I had a great-uncle who was a “human calculator”.
asserted
who → have → uncle
It’s an odd, rare ability that allows people to multiply large numbers quickly in their heads.
asserted
people → ’ → heads
I remember using a hand calculator and seeing if my uncle could get it right without a tool faster than I could; more often than not, he could.
uncertain
he → remember → tool
Human calculators used to be very valuable as employees, back when calculation was done by hand.
asserted
calculation → use → hand
Today they’re just a curiosity.
asserted
they → ’re → ?
Technology came along and superseded that particular human ability, as it has so many others.
asserted
it → come → others
The story of John Henry being superseded by the steam drill, or Paul Bunyan by the chainsaw, is a metaphor for the march of progress.
asserted
Henry → supersede → progress
In some cases, like Garry Kasparov or Lee Sedol losing to computers at chess and Go, the moment really happened.
asserted
moment → lose → chess
This week marked another important such moment in the history of man versus machine.
asserted
week → mark → machine
OpenAI announced that its new model, Astra, managed to solve ten major outstanding problems in math and theoretical computer science.
asserted
model → announce → math
Here’s a simple explanation of the problems.
asserted
explanation → ’ → problems
The general consensus seems to be that these are extremely important, stunning breakthroughs.
asserted
these → seem → ?
This does not mean that computers are now capable of doing every kind of math better than humans can.
asserted
humans → mean → math
Some people have argued that AI is good at results where the solution can be found by reading the entire literature and combining existing insights — exactly the kind of thing you might expect a computer to be superhuman at — but still not as good as humans at making truly novel leaps of insight.
uncertain
computer → argue → insight
This may represent a real, general limitation of LLMs’ capabilities — as Tom Zahavy of Google DeepMind put it, it may still be the case that “LLMs can’t jump.”
uncertain
LLMs → represent → it
But the trend line is becoming clearer.
asserted
line → become → ?
The University of Toronto’s Daniel Litt, one of the most prominent skeptics of AI’s potential for frontier math research, recently conceded a major bet about what AI could do:
uncertain
AI → concede → what
Litt appears to no longer believe that there is any important type of math that AI won’t soon be able to do, writing: “The models don’t yet seem able to do certain kinds of high quality research, but I also expect this is a matter of (not too much) time.”
asserted
this → appear → time
Some mathematicians have reacted to this development with despair.
asserted
mathematicians → react → despair
Kirwin Hampshire’s post is probably the most evocative and the most well-read:
asserted
post → read → ?
He writes:
I am suffering a profound spiritual crisis due to these developments.
asserted
I → write → developments
I have been screaming internally for days.
asserted
I → scream → days
It feels as though I am living inside of a nightmare…
asserted
I → feel → nightmare
For me, the affective quality of learning mathematics is empathetically tethered to an act of discovery and creation…
asserted
quality → learn → discovery
If The Library of Babel existed, would authors continue to write books?…
Perhaps I shouldn’t tell you this, but my aim is to be open: These developments have triggered some deranged thoughts in me.
asserted
developments → exist → me
I have wondered if it is the express goal of these companies to make me kill myself…
asserted
me → wonder → myself
The story of human discovery and the triumph of the human spirit will soon be excised from this discipline…
asserted
story → excise → discipline
[T]he process of prompting novel proofs will be as auraless as ordering doordash.
asserted
process → prompt → doordash
Watch as magic and mystery evaporate.
asserted
magic → watch → ?
Watch as the sun sets on our heroic age…
asserted
sun → watch → age
There is nothing I can do.
asserted
I → be → ?
There may be nothing you can do.
uncertain
you → do → ?
I have no prescriptions, policy recommendations, or coherent call to action.
asserted
I → have → action
I just want to be honest and open about my emotional and spiritual response.
asserted
I → want → response
I want to feel seen….I
asserted
I → want → ?
need the architects of our new mathematical paradigm to look me in the eye and acknowledge our shared humanity and soul before they deliver the coup de grâce.
asserted
they → need → coup
Math PhD student Tasmin Chu, meanwhile, urges a more confrontational path, calling on mathematicians to avoid working with AI companies and to aggressively preserve the way that math research is currently done.
asserted
research → urge → way
This seems extremely unlikely (and would fail if it were attempted), but it demonstrates the depth of emotion out there.
asserted
it → seem → emotion
Even the mathematicians who don’t share Hampshire’s despair have expressed alarm at the sudden disruption of their profession.
asserted
who → share → profession
The entire way that mathematical research works — training grad students, working on problems, collaborating with colleagues, building theories — is going to have to be overhauled.
asserted
research → work → theories
…and 103 more, not listed.
The Aporia
