The secret to fixing a fatal flaw at the heart of quantum theory may lie in three obscure textbooks from the 1980s. But physicists can be forgiven for overlooking the potentially transformative ideas within, as the volumes appear simultaneously amateurish and intimidating.

The few physical copies that exist of Jean Écalle’s magnum opus look like little more than glorified photocopies. Oversize mathematical symbols scrawled in thick black ink frequently interrupt the neatly typed sentences. The text is also written in French, an inconvenience for researchers in the English-speaking world.

The mathematics itself poses another barrier. The trilogy’s 1,110 pages brim with original mathematical objects and bizarre coinages. Odd-sounding terms like “trans-series,” “analyzable germs,” “alien derivations” and “accelero-summation” abound.

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