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In 1940, from a jailhouse in Rouen, France, André Weil wrote one of the most consequential letters of 20th-century mathematics.

He was serving time for refusing to join the French army, and he filled his days in part by writing letters to his sister, Simone, an accomplished philosopher living in London.

In a previous letter, Simone had asked André to tell her about his work. With war all around, André began his reply cautiously, warning his sister that past a certain point “you will understand nothing of what follows.”

Over the next 14 pages, he sketched his idea for a “Rosetta stone” for mathematics.

Following the example of the famous engraving by that same name — a trilingual text that made ancient Egyptian writing legible to Western readers through translation into Ancient Greek — Weil’s Rosetta stone linked three fields of mathematics:
number theory, geometry, and, in the middle, the study of finite fields.

Other mathematicians had proposed ideas in this direction, but Weil was the first to spell out an exact vision.

His letter presaged the Langlands program, a major initiative in contemporary mathematical research

https://www.quantamagazine.org/a-rosetta-stone-for-mathematics-20240506/