterbewegung 46d ago
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...

[−] woolion 46d ago
I just re-read my comment (too late for edits) and there are a number of typos (including missing "not") that significantly degraded the syntax, but the point kind of came across anyway.
[−] Izikiel43 46d ago
Globalization was great for poor countries, not so much developed economies.
[−] gradstudent 46d ago
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.

[−] sendes 46d ago

> 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.

[−] GodelNumbering 46d ago

> 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...

[−] vasco 46d ago
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 46d ago
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 46d ago
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.)

[−] dude250711 46d ago
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.

[−] syntheticmind 46d ago
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[−] imta71770 46d ago
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[−] alex1sa 46d ago
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[−] onlinealarmkur 46d ago
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[−] bluecheese452 47d ago
Enough Terence Tao spam.