Steps / Historical AI

The method — four checks

How do you trust a machine that read a page from 1748?

You make it prove itself. A transcription is a guess until it survives checks that don't depend on trusting the machine. For mathematics those checks can be brutal, because math is the rare thing you can verify without knowing the answer in advance.

A worked example — Euler's π, printed 1748

We asked the pipeline to read the value of π Euler printed. Then we checked every digit.

Introductio in analysin infinitorum · Caput VIII127 digits transcribed
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132723066470938446
digit 113 ↑

112 digits correct. The pipeline flagged the 113th. It reads 7. The true value is 8. This is not a transcription error. It is de Lagny's mistake, computed by hand in 1719, uncaught until Vega corrected it in 1794, and reproduced faithfully by Euler in 1748. The tool transcribed exactly what was printed, and the validation layer pointed straight at a 250-year-old error.


The verification stack

A reading that passes all four is not a guess. It is a fact that survived four ways of being wrong.

01 — Read

Transcribe to LaTeX

A vision model reads the page, prose and formulae, into structured text and LaTeX. Two independent passes, so disagreement is measurable.

02 — Render

Render it back

The LaTeX is rendered to an image and matched against the source. Garbled output cannot hide, because it will not render to the same marks.

clean typeset: 5 / 5 equations, visual match 1.00
03 — Validate

Check the math is true

A symbolic engine evaluates each equality. A reading of cos(π) = 1 is rejected on the spot, because it is false, no matter how cleanly it renders.

Euler's sin/cos relations: 10 / 10 validate as true
04 — Contextualize

Check it against the text

The equation is compared to what the surrounding prose claims it should be. A formula that contradicts its own caption is flagged for a human.


On the evidence so far

4,397
mathematical expressions transcribed and checked across a full 1748 Euler volume
60 → 5
equations flagged by validation, triaged to five genuine anomalies for a human
112/127
digits of Euler's π verified — the divergence is de Lagny's 1719 error

The flagged readings are the point

Across all 356 leaves the pipeline flagged 60 equations, then sorted them: 18 were Euler's printed decimals, verified correct to 23 digits. 14 were true identities the symbolic engine couldn't prove but the numeric check confirmed. Others were his own 18th-century conventions, division by zero and the infinite i. That left five genuine anomalies for a human, including a candidate second error in his printed value of 1/π, which diverges from the true value near the sixteenth decimal. That one is flagged, not confirmed. It could be a printing error or a digit misread on a long string, which is exactly what the human check is for. Ordinary OCR can never produce that list. It is the tool doing scholarship, not just typing.


Four fronts

Where the method stands, honestly.

Printed mathematics

Off-the-shelf vision models already read it, and the stack makes it trustworthy. Running now across a full 1748 Euler volume.

Working

Handwritten mathematics

Leibniz and Euler in manuscript. Reading the hand is the open problem, but render-and-validate transfers unchanged once the LaTeX exists.

In training

Archaic & non-Latin hands

Fine-tuned on the transcribed slices of existing scholarly projects. Confidence is labelled, never assumed.

In progress

Figures & diagrams

An engineering drawing becomes a structured, editable process graph of components and connections, not just a caption.

New capability

The point of all four checks.

A tool a historian can trust is not one that is usually right. It is one that tells you, every time, exactly how it knows.

Read the write-up →  ·  Open-source verification stack & Euler errata →  ·  The collection →