A coordinate system for settled scholarship · companion to the open-problems atlas
The central questions rarely settle — but the fields still produce results of distinct kinds: forensic facts won by evidence (decipherments, datings), retired errors (views refuted or shown incoherent), and distinctions and frameworks that stuck, adopted not by proof but by fruitfulness. The axes are kind of result, how it is secured, and status. Where the open-problems atlas maps constitutive contestation, this maps what got nailed down.
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Anchor set
The Open Problems Atlas
A coordinate system for settled science · companion to the open-problems atlas
A scientific result is held on the weight of evidence, never proven — so the deep facts about it are how strongly it is warranted and over what domain it is valid. Newton was not refuted by Einstein; he was bounded. The axes are kind of result, strength of warrant, and role — including the great frameworks now known to be special cases of deeper ones.
Project by
Anchor set
The Open Problems Atlas
A coordinate system for proven mathematics · companion to the open-problems atlas
A theorem is permanent — true forever, given its axioms — yet “proven” is not one thing. Established mathematics runs from one-line classical arguments to ten-thousand-page collaborations, to machine-checked formal artifacts, to results that stand only conditional on unproved conjectures. The axes here are kind of result, character of the proof, and role.