The Lengths of Proofs: Kreisel's conjecture and Gödel's speed-up theorem

We collect and compare several results which have been obtained so far in the attempts to prove a statement conjectured by Kreisel, about the lengths of proofs. We also survey several results regarding a speed-up theorem announced by Gödel in an abstract published in 1936. Finally we connect this to Kreisel's conjecture. Bibl. – 63 titles.