The Lamp Can Only Be Lit From Within: 25 Fields Medalists, a Severe Misalignment, and Hamo's Understandability Principle

AI for Inner Explorers.

Reading 25 Fields Medalists' "A Severe Misalignment of AI in Mathematics" against the one principle Hamo holds from "AI for Psychology" to "Psychology for AI".

On 11 September 2026, 25 Fields Medalists published a statement: the way AI companies are pushing mathematics forward has become severely misaligned with the goals of the mathematical community. This article does three things. First, it reads the statement accurately — including what it does not say. Second, it lines the statement's core up against Hamo's own principle. Third, it turns that ruler around and measures Hamo with it, because we are an AI company, and so we already sit on the side the statement criticises.

What humans cannot understand is misaligned with humanity's long-term value.

The one principle Hamo holds from "Today" to "Beyond" · this article is the first time it has been written down

The conclusion in one paragraph. The core of the statement is this: solving problems is only a proxy for understanding, and AI companies are optimising the proxy. Hamo faces the same structure in psychology, and in a sharper form — in mathematics the one who needs to understand is a community; in psychology it is the client, personally. So "Today", Hamo has already written three rules into code: no progress verdicts, the lamp can only be lit from within, and Hamo takes no credit. In the "Beyond", the part of this statement we most need to hear is one step on our loop — "Models, distilled → General AI, informed": what we hand over must be structure people can read, not a machine that is better at reaching conclusions about minds and that nobody can read.

Part One · Reading the statement accurately

What it says, and what it doesn't

1. What the statement says

The statement runs nine paragraphs. It was published at mathandai.org and reposted in full the same day through signatories' personal channels. All 25 first signatories are Fields Medalists, listed side by side in alphabetical order by surname — no lead signers, no ranking. According to the signatories, the text came out of discussions among them over the preceding week; because the matter was urgent, there was no time for a round of public consultation of the kind the earlier Leiden Declaration went through. The site is open for anyone to co-sign (confirmed by ORCID or an academic email); as of writing (2026-09-12), roughly 4,930 people had.

Here are all 25 signatories, in the order the statement lists them, with the year each received the Fields Medal — from 1978 to 2026, nearly half a century:

What the nine paragraphs say, paraphrased one by one (this is not a translation of the original):

The sentence that carries the most weight is in P5 — solving problems is "a tool and proxy for achieving the primary goal of conceptual understanding and insight".

— A Severe Misalignment of AI in Mathematics, mathandai.org, 2026-09-11

2. What it doesn't say — reading it right matters more than reading it fast

The statement travelled fast, including across the Chinese-language internet, and a few common extrapolations need to be cleared away first; otherwise everything that follows is built on sand:

• It names no company and makes no specific demands. It is a statement of values, not a list of asks. The words proof, Lean, formal verification and transparency appear nowhere in it.
• It does not say "proofs humans can't understand have no value." What it says is: solving problems is a proxy for understanding; mass-producing true/false judgments may destroy the soil; ideas conceived by AI need people to develop them before they come alive. A signatory has indeed said on social media before that AI solutions of this kind add almost no value — but on the condition that the process is hidden. That is a personal qualification, not the text of the statement.
• It is not against AI. P8 says plainly that AI can enhance mathematical research, and that what decides the outcome is the people who control the technology.
• None of the 25 signatories is a lead signer. Many reports open with one or two famous names "and others, 25 in all" — that is giving examples, and it is not wrong; just know that in the original all 25 stand side by side, which is why this article lists every name. Subheadings in the coverage such as "three core concerns" are editors' summaries, partly drawn from a signatory's personal posts rather than from the statement itself.

The timing has a concrete backdrop. Three days earlier, OpenAI announced a finite-time blow-up result for the Navier–Stokes equations, produced by an internal AI system and accompanied by a Lean formalisation, which immediately set off a dispute over attribution and priority; when the statement was reposted through a signatory's personal channel, it came with The Economist's same-day coverage attached. But the statement's text deliberately frames the issue as a general problem rather than a single case — and that is the premise that lets this article hold it up against Hamo.

3. The core: the proxy ate the purpose

Compress the nine paragraphs into one layer of structure and you get three concerns stacked on a single judgment:

The word the statement itself uses is alignment, and it is worth pausing on. The alignment it means is not a model aligning with human instructions; it is the output of a piece of work aligning with what that work was for. That is exactly the territory Hamo's "Psychology for AI" is heading into.

Part Two · The same structure, in psychology

What is already in code today, and what must be held in the Beyond

4. In psychology, this structure is sharper

Carry the statement's structure across:

The last row is the crucial difference. When AI solves a problem in mathematics, the community can still slowly digest it into a textbook. In psychology, understanding has to happen inside the client. An AI that hands over "a conclusion about your interior" takes away precisely what therapy was meant to grow — P7's "years of training were never only about producing answers" becomes, here, "session after session was never only about receiving an explanation."

And the cost is even more asymmetric. There is a sentence in a comment in Hamo's code, written before the statement, that reads like a paragraph added to it:

A client who is collapsing has less capacity to reject a wrong reading, not more.

— psvs/domain_guard.py, explaining why the "no verdicts about the client's interior" red line must scan every state bucket

A mathematician can reject a wrong proof; a person who is collapsing can hardly reject a wrong reading. So Hamo's principle has to be stated more strongly than the statement's:

What humans cannot understand is misaligned with humanity's long-term value. It does not mean "AI must be one hundred percent explainable". It is a position rule: judgments and decisions about a person must exist in a form people can read, check, and refuse. What people cannot read may serve as an instrument; it may not serve as a judge.

5. Today · AI for Psychology: the principle is already written in code

Every row below is the original meaning of code or of already-published writing, not something written for this article. All of it predates the statement — not a response to it, but the same judgment written down in a different field, at a different time.

Read this table next to the statement and Hamo's answers to the same problem, in psychology, share one shape: let the system see, record and support human understanding — but never complete that understanding on the person's behalf. The awareness map keeps the ledger and never lights the lamp; the covenant is held, not scored; the red line allows curiosity, never verdicts.

6. Beyond · Psychology for AI: where we most need to listen

The second stage on our homepage is described in one sentence: "We believe that layer belongs in general AI, and we are building it in the open." It comes with a loop — Care, delivered; Minds, understood; Models, distilled; General AI, informed — which finally closes: AI that genuinely understands minds makes the care itself better.

The first two steps of the loop are Today; the last two are Beyond. The kind of misalignment the statement criticises is most likely to happen at "Models, distilled → General AI, informed": if what we hand to general AI is an ability to read minds better than anyone, which nobody can read, then we will have swapped the statement's "mass-producing true/false statements" for "mass-producing conclusions about people" — and the objects are people, not propositions.

So this principle decides what may pass the gate. The homepage wording has in fact already chosen its side: "structure, not just transcripts". What PSVS, AI Mind and Persistent Self hand on should be structure people can open and understand — state, memory, narrative, self; one of the design goals the whitepaper sets for Persistent Self is to "provide a transparent, user-editable visualisation". A structure about you earns the right to flow into general AI only if you yourself can read it and change it.

On "building it in the open", this is how far Hamo has delivered so far:

• Open weights for the scoring model, under the HAMO-RAIL-S licence with four use restrictions: no standalone clinical determinations, no consequential decisions about individuals, consumer-facing deployments must keep an independent crisis path and disclose AI involvement, and no re-identification of individuals;
• An Apache-2.0 toolkit — the crisis gate, a reference server, a synthetic exam, fine-tuning documentation, and a feedback template for "I disagree with this score";
• A model card that discloses, unprompted, the text overlap between the training set and the exam, and the roughly 0.3 percentage points of optimism it introduces;
• Our public line on open source is: we open-source the harness, not the horse — the model comes as a bonus. What is public of the harness today is the toolkit above: the crisis gate, the smoothing reference, the reference server and the self-check exam; the spine runtime, the admission-table schema, the full evaluation suite and the red-team set are not yet public.

"A component that reads someone's psychological state should not be a black box owned by anyone — including us."

— Hamo blog, "Open-Sourcing hamo-score-0.6b"

A discipline of tone. When the homepage was redesigned we set a rule: copy about the Beyond only says "we believe" and "we are building", and makes no present-tense claims about general AI. That is the other side of the "hasty announcements" P6 criticises — the Beyond has not arrived, so don't pop the champagne on its behalf.

Part Three · Turning the ruler on ourselves

We sit on the other side of the table

7. We are an AI company — what the statement criticises could be us

The statement's criticism is aimed at AI companies, and Hamo is an AI company. Ask its question straight back at ourselves: what is our "number of problems solved"?

• The scorer's agreement rates — 85.1% at dimension level, 97.1% at decision level (v7, graded on the 453-turn final exam);
• Downloads on Hugging Face;
• Token consumption, session length, return rate.

All of these are proxies. What we are already aware of: the AWEHB article states that every agreement rate is reliability evidence, not validity evidence — a ruler that gives the same reading every time is not thereby proven to measure length; and AWEHB, as a formative index, has not yet been validated against any external criterion. The covenant and the awareness map both hard-code that they never feed engagement optimisation.

The "hasty announcement" P6 criticises happened to us this month too. In Hamo's internal AWEHB research article, a correction itself later turned out to be wrong — it had ruled two figures that in fact came from the same exam "unrelated"; only after reproducing the number did we find that what was actually wrong was just the value and the level — so it had to be corrected again. That episode stays in the article rather than being erased, because it shows exactly this: the speed of announcing must be slower than the speed of checking.

The stronger the claim, the more it has to account honestly for where it still falls short. The next section is that account.

8. Honest boundaries: where Hamo still can't be read

Each item below has been checked against the code. These are the places where the principle has not yet been delivered inside Hamo:

So for now this principle is a "position principle", not yet a "purity manifesto". Things people cannot read may exist, but only inside instruments — with named outputs, clear boundaries and auditability; judgments about a person, and that person's understanding of themselves, must stay on the side people can read. The two rows that most need fixing first are "Visible, but not yet stopped" and "The people who can read it are not the people who most need to" — the first decides whether a client can be overwhelmed by a wrong reading; the second decides whether the therapist, as principal, can genuinely exercise oversight.

9. Before entering the Beyond: five understandability checks

The statement makes no specific demands because it addresses a whole profession. Hamo addresses its own system, so it can — and should — turn the principle into checks that can be ticked off one by one. Before any component crosses from "Today" toward the "Beyond", it must pass these five questions:

1. It can say why. Could a supervisor check where this score, this judgment, came from?
2. The person can read it and change it. Can the person being modelled understand, and edit, this structure about themselves?
3. Provenance is traceable. Who had this insight first — the client, the therapist, or the model? Would the system take credit on the model's behalf?
4. A proxy is labelled as a proxy. Is this number reliability or validity? Is it being optimised as if it were the goal?
5. It hands over structure, not conclusions. What it passes to general AI, or puts in front of a client — is it a structure that can be inspected, or a verdict about a person?

These five questions apply to every arrow on the loop, and they apply first to "Models, distilled → General AI, informed". A component that cannot pass questions 2 and 5 should not pass the gate, however capable it is.

10. Closing

The question the statement leaves in P7 is: as AI changes how work is done, do not forget what that work was originally meant to achieve.

What mathematics was meant to achieve is understanding. What psychological care was meant to achieve is a person's understanding of themselves. What Psychology for AI is meant to achieve is an AI that understands minds — and lets people check how it understands. The three are the same thing.

The comment on the awareness map holds everything Hamo understands about its own role: the client's awareness space lives in the client; Hamo can never hold it; Hamo just records the moment each lamp lit.

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The lamp can only be lit from within. What Hamo can do is record the moment it lights — and never put the credit in its own name.

External sources: A Severe Misalignment of AI in Mathematics (mathandai.org, 2026-09-11); same-day repost on a signatory's personal blog; QbitAI coverage (2026-09-12). Apart from one quoted sentence, all content from the statement is paraphrased; this article does not represent the views of the signatories.

Hamo sources: psvs/covenant.py · psvs/awareness_map.py · psvs/domain_guard.py · psvs/approach_modules.py · the hamo.ai homepage · Hamo blog, "Measuring the Move" · an internal engineering document on the harness. Code assertions went through one adversarial review, as of 2026-09-12.

Grounded in code, not slideware.

Hamo AI — making minds aware, and awake.

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