Dirichlet, Peter Gustav Lejeune (1805–1859)
Peter Dirichlet was a German mathematician who made significant contributions to number
theory, analysis, and mechanics, and
who is credited with the modern formal definition of a function.
He taught at the universities of Breslau (1827) and Berlin (1828–1855) and
in 1855 succeeded Carl Gauss at the University
of Göttingen but died of a heart attack only three years later. Dirichlet
continued Gauss's great work on number theory, publishing on Diophantine
equations of the form x5 + y5 = kz5. His book Lectures on Number Theory (1863)
is similar in stature to Gauss's earlier Disquisitiones and founded
modern algebraic number theory.
In 1829 he gave the conditions sufficient for a Fourier
series to converge (though the conditions necessary for it to converge
are still undiscovered).