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.

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