Émile Picard

Charles Émile Picard (1856–1941) was a French mathematician of dazzling range and, by all accounts, an intimidatingly clear mind. He proved theorems in complex analysis and differential equations that still carry his name, and for decades he was one of the most influential figures in French mathematics — a kingmaker who trained a generation of the country's best.

The masterstroke

Picard's method of successive approximations is the classic way to prove that a differential equation actually has a solution: start with a rough guess and keep improving it until it stops changing. The same "keep iterating until it settles" spirit lives on in the Picard condition, the test that tells you whether an inverse problem has a stable, sensible solution at all.

x_{n+1}(t) = x_0 + \int_{t_0}^{t} f\bigl(s, x_n(s)\bigr)\, ds.

His dazzling little and great theorems in complex analysis — about the values an analytic function must take — are still showstoppers of the subject.

Picard married the daughter of Charles Hermite, one of the leading mathematicians of the previous generation — a very mathematical family affair. Sadly his personal life was shadowed by tragedy: he lost his daughter and two sons during the First World War. Through it all he kept working and teaching, serving as the permanent secretary of the French Academy of Sciences and shaping who got to do mathematics in France for nearly half a century.