Undecidable Problems — Gareth Jones / Serious Science

Mathematician Gareth Jones on Gödel's incompleteness theorem, the halting problem and why the subsets of the natural numbers are uncountably infinite. Read the full text on our website: http://serious-science.org/undecidable-problems-9772 'In the early part of the 20th-century mathematicians had a great sense of confidence that their subject could answer eventually any reasonable problem. This confidence was shattered in the 1930s. Alonzo Church and Alan Turing independently showed that there are problems in mathematics which cannot be solved in the sense that there is no algorithm to solve them. ' Gareth Jones, Emeritus Professor of Mathematics, University of Southampton Prime Numbers: http://serious-science.org/prime-numbers-jones-9723 Logic and Mathematics: http://serious-science.org/logic-and-mathematics-7243 Be the first to find out about our new videos and articles. Learn interesting facts about various topics and people. Discover the answers to the big questions. Be in the know. http://serious-science.org/ Follow us: We are on Patreon: https://www.patreon.com/SeriousScience Facebook — https://www.facebook.com/serious.science.org/ Twitter — https://twitter.com/scienceserious YouTube — /user/SeriousScience Instagram — https://www.instagram.com/serious.science Tumblr — http://serious-science.tumblr.com/ VK — https://vk.com/seriousscience

Category