Hilbert's Tenth Problem (HilPro)5 ECTS

Lehrveranstaltungen:

• • Hilbert's Tenth Problem
    (Vorlesung, 2 SWS, Wolfgang Degen, Lehrstuhl Informatik 10, Cauerstraße 6; Vorbesprechung: 19.10.2010, 14:00 - 15:00 Uhr, 0.141)

Inhalt:

In 1900 at the International Congress of Mathematicians in Paris Hilbert formulated 23 mathematical problems which dominated mathematical research throughout the 20th century. The 10th of these (H10P) asks for the existence of a certain algorithm A, namely: given a polynomial with integer coefficients, A should decide whether or not this polynomial possesses zeros in the integers. Around 1900 such a question could not be handled with hope for success. So it took 70 years of efforts by several logicians and mathematicians until Matiyasevic solved solve H10P in 1970 in the negative.

Literatur:

• Davis : Computability and Unsolvability (Second Edition!), Dover,1982

• Hardy and Wright : An Introduction to the Theory of Numbers, Oxford 1960 (and later editions)