Wartime codebreaking joins mathematics and state power

His research addressed Waring's problem, exponential sums, prime numbers and the geometry of numbers.

Japanese invasion, migration, overseas appointments and the founding of the People's Republic changed where and how he worked.

He promoted optimization and operational research in factories and agriculture, connecting advanced mathematics with mass development programs.

Turing became a founder of theoretical computer science and made influential contributions to logic, cryptanalysis and artificial intelligence.

His abstract device clarified what it means for a procedure to be mechanically calculable.

His 1952 conviction and forced hormonal treatment show how a state could exploit mathematical talent while criminalizing the mathematician.

Itô created stochastic calculus, a mathematical framework for systems influenced by continuous random change.

The theory made it possible to calculate with processes whose paths are too irregular for ordinary calculus.

The result connects functions of stochastic processes to differential equations and now underpins work in physics, biology and finance.

Itô produced foundational work while probability struggled for status and Japan experienced severe wartime disruption.