Mathematics and Espionage

One is sometimes surprised to learn it, but intelligence agencies employ many mathematicians. To such an extent that they are probably the first employers for the profession! The usefulness of cryptology to encrypt or to decrypt confidential messages is no longer in question. But in a world of information submerged by digital data that circulates (too?) freely, securing transactions, searching for the "right" file have become highly strategic issues. Combinatorics, probabilities, statistics, data analysis... have become indispensable and will only continue to develop. Do you want to be a spy, become the next Matha (sic.) Hari? You know what you have left to do!

It comes to us from Antiquity and is a jewel of plane geometry. Much more recent and lesser-known than the theorems of Thales and Pythagoras, Heron's formula makes it possible to determine the area of a triangle using only the knowledge of the length of its sides. This is only the tip of the iceberg because this geometric nugget generalizes greatly beyond the triangle. Thus, the brilliant Euler found a stunning version for the tetrahedron. Brahmagupta and then Bretschneider proposed a variant for quadrilaterals. Finally, like its illustrious predecessor the Pythagorean theorem, Heron's formula can give rise to astonishing arithmetic research, such as that of "Heronian triplets". Welcome to geometry!