I have been thinking a lot about how social dynamics are going to shift in the new era of cognitive abundance. I don’t pretend to have any kind of crystal ball, but there are numerous historical precedents for what happens when you provide a new resource practically for free.
A bit less superficially, the study of systems where certain processes are sped up leads to new bottlenecks. This appears under many guises, e.g. Chad Jones’s theory of weak links. Speeding up one link in a chain of processes only exposes the next, and so on. The trajectory that seems pretty likely to me looks a bit like the following.
The gold rush
As more and more members of the scientific community become aware of the increasing capabilities of LLM, there will be a rush to mine out everything that fits in the horizon of a single chat window. That rush has commenced, and will only accelerate until all the conjectures addressable with minimal effort are mined out. I don’t know how long that will take, but let us do some back of the napkin math. I am now hearing of about 1-5 conjectures per day (just in quantum information theory) that are being revisited with LLM tools. Suppose this rate remains constant (a bad assumption, new people keep trying out the tools). By the end of 2026 it is easily plausible that up to 1000 conjectures will have received elevated scrutiny, right?
Does our little field even have 1000 open conjectures!?
But the dynamics are so much more insane than this. You can bet, with no uncertainty, that there are people already setting up massive automated assays, scanning papers en masse for open conjectures and deploying LLMs in swarms to solve or disprove them. Anecdotally I have heard crazy numbers: reports of certain actors spending upwards of tens of thousands of euros to accelerate this search. So, probably, within a couple of months all of the easy conjectures will have been revisited. My point, I hope, is clear: I don’t believe open conjectures will be an abundant commodity much longer. Oh no.
The inflationary era
When Spanish galleons flooded Europe with Potosí silver in the sixteenth century, Spain did not get rich. Prices rose roughly sixfold over the following century and the windfall evaporated into inflation.
The gift of abundance inevitably and irrevocably changes our value systems. When you know that I know that your paper was generated in one afternoon with a single prompt, then you know that I won’t be so impressed any longer. The contribution (the prompt, the planning docs) is so much smaller, so much less consequential. When this all becomes common knowledge, the value we attribute to one-shot proofs and papers will simply be lower. I certainly experienced this multiple times over the past months as I discovered new capabilities of LLMs and coding agents. In November 2025, after I generated over the course of a weekend a full MSc-grade result, complete with an associated Lean proof, I instantly devalued such contributions. A weekend of work is not the same as six months of concerted effort. What used to be for me a major signpost on the road to expertise and maturity got demoted to a homework exercise. Since Q4 2025 I have completely lost the capacity to be interested in, and impressed by, results generated largely by LLMs, and I have turned my focus towards what is *hard *to generate with them. I don’t feel motivated to get out there and snipe at conjectures; it doesn’t seem fulfilling or meaningful to me in any way. These days I am left relatively unmoved by breathless announcements of newly settled conjectures. Do I have sour grapes that I didn’t come up with the same proof? Ummm, no. I mean, really! How much credit do you give to someone who clumsily prompted a chatbot to “go prove the X conjecture, try really hard, don’t make mistakes, and don’t stop until you have proved it or found a counterexample”? Be honest now.
What I actually feel is a sense of pity, and once the excitement wears off, I bet you will feel similarly.
The new equilibrium
As consensus in the scientific collective shifts and value systems are rebuilt, I am sure we will not give much value at all to an LLM-assisted proof of a conjecture. In fact, as we look back on the gold rush about to hit, we will probably not be so willing as we used to be to hand out faculty jobs to those who settled a famous conjecture. Instead, we will collectively ask ourselves what is still hard. I have an answer, which I freely admit may need revision as LLMs get better.
- It is easier than ever to launch an automated attack by a swarm of agents on a known conjecture.
- It is much harderto come up withinterestingconjectures. - It is ridiculously hardto come up with clean and compelling definitions that organise a rapidly growing field in a conceptually clean way.
My current feeling is that we will very soon assign much more value to theory builders, to those who can navigate the oceans of mathslop and physicslop and organise concepts in succinct and compelling ways. We will celebrate the people who can absorb vast amounts of discordant information and create clarity in the form of organising principles, new conjectures, and, most importantly, new definitions that scaffold and provide foundations for swarms of AI agents to build on.
The era of the conjecture-prover as celebrated actor is over. It was fun while it lasted. Let us raise a toast, hand them their hat and coat, and bid them farewell.