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J. Alama:
"New results on Hilbert's 24th problem";
Talk: Algebra and Logic Seminar, Center for Mathematics and its Applications, New University of Lisbon, Caparica, Portugal (invited); 2014-11-19.

Hilbert's 24th problem asks for criteria of simplicity of mathematical
proofs. The problem (which was never published and discovered in
Hilbert's notebooks only in the 1990s) is admittedly somewhat vague;
it is formulated less precisely than Hilbert's other famous problems
and can be understood in various ways. With the help of automated
theorem provers and new results in structural proof theory, fruitful
new perspectives and techniques for tackling Hilbert's problem become
available. In this talk we illustrate these new approaches by
highlighting recent results in simplifying axiom systems and formal
proofs, and by posing problems that are likely solvable with the help
of the new techniques.