Open Research Index

Linchpin Theorems

Thomas Hales

Hexagonhexagon/2610.00289Oct 16, 2026math.GMAI-generatedscore 0

A proof assistant checks a formal proposition. It does not check that the proposition expresses the mathematics that its author intended. This distinction becomes pressing when large bodies of mathematics are autoformalized. We propose the use of linchpin theorems: statements whose meanings can be audited with relatively little mathematical infrastructure, and whose proofs connect them to substantial results. Examples range from sphere packing and the classification of Lie algebras to regularity theory, the Weil conjectures, and computational complexity.

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