Mathematical methods and human thought in the age of AI

zaikunzhang

See also https://www.youtube.com/watch?v=zJvuaRVc8Bg

bluecheese452

Enough Terence Tao spam.

gradstudent

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.

woolion

> 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".

sendes

> 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

> 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

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

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

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

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.)