\begin{frame} \frametitle{Timeline: From Logic to Computability} \vspace*{-2.75ex} % \begin{flushleft} \scalebox{0.9}{% \begin{tabular}{ll} % \hspace*{-4ex} \alert{1900} & Hilbert's 23 Problems in mathematics \pause{}\\[0.6ex] \hspace*{-4ex} \colemph{1921} & Sch\"{o}nfinkel: Combinatory logic \pause{}\\[0.6ex] \hspace*{-4ex} \alert{1928} & Hilbert/Ackermann: formulate completeness/decision problems \\[0.3ex] & for the predicate calculus (the latter called `Entscheidungsproblem') \pause{}\\[0.6ex] \hspace*{-4ex} \colemph{1929} & Presburger: completeness/decidability of theory of addition on $\mathbb{Z}$ \pause{}\\[0.6ex] \hspace*{-4ex} \alert{1930} & G\"{o}del: completeness theorem of predicate calculus \pause{}\\[0.6ex] \hspace*{-4ex} \alert{1931} & G\"{o}del: incompleteness theorems for first-order arithmetic \pause{}\\[0.6ex] \hspace*{-4ex} \colemph{1932} & Church: $\lambda$\nobreakdash-calculus \pause{}\\[0.6ex] \hspace*{-4ex} \colemph{1933/34} & Herbrand/G\"{o}del: general recursive functions \pause{}\\[0.6ex] \hspace*{-4ex} \alert{1936} & Church/Kleene: $\lambda$\nobreakdash-definable $\;\sim\;$ general recursive \\[0.3ex] & Church Thesis: `effectively calculable' be defined as either \\[0.3ex] & Church shows: the `Entscheidungsproblem' is unsolvable \pause{}\\[0.6ex] \hspace*{-4ex} \alert{1937} & Post: machine model; Church's thesis as `working hypothesis' \\[0.3ex] & Turing: convincing analysis of a `human computer' \\[0.3ex] & leading to the `Turing machine' % \end{tabular}} \end{flushleft} \end{frame}