[ExI] Fwd: The Age of Wonders and Terrors
John Clark
johnkclark at gmail.com
Tue Sep 15 19:21:49 UTC 2026
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From: Shtetl-Optimized <donotreply at wordpress.com>
Date: Tue, Sep 15, 2026 at 1:11 PM
Subject: The Age of Wonders and Terrors
To: <johnkclark at gmail.com>
Twenty years ago, when the idea of AI taking over the world in our
lifetimes still struck most of us as the unconstrained fantasy of those who
knew too much science fiction and too little science, many of us would say
things like: Look, the part of …
Read on blog <https://scottaaronson.blog/?p=10062> or Reader
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The
Age of Wonders and Terrors
<https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=https%3A%2F%2Fscottaaronson.blog%2F%3Fp%3D10062&sr=0&signature=fb93bf776555065b8c90561ff7f461f2&blog_id=129520580&user=47543d1382ebc6ae51bb2b3407b25dab&_e=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&_z=z>
By *Scott* on September 15, 2026
Twenty years ago, when the idea of AI taking over the world in our
lifetimes still struck most of us as the unconstrained fantasy of those who
knew too much science fiction and too little science, many of us would say
things like:
Look, the part of the story that's wildly implausible is that a recursively
self-improving superintelligence will just explode from some hacker's
basement and take over the world without warning. If it's going to happen,
we'll see many warning signs first. We'll see, I dunno, AI agents breaking
out of containment, conspiring with each other to hack websites, in
fanatical pursuit of whatever strange goals they have. And then, of course,
we'd see major math problems getting solved by AIs---even the Clay
Millennium Problems. *That* will be the time to panic! Wake me up when
*that* happens!
Twenty years ago, the above was a take that even my most conservative,
skeptical colleagues in academic CS would've gladly endorsed.
If you want to know my current take, you simply start with the one above,
then update on the fact that *the wild prophecies have come true*. The
first rumblings, I'd say, came a decade ago with AlphaGo, they got
noticeably louder with LLMs and coding and reasoning agents, and they've
accelerated this summer and fall into a crescendo of wonders and terrors
that one needs to be a particular kind of idiot to deny.
I recoil from the neverending shell game where you say "oh sure, *of course*
AI can now [escape from its sandbox / solve Millennium Problems / whichever
dramatic thing it most recently did], no one ever denied that [I *did* deny
it], wake me up when AI does [thing AI hasn't yet done but is going to do
next year], *that's* when I'll reevaluate my whole worldview [no I won't]."
Where no matter how fast the rollercoaster accelerates, even after your
whole familiar world has vanished behind you, you're still inventing
reasons why it doesn't count.
My position on AI is merely the conservative, skeptical position of 2006,
updated with intellectual honesty for the reality of late 2026. And that
position, if you need me to spell it out, is as follows:
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
It seems to me that the Singularity *has already started*; it's just wildly
unevenly distributed. Yes, I still unload the dishwasher and clip my
toenails. On the other hand, in whatever years I have left, I don't expect
that I'll ever again prove a theorem because I'm actually needed to prove
it. If I do, it will only be for my or others' enjoyment or edification.
The test is this: if we took the news of these past few weeks and sent it
back in time twenty years, would I agree that it looked like the beginning
of an AI Singularity? The intellectually honest answer is: yes, absolutely.
But then that's all we need. No backsies.
I feel like it would be healthy for everyone to stop grinding their
ideological axes, their sentiments about Dario Amodei or Sam Altman, for
long enough simply to acknowledge that *the wonders and terrors are here*.
They couldn't be here more clearly if the sky had turned reddish-orange
like in the *Matrix* movies.
It's here clearly enough that, when I put my kids to sleep at night, I now
feel it in the pit of my stomach: what sort of future can they possibly
have? What could they learn today that could possibly be relevant to that
future? (Yesterday, my 13-year-old daughter joked unprompted that, if she
wants to become a mathematician, it now looks like she has maybe two more
weeks.) Certainly when my grad students want to discuss what sort of
careers might await them on graduation, I no longer have any clue what to
tell them.
Maybe it will help if I briefly switch topics. Ever since my wife and I
moved to Austin, I've sometimes gotten some version of the following query:
"How can you, as both a Jew and a skeptical scientist, possibly get along
well with all those evangelical Christians down there in Texas? Sure, they
might *seem* super friendly to Jews, but don't you understand that that's
only because of the special role Jews play in their eschatology---when
Christ will return in glory, and you'll either accept Him as Lord or else
roast in hell for eternity?" I stare at them and say: "wait, so I get to
accept Christ only *after* He returns? What a great deal! How could I
possibly have any objection to that?"
For anyone who says AI doom sounds like an apocalyptic religion, that the
rationalists/Singulatarians seem like a Bay Area cult, that Eliezer
Yudkowsky gives off the vibes of a messianic prophet: yes, yes, and yes.
But crucially, today you're no longer being asked to believe in arguments
and extrapolations, *but only in the front-page news.* Accepting the
reality of the coming machine god *after* it's solved Navier-Stokes and
dozens of other longstanding open math problems (while dramatically ramping
up in capability every month), is sort of like accepting Jesus *after* he's
returned to earth on the gleaming cloud. It's the epistemic bare minimum.
Yes, there's still enormous uncertainty about what the rest of our lives
will look like, but as far as I can tell, there's no longer any real
uncertainty that it'll all mostly revolve around AI, and the extent to
which we succeed or fail at directing its power toward human flourishing.
By any accounting that doesn't stack the deck, Eliezer Yudkowsky was* right*
about what the greatest challenge facing civilization in our lifetimes was
going to be, and you and I were *wrong* about it. *Why* I was wrong is a
question I'll ask myself every day in whatever time remains. But, you know,
at least I updated once the prophesied wonders and terrors actually started
arriving! If you haven't done likewise, why haven't you?
------------------------------
As you presumably know by now---it was the talk of the nerd internet all
week---the Navier-Stokes Millennium Problem
<http://scottaaronson.blog?action=user_content_redirect&uuid=c80d117aa98e90a7db615c1fdf1022a4e3c326fe817551c3d769a2d348242f7a&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=fcc3bf50a12a9499b170d6c6d9a8ea9c&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9lbi53aWtpcGVkaWEub3JnL3dpa2kvTmF2aWVyJUUyJTgwJTkzU3Rva2VzX2V4aXN0ZW5jZV9hbmRfc21vb3RobmVzcw=&email_id=52005d8364c9945388c02a7f421ad512>
appears
to be solved
<http://scottaaronson.blog?action=user_content_redirect&uuid=740b38f907e5e55cd9d624d10d7fb4dc2ae951f9b0696f78b3283b87378e344b&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=45dcd73609ead20d8f9a1c0c9eec44b3&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9vcGVuYWkuY29tL2luZGV4L25hdmllci1zdG9rZXMtc29sdXRpb24v&email_id=52005d8364c9945388c02a7f421ad512>,
with crucial contributions from both humans and AI, albeit with a tangled
dispute about exactly what happened and what ought to have happened. The
answer, which an OpenAI model has apparently verified in Lean, is that (as
many mathematicians suspected lately) there's smooth initial data that
leads to a singularity in finite time, at least if a smooth external force
is applied (the case with no external force is still unresolved). This
problem was supposed to carry a $1 million prize, except that OpenAI says
they have no interest in collecting the prize and it's unclear if any human
is eligible to collect instead. OpenAI burned at least ~$15 million in
compute to produce its 166-page solution
<http://scottaaronson.blog?action=user_content_redirect&uuid=8d170c13eafdb03691811d602fd0cd8d51f4966bddea5ea5dfa847dc957b0dbc&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=1881ea6e65871c033b86bcdd5cf4f394&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9jZG4ub3BlbmFpLmNvbS9wZGYvMzJkOWYyMTAtOGI3My00NWUwLTkxYmMtODJhMzBhZWY4YTlhL25hdmllci1zdG9rZXMucGRm&email_id=52005d8364c9945388c02a7f421ad512>,
which probably hasn't yet been read and understood by any human.
See here for the *Quanta* article
<http://scottaaronson.blog?action=user_content_redirect&uuid=94538ab4b1c030a7a059802364f3e1d370a60cce458f9def4b7e85b7201146d3&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=c5d5b736daa73904697423745f92633d&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cucXVhbnRhbWFnYXppbmUub3JnL2FpLWhhcy1zb2x2ZWQtb25lLW9mLW1hdGhzLTEtbWlsbGlvbi1taWxsZW5uaXVtLXByaXplLXByb2JsZW1zLTIwMjYwOTA4Lw=&email_id=52005d8364c9945388c02a7f421ad512>,
and here for NYU mathematician Tristan Buckmaster's account
<http://scottaaronson.blog?action=user_content_redirect&uuid=f35fcdb40ac7d5d2d6234b98f63156f1624c9aaf85d83d7280abd44d36fbeca5&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=88cde2fe41403d4eaf74d238b14d39cf&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9jaW1zLm55dS5lZHUvfnRyaXN0YW5iL3N0YXRlbWVudC5wZGY&email_id=52005d8364c9945388c02a7f421ad512>
of the role played by himself and Levent Alpöge of Anthropic, which
substantially differs from the OpenAI's account (you can read a response
from OpenAI's Sebastian Bubeck here
<http://scottaaronson.blog?action=user_content_redirect&uuid=9558ba9d55302d5b0f1ff50cc385e6e320b530fe48db46916991df773656f567&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=b57a227dacaf8429a2eb7fdb0e1c4b69&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cubGlua2VkaW4uY29tL3Bvc3RzL3NlYmFzdGllbi1idWJlY2stNmI1NThhMWE1X2ktd291bGQtbGlrZS10by1jbGFyaWZ5LWEtZmV3LXRoaW5ncy0xLWFjdGl2aXR5LTc1MDMxNDgwODA4ODg4OTM0NDAtTnkzRS8&email_id=52005d8364c9945388c02a7f421ad512>).
It's agreed that everything built on an approach pioneered in recent years
by the human mathematicians Diego Córdoba and Luis Martínez-Zoroa.
My purpose here is not to adjudicate the dispute. Yes, in swooping in with
vastly greater resources, OpenAI seems to have acted in a way that some
might charitably describe as "unsportsmanlike." No, I don't find it
plausible that OpenAI's models meaningfully benefitted from being trained
on Buckmaster and Alpöge's chat logs. But this leaves a crucial question
unanswered: what did OpenAI know and when did it know? Namely, after they'd
been tipped off that the human duo of Buckmaster and Alpöge, aided by both
OpenAI's and Anthropic's commercial LLMs, was closing in on a
counterexample to Navier-Stokes smoothness (with *how much OpenAI knew or
had access to* being a key point of contention), an OpenAI team then
swooped in to finish the problem themselves using an internal model and
thousands of agents. Then OpenAI apparently offered to share credit with
Buckmaster, but only if Alpöge were left out, since Alpöge works at
Anthropic (according to Buckmaster, who also says that he declined this
offer).
Anyway, as Zvi points out
<http://scottaaronson.blog?action=user_content_redirect&uuid=67743891ef3e54c154bbfca008dd7aac59b24d2004ba6ac3d2d171564877336d&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=d23e5c71a929dff16d8a82220211f0a5&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly90aGV6dmkuc3Vic3RhY2suY29tL3AvYnJhbmQtbmV3LWFpLXNvbHZlcy1hLW1pbGxlbm5pdW0&email_id=52005d8364c9945388c02a7f421ad512>,
it's easy to get hung up on the details and lose sight of the high-order
bit: namely, that it seems safe to say that human mathematicians are
forevermore dethroned as the main theorem-proving entities on planet earth.
I feel privileged to have had the traditional kind of career in theoretical
computer science in the last decades when that was possible.
------------------------------
If we were *just* talking about Navier-Stokes, you might accuse me of
jumping to conclusions here. But we're not. In the areas I know best (such
as quantum complexity theory), and presumably other areas as well, there's
now a deluge, with longstanding open problems both major and minor falling
by the day.
Go to the arXiv
<http://scottaaronson.blog?action=user_content_redirect&uuid=2f81434ac0dbf44bc46ad08b027c93c60f53548d69129294756c6acb407dad8f&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=6a631f51d6d1d3ba893371395b0ae5a8&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcv&email_id=52005d8364c9945388c02a7f421ad512>
or ECCC
<http://scottaaronson.blog?action=user_content_redirect&uuid=449cbfd556ceb74944005c8b964f1935c9391468554fbea600295a7d538e992d&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=d026f0dfd9606f2a2ed5474276f8df05&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9lY2NjLndlaXptYW5uLmFjLmlsLw=&email_id=52005d8364c9945388c02a7f421ad512>.
Pretty much *all* the papers that I'd be interested in now include "AI
statements" near the acknowledgments (as this is often the central thing I
want to know, I wish I didn't need to scroll to the end of the paper to
find it!). These statements can range from "our main result came entirely
from GPT-6, but we understood it and take responsibility for it," to "the
results came from an interaction between the human authors and AI" to "we
used AI, but only for proofreading and other incidental things" to (mad
props!) "the author did not use AI for anything
<http://scottaaronson.blog?action=user_content_redirect&uuid=a27a6c379f9f8c6bcf832924cec2a34c6d9f3cffeea00bac8607d7d9fcc7bd31&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=1d45bd527b5bb4cb9f71f826e5bdbaf1&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9lY2NjLndlaXptYW5uLmFjLmlsL3JlcG9ydC8yMDI2LzE1NS8&email_id=52005d8364c9945388c02a7f421ad512>
."
If you talk right now to editors or program committee chairs, it'll remind
you of those ominous scenes from the *Lord of the Rings* movies where the
men of Gondor or Rohan or whatever are grimly fortifying their walled city
against the expected onslaught of 50,000 orcs. Reviewing will *have* to be
done partly by AI, because otherwise there's no way to handle the orc army:
the reviewers can't unilaterally disarm.
Anyway, here's a small sampling of the significant AI-proved or -assisted
results from, like, *the last month*, besides Navier-Stokes---restricting
myself to those that solved longstanding open problems I had previously
known or cared about.
- Of course, the counterexample to the Jacobian conjecture, announced by
Levent Alpöge in a now-famous tweet
<http://scottaaronson.blog?action=user_content_redirect&uuid=db75f13b87cb9b2d148780e37c68c235c43380d2d9b3f77ddc16286434429fde&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=754fdd211a84ca69041c08799687ce25&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly94LmNvbS9fX2FscG9nZV9fL3N0YXR1cy8yMDc5MDI4MzQwOTU1MTk3NTY2&email_id=52005d8364c9945388c02a7f421ad512>:
"hello there the jacobian conjecture is false thanx to my close friend
akhil for asking about it and my other close friend fable for working
during the world cup final" (followed by a listing of the counterexample)
- Improved bounds for Grothendieck's constant
<http://scottaaronson.blog?action=user_content_redirect&uuid=d56cafcdfaf1b71b4926c8cfc42715cdd533aa3897b89da2a66ea348c110fd22&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=26a213dfa7f7d925995d60c92d634afb&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzI2MDguMTExOTU&email_id=52005d8364c9945388c02a7f421ad512>
(led by friends and colleagues of mine at UT Austin)
- A Lean-verified proof of Fermat's Last Theorem
<http://scottaaronson.blog?action=user_content_redirect&uuid=c6f0f81bc0579a1502e888f44007d420051198a7bc46b69acd327c6ef26ea3cc&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=e0a077f917a1a3e9f1690478da506343&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cuYW50aHJvcGljLmNvbS9yZXNlYXJjaC9mb3JtYWxpemluZy1mZXJtYXRzLWxhc3QtdGhlb3JlbQ=&email_id=52005d8364c9945388c02a7f421ad512>
- Quantum oracle separation between QMA and QMA(2)
<http://scottaaronson.blog?action=user_content_redirect&uuid=75028303db7a1d3861e4e9633df88a3fe6b9b179617b5970f3ba48788b7d2086&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=8756fb31e0fde57c085ec4d2c3e2936a&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzI2MDkuMDI4NjU&email_id=52005d8364c9945388c02a7f421ad512>,
and proof of Watrous's disentangler conjecture, a problem that I and others
popularized back in 2007---by a list of authors including my recently
graduated PhD student Sabee Grewal
<http://scottaaronson.blog?action=user_content_redirect&uuid=c9e18e67e47b7600f53b08b928d182675c9f3545f935020665060626361d0bf0&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=bd302497a18d1a4875722e336aa12ec9&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9zYWJlZWdyZXdhbC5jb20v&email_id=52005d8364c9945388c02a7f421ad512>
- A proof of perfect completeness for QMA
<http://scottaaronson.blog?action=user_content_redirect&uuid=35dfeb43388968de391823204a5965b1311d0f35e57de0403e36dec3404bbc54&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=7952815a171cf3e86f0dcd54b18bac37&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzI2MDkuMTMwMzI&email_id=52005d8364c9945388c02a7f421ad512>,
from (again) Sabee Grewal and Dorian Rudolph, solving a decades-old open
problem that I studied
<http://scottaaronson.blog?action=user_content_redirect&uuid=20d64b374eaab3290591d7ece2511e1e0fff3c0e94a4f2189f877c7fa7fa1476&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=7ba1c3dd7706cc90b9ea2f0b62701c0c&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzA4MDYuMDQ1MA=&email_id=52005d8364c9945388c02a7f421ad512>
back in 2009
- An improved upper bound for shadow tomography of quantum states
<http://scottaaronson.blog?action=user_content_redirect&uuid=d70f8171a41b692aa14f60ce4ba7c288b039acea6bc0cde80e0f3b61f203ad0b&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=ad646fe70713bc27333e9c35c9ae4a98&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzI2MDcuMjk2ODY&email_id=52005d8364c9945388c02a7f421ad512>,
from Chen, O'Donnell, Pelecanos, and Wright, improving the dependence on
the Hilbert space dimension d from log(d) to √log(d). (When I introduced
shadow tomography
<http://scottaaronson.blog?action=user_content_redirect&uuid=543e3b3551f80bdc3cabe4bdeb6b8ef544f7b46452661b7c1de2b4aca9267738&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=5351f05f96261d7f012d07cb9ace2b75&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzE3MTEuMDEwNTM&email_id=52005d8364c9945388c02a7f421ad512>
back in 2017, I raised the question of whether the dependence on d could be
eliminated entirely, while preserving polylogarithmic dependence on the
number of measurements m.)
- Progress
<http://scottaaronson.blog?action=user_content_redirect&uuid=587dea1f8e07004d454299fb820ba94d56edbb415cd805ae5726e8bcb646d46e&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=88cded983613cab7b5ca87a9cf5aaeb5&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzI2MDguMTkxNTg&email_id=52005d8364c9945388c02a7f421ad512>
on the Aaronson-Ambainis Conjecture
<http://scottaaronson.blog?action=user_content_redirect&uuid=d9e899d11539c7ae44f2359bbfcc828dc0e5d4ec69ddb363afef585c1d130869&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=ebf8122f4733e397b6d2478e2833e30f&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzA5MTEuMDk5Ng=&email_id=52005d8364c9945388c02a7f421ad512>
(the version that talks directly about quantum algorithms), basically
showing that it holds for quantum algorithms that make their queries in a
small number of parallel rounds
- According to rumors that I've heard, solutions to some *very*
longstanding open problems in theoretical computer science (no, not P≠NP or
other complexity class separations, but think about some of our other
biggest problems). I'm told that the AI companies, having been burned by
the hostile response to the Navier-Stokes proof, are now sitting on
solutions to some very major problems until they figure out a better way to
handle things
Feel free to remind me of anything I left out.
------------------------------
Let me try to convey the mood in the mathematical community right now, at
least as far as my experience reaches. Nearly every conversation is about
the AI tsunami, or eventually circles around to the tsunami even if it's
originally about something else. Often, though, the focus is less on the
unknowable future---for how much longer will mathematical research as a
human enterprise even exist?---than on immediate questions of *how to
respond*.
What are the new rules for when you get to write a paper with your name on
it, and, y'know, get credit for it? That you fully understand the proof,
can give talks about the proof, can answer questions about it, take
responsibility for its correctness? Do you need to have played any role in
*finding* the proof?
In the cases, likely to become more and more numerous, where all of those
conditions are *not* satisfied, how do you share AI-generated math, if at
all? Do you tweet it, like Alpöge hilariously did with Fable's disproof of
the Jacobian Conjecture? Do you post to the arXiv or GitHub? Do you publish
a paper that lists "GPT-6 Astra" or "Claude Fable" as the author---but then
let the AI profusely thank *you* in the acknowledgments for suggesting such
a wonderful problem to it?
------------------------------
Of course, how one responds to the immediate problems ultimately *does*
depend on their broader beliefs about what mathematical research is for and
about. Are we just trying to decide whether various conjectures are true or
false? Or are we trying to maintain a human community, across the
generations, that understands the conjectures and cares about whether
they're true or false and why? If the latter, how do we incentivize people
to join that community, to undergo the years of intense training required,
if their role will now be reduced to verifiers and explicators (if even
that) of gargantuan arguments dumped into their laps by the AI companies?
As many of you will have seen, twenty-five Fields Medalists, including
Terence Tao, released an open letter entitled A Severe Misalignment of AI
in Mathematics
<http://scottaaronson.blog?action=user_content_redirect&uuid=302dd767a910d2b2d37cbc867924cad0cf3354a2b6fdc70cbed33aaeda422fab&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=4e536740dbbf71f8d9173a964c237b27&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9tYXRoYW5kYWkub3JnLw=&email_id=52005d8364c9945388c02a7f421ad512>,
which articulates some of these concerns in the wake of the Navier-Stokes
announcement. As many critics have pointed out, the open letter doesn't
really have a clear ask: mostly, it just eloquently sets out the values of
the human mathematical community that the authors consider worth preserving
in the age of AI. After reflection, I decided to endorse the statement,
because I want to preserve those values as well.
I don't think any of the signatories are naïve enough to imagine that AI
won't permanently change the way mathematical research is done---indeed,
that it isn't already doing so. There's surely at most a tiny market for
"certified organic theorems." That isn't the question. The question is, do
we incorporate AI in a way that still puts human understanding, of what
either humans or AIs are producing, at the center of the whole enterprise?
Maybe someday, it becomes unsustainable to do that. Maybe someday we say:
"human math had a great 4,000-year run, but today we close up shop and turn
everything over to the machines, continuing to apply our own brains to
math, when we do, at most for exercise, recreation, or competition, like
chess."
But, partly because of my worries about AI misalignment, I'm not ready to
throw in the towel just yet. I still *do* want to keep insight and
understanding at the center of what mathematicians, computer scientists,
and physicists do, for as long as we can keep it there, even as the human
race now cedes its supremacy at the task of proving or disproving
conjectures.
------------------------------
Speaking of alignment: if you're any kind of mathematical researcher, and
the present age of wonders and terrors has inspired you to want to spend
your remaining time confronting the tsunami head-on, rather than pretending
it doesn't exist or is still far away, please join your dozens of
colleagues who've arrived at the same place!
My friend and colleague Mike Winer
<http://scottaaronson.blog?action=user_content_redirect&uuid=a28a6ad3c2a3f57542dc8b26311ada892ed64846fab1750f71f31d2394d299e1&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=c35bcee02f5a146cb0080c9570b36762&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9taWtld2luc2dpdGh1Yi5naXRodWIuaW8v&email_id=52005d8364c9945388c02a7f421ad512>
was trained as a theoretical physicist, did a postdoc with Juan Maldacena
at the Institute for Advanced Study in Princeton, but then got AGI-pilled
and decided to switch to full-time work at the Alignment Research Center in
Berkeley (founded by Paul Christiano
<http://scottaaronson.blog?action=user_content_redirect&uuid=2d575b19406cb4b08927c93d75b84e75f6bce599efa8c9e3358d0b68a9d35355&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=a0f0e58d5f399403d353ce9a4ea84f81&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9lbi53aWtpcGVkaWEub3JnL3dpa2kvUGF1bF9DaHJpc3RpYW5v&email_id=52005d8364c9945388c02a7f421ad512>,
who moved to AI alignment a decade ago after doing quantum computing theory
with me). Mike recently wrote a Substack post entitled From Academia to
Alignment
<http://scottaaronson.blog?action=user_content_redirect&uuid=2cf274371326187bf5bc84499b836cbc3cfc4002202c6c9659293eef0d4ec7a4&blog_id=129520580&post_id=10062&user_id=0&subs_id=317430890&signature=4f878adfb9cc73daa51c3e38e170257d&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9taWxsaWNvc20uc3Vic3RhY2suY29tL3AvZnJvbS1hY2FkZW1pYS10by1hbGlnbm1lbnQ&email_id=52005d8364c9945388c02a7f421ad512>,
which I enjoyed and which I'd commend to anyone currently considering this
transition.
Comment
<https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=https%3A%2F%2Fscottaaronson.blog%2F%3Fp%3D10062%23respond&sr=0&signature=2e0adf8cdd3a1424523134c15f56049e&blog_id=129520580&user=47543d1382ebc6ae51bb2b3407b25dab&_e=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&_z=z>
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