[ExI] Dispatches from the last days of human relevance

Thu May 28 09:59:18 UTC 2026

*Quantum computer expert Scott Aaronson wrote this yesterday:*

*===*
*Dispatches from the last days of human relevance*

*By Scott Aaronson *

As most readers have presumably heard by now, Paul Erdös's Unit Distance
Problem
<https://scottaaronson.blog/?action=user_content_redirect&uuid=e1d2b543d54abdae09f00c47c6aa74342497f5457524d607965c77ef3254481e&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=55586574732a954c4bb2821126597460&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9lbi53aWtpcGVkaWEub3JnL3dpa2kvVW5pdF9kaXN0YW5jZV9ncmFwaA=&email_id=3d774be550584f63265fb5d090b4cbe2>
from
1946---one of the central open problems from the field of discrete
geometry---has been solved
<https://scottaaronson.blog/?action=user_content_redirect&uuid=2be8a5c817e27621b3b3979214d8fa0cac66888c57f1c2abff8e9ad6e2eb5112&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=0144bc4f1f16ae2b2fc37161b71846a6&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9jZG4ub3BlbmFpLmNvbS9wZGYvNzRjMjQwODUtMTliMC00NTM0LTljOTAtNDY1YjhlMjlhZDczL3VuaXQtZGlzdGFuY2UtcHJvb2YucGRm&email_id=3d774be550584f63265fb5d090b4cbe2>
by
GPT5.5Pro. Erdös had conjectured that, given n points in the plane, at most
n1+o(1) pairs of them could be unit distance apart. Using high-powered
results from algebraic number theory, GPT refuted this, constructing a set
with n1+ε unit-distance pairs, for ε ~ 10-38. Shortly afterward, Will
Sawin, a human (!), improved GPT's construction
<https://scottaaronson.blog/?action=user_content_redirect&uuid=37f0d9ae78da57f36de87c6b77ae7c3d55abff4d7c75591804dbaea62bde7d8a&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=3425c56e3c084c36294de6c210355fd6&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzI2MDUuMjA1Nzk&email_id=3d774be550584f63265fb5d090b4cbe2>
to
get ~n1.014 pairs. Meanwhile, the best known upper bound remains n4/3,
improving Erdös's n3/2.

he entire process seems have been one-shot: my former student Lijie Chen
<https://scottaaronson.blog/?action=user_content_redirect&uuid=ebc57c05f4749aea70cf7d5ecd98ee20bdf8fb2cc4de12161d30be984bec0759&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=4048061081474004a084cc98808bb12f&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9jaGVuLWxpamllLmdpdGh1Yi5pby8&email_id=3d774be550584f63265fb5d090b4cbe2>
simply
gave GPT the problem, then GPT thought for a while and output a
several-page argument that, on analysis by human experts, turned out to be
correct. *Of course* there's selection bias here; we're not hearing as much
about the hundreds of other problems GPT was given that it *didn't* solve
(isn't that the case with humans too?). Clearly, too, GPT was helped by the
facts that human mathematicians had wasted most of their time trying to
prove Erdös right rather than looking for a counterexample, and that, even
if they *did* look for a counterexample, they'd need to be experts in
algebraic number theory to find this one, which hardly any discrete
geometers are. So, *maybe* that suggests that AI, right now, is "merely"
picking various medium-hanging fruits that human mathematicians missed for
contingent reasons? With emphasis on the "right now."

In a companion paper
<https://scottaaronson.blog/?action=user_content_redirect&uuid=59733452193bf809b2ca0c47b9770c67fbd4bf46690a2b86dd26ffc5712b1842&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=811217d6c8c60f0249d52477395c5d92&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9jZG4ub3BlbmFpLmNvbS9wZGYvNzRjMjQwODUtMTliMC00NTM0LTljOTAtNDY1YjhlMjlhZDczL3VuaXQtZGlzdGFuY2UtcmVtYXJrcy5wZGY&email_id=3d774be550584f63265fb5d090b4cbe2>,
OpenAI helpfully included commentary from Timothy Gowers, Noga Alon, Will
Sawin, Daniel Litt, and many other experts, reflecting on the breakthrough,
the path that GPT took to get to it (which can actually be seen by
examining its chain-of-thought), and what this might mean for the future of
mathematical research.

I heard the news maybe an hour after it broke, when some UT grad students
came to my office to tell me. For what it's worth: these students were
morose, musing about how everything might soon be over for young scientists
and mathematicians like themselves. I don't know whether they're right, but
I feel like I should tell the truth about what their reaction was.

Then, a few days later, a team at DeepMind, including my UT Austin
colleague Swarat Chaudhuri
<https://scottaaronson.blog/?action=user_content_redirect&uuid=c9ded037d91b3fec4522167735ae5d9fa3c6596215e5a1d5b52ea22a5f4f50a3&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=eda9f82ed32b6709ea52fa16f827ef2d&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cuY3MudXRleGFzLmVkdS9+c3dhcmF0Lw=&email_id=3d774be550584f63265fb5d090b4cbe2>,
announced that they were able to use a system called AlphaProof Nexus to settle
nine more (!) Erdös problems
<https://scottaaronson.blog/?action=user_content_redirect&uuid=5a498efc50c29c675ee47a1cbefa0488e005d7f8f36d692bb42c919d48780d6d&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=a8250812ab38ac3098646c6ef1c0cd86&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzI2MDUuMjI3NjN2MQ=&email_id=3d774be550584f63265fb5d090b4cbe2>,
many of them in additive combinatorics, along with miscellaneous other open
math problems. Notably, in this case the AI also fully formalized its
proofs in Lean.

And then, just today, Jelani Nelson alerted me to a new CS theory paper
<https://scottaaronson.blog/?action=user_content_redirect&uuid=2f75a414d1047af3be8608ba1520b2365802088d1fc34953e27cd8f9f4c064db&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=d0776e6e7bccffb99d3cd67b95d79601&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9hcnhpdi5vcmcvcGRmLzI2MDUuMjQxMzA&email_id=3d774be550584f63265fb5d090b4cbe2>,
which solves a longstanding open problem about electrical flows on graphs
using a proof from GPT5.5Pro.

It seems to me that we're now over the top of this particular
rollercoaster, and it will keep accelerating until we reach the bottom,
wherever that might be. I don't know whether to hope or dread that
solutions to P versus NP and all our other great problems will be included
in the ride---that our role, as human mathematicians, will be reduced to
(at most) deciding which questions we find interesting and then
understanding AI models' answers to those questions.

But *maybe* that won't happen. Maybe the new AI mathematicians will soon
hit a wall, because they lack the uncomputable quantum gravity microtubules
of Penrose and Hameroff, or some other magic human ingredient. The
fantastical thing is that, one way or the other, we're going to find out
empirically before very long.
------------------------------

Readers may have also seen the news that multiple prizewinning entries in a
short fiction contest called the Commonwealth Prize, give overwhelming
indications of having been written by AIs
<https://scottaaronson.blog/?action=user_content_redirect&uuid=e4dbe589f08e7a382fa1e24ee575fcdb4f50c2b1b9f9aaa645c3872f8b112881&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=e183475a5160d29a1dd6432570a0c732&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cudGhlZnAuY29tL3AvYWktZ2VuZXJhdGVkLWxpdGVyYXR1cmUtY29udHJvdmVyc3k&email_id=3d774be550584f63265fb5d090b4cbe2>.
As Kelsey Piper puts it
<https://scottaaronson.blog/?action=user_content_redirect&uuid=911956d9089fc9b3fea5c2521362de01cf006717953016c499cd16f7ab096401&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=975bd515640800e82b68feca4a2565fc&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cudGhlYXJndW1lbnRtYWcuY29tL3AvdGhlLWxpdGVyYXJ5LXdvcmxkLWlzLXNsZWVwd2Fsa2luZw=&email_id=3d774be550584f63265fb5d090b4cbe2>
:

There are, let’s say, also some noticeable similarities in the prose style
between the winning stories that were flagged for AI use. AI chatbots love
metaphors and similes, and they often spit out ones that sound vaguely
pleasing but are logically incoherent or ascribe properties to things that
don’t make sense.

“The Serpent in the Grove” gave us, “The girl smiled like sunrise over a
sink.” “The Bastion’s Shadow” says, “She carried it now in her bag, heavy
as a charm.” “Mehendi Nights” describes something as “swaying against
plaster like a warning bell.”

The Commonwealth Foundation, whose judges chose these stories, hasn't
exactly covered itself in glory---saying, on the one hand, that it strictly
forbids AI use but on the other, that it will continue taking authors at
their word that they didn't use AI, no matter the immensity of evidence to
the contrary. As many others have pointed out, judges more familiar with AI
would've ironically been better placed to notice the signs of its use.

If only
<https://scottaaronson.blog/?action=user_content_redirect&uuid=5e021e3ed9a7b77b5000ded3fd169539c4fe016a4c5beb1da74b8ae402bacf62&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=f492cfba4036852aa2cae92c79484627&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9zY290dGFhcm9uc29uLmJsb2cvP3A9OTMzMw=&email_id=3d774be550584f63265fb5d090b4cbe2>
there
were some sort of automated way to detect AI-generated text. Someone should
really get on that problem, don't you think?
------------------------------

But maybe we should just throw in the towel---as some of my colleagues have
already done in the context of undergraduate projects? Maybe we should
simply say that a good story is a good story, regardless of what manner of
entity produced it?

As it happens, just last week I read my very first AI-written story that
affected me *as* a story, to the extent that I wanted to read it more than
once. This happened when I gave GPT5.5Pro the following simple prompt:

Write me a story about the most ancient Israelites that’s riveting like the
stories of the Bible but that’s also consistent with all of the
archeological evidence.

You can read the result here
<https://scottaaronson.blog/?action=user_content_redirect&uuid=def2608d0d93d9fa0ad1732ac633eb113eb08c72c2552f48b50b9ed686fbe65b&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=9a31cce536039c20571acf5872aa1f0c&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly9jaGF0Z3B0LmNvbS9zL3RfNmEwZDEwYzVhNjE4ODE5MWFlNTVjMWRkZjBjYTgwMTU/ZmJjbGlkPUl3WTJ4amF3U0VtX2hsZUhSdUEyRmxiUUl4TVFCemNuUmpCbUZ3Y0Y5cFpCQXlNakl3TXpreE56ZzRNakF3T0RreUFBRWVmZW5vUVJUTmZTZ2xzNnJzdHQtNFY2T1NqUkhHRnJEaWZfS0tEUGFDX09EU2VRcnI4bHNHNzlMd0Fra19hZW1fMmUxT3ZwU1hhR1kwU19yUUVQOE9GQQ=&email_id=3d774be550584f63265fb5d090b4cbe2>.
One of my Facebook friends called it "disturbingly good," and I share that
assessment. Of course, I'm well aware that GPT could easily generate a
thousand stories like this one---sampled from the same probability
distribution---and then I could even do statistics on which tropes were the
most common. This makes it feel silly to overindex on the first story that
happened to be output, and yet somehow I did.
------------------------------

I feel like at this point, both the prophets of AI utopia like Ray
Kurzweil, and of AI doom like Eliezer Yudkowsky, could be forgiven for
asking: *dude, will you listen to us YET?* Do you *still* find it prudent
to call this new form of terrestrial intelligence a stochastic parrot, a
laughable fraud, or a fad that's about to go away? Fear it all you want,
hate it even, but at least respect it!

Which brings me to the *other* big AI news from the past week, namely that
Pope Leo released his first encyclical, which is entitled "Safeguarding the
Human Person in the Time of Artificial Intelligence."
<https://scottaaronson.blog/?action=user_content_redirect&uuid=c702a02abe7da27822219ce16f3946d4628fbad20ef8572be0eb5baa27e1916e&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=1607283b52777e24854b860b34c47f68&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cudmF0aWNhbi52YS9jb250ZW50L2xlby14aXYvZW4vZW5jeWNsaWNhbHMvZG9jdW1lbnRzLzIwMjYwNTE1LW1hZ25pZmljYS1odW1hbml0YXMuaHRtbA=&email_id=3d774be550584f63265fb5d090b4cbe2>
I
read it and ... well, I certainly agreed with the theme that such a
world-changing technology needs to be developed for the common good (as the
Pope would have it, like the walls of Jerusalem), rather than for the
profit or vanity of any one individual or company (in his analogy, like the
Tower of Babel). I had quibbles with some of the other parts. Zvi
Mowshowitz, as he often does, had a superb paragraph-by-paragraph analysis
<https://scottaaronson.blog/?action=user_content_redirect&uuid=993596768aa7b6ff8c864bcb8eedf0e25c930a2a64e5a16fe4c2b2333f2e9e9e&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=e420677c6d2b6e00b2b7f91d9f452c1d&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly90aGV6dmkuc3Vic3RhY2suY29tL3AvcnRtaC1wb3BlLWxlb3MtbWFnbmlmaWNhLWh1bWFuaXRhcw=&email_id=3d774be550584f63265fb5d090b4cbe2>.
Amusingly, there are indications that parts of the encyclical were written
by AI
<https://scottaaronson.blog/?action=user_content_redirect&uuid=a073407aa10469bd997935388d66fed198836765e7bf636a1aeec4181d287227&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=66bbed006c0aaf803b2b998c484542d7&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cucmVkZGl0LmNvbS9yL3NsYXRlc3RhcmNvZGV4L2NvbW1lbnRzLzF0b2E4NzIvY2xhdWRlX2F1dGhvcl9vZl90aGVfaHVtYW5pdGFzX2V2aWRlbmNlX3RoYXRfdGhlLw=&email_id=3d774be550584f63265fb5d090b4cbe2>
.

To me, though, maybe the most notable part was that Chris Olah, who leads
Anthropic's interpretability team, was standing next to the Pope at the
ceremony
<https://scottaaronson.blog/?action=user_content_redirect&uuid=e186265da8905c70bd21a63d9831a6dc8ee6f863b5d56d0ff111e3dcc825e1e0&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=325ef2e8fc8da9725abe2bc6f2c79474&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cuZm9yYmVzLmNvbS9zaXRlcy9hbGljaWFwYXJrLzIwMjYvMDUvMjUvYW50aHJvcGljLWJpbGxpb25haXJlLWNvZm91bmRlci1qb2lucy1wb3BlLWxlby13YXJucy1haS1qb2ItbG9zc2VzLXdpbGwtc3BhcmstbW9yYWwtaW1wZXJhdGl2ZS1vZi1oaXN0b3JpYy1wcm9wb3J0aW9ucy8&email_id=3d774be550584f63265fb5d090b4cbe2>,
and delivered his own remarks
<https://scottaaronson.blog/?action=user_content_redirect&uuid=1439706fd8a5b068651273d47abd8df1484ecfa6cdbdf1fca07e8a1243fe750e&blog_id=129520580&post_id=9782&user_id=0&subs_id=317430890&signature=9e2000bce6617fb2f88e03348c936ec2&email_name=new-post&user_email=johnkclark@gmail.com&encoded_url=aHR0cHM6Ly93d3cuYW50aHJvcGljLmNvbS9uZXdzL2NocmlzLW9sYWgtcG9wZS1sZW8tZW5jeWNsaWNhbA=&email_id=3d774be550584f63265fb5d090b4cbe2>.
I felt like Chris, who I met even before Anthropic existed, was a
non-obvious yet inspired choice here, one of the rare figures in frontier
AI whose technical *and* moral authority are both completely unimpeachable
by anyone.

And so, at this momentous era for the human project, and no less of an
authority than that of the Vicar of Christ himself, the Supreme Pontiff and
the Successor of Peter, I hereby throw myself on the wisdom and mercy of
... uhh, Chris Olah and his team at Anthropic.

Chris, if I am soon to share the earth with entities that can prove the
Riemann Hypothesis and solve quantum gravity after 30 seconds of thought,
then may you understand those entities well enough to cause them to be nice.
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