\begin{frame}{Alonzo Church \& Alan Turing} \begin{center} \includegraphics[height=25mm]{Church-Turing.pdf} \end{center} Two of the founders of the \emph{theory of computability}. \medskip Alonzo Church (1903-1995) is inventor of the \emph{$\lambda$-calculus}. \medskip Alan Turing (1912-1954) \begin{itemize} \item introduced the \emph{Turing machine}, \item invented the \emph{Turing test}, \item key role in cracking the German \emph{Enigma machine}. \end{itemize} \medskip Both proved \emph{undecidability of validity in predicate logic}. \end{frame} \themex{Not all Languages are Recursively Enumerable}