Past, Present, and Future Directions in Foundations of Mathematics

VideoLectures.Net View the talk in context: http://videolectures.net/godelfellowship2011_friedman_ppf/ View the complete Conference honoring the Winners of t...

VideoLecturesChannel5.7K views01:09:51

🔥 Related Trending Topics

LIVE TRENDS

This video may be related to current global trending topics. Click any trend to explore more videos about what's hot right now!

THIS VIDEO IS TRENDING!

This video is currently trending in Pakistan under the topic 'f'.

About this video

VideoLectures.Net View the talk in context: http://videolectures.net/godelfellowship2011_friedman_ppf/ View the complete Conference honoring the Winners of the Kurt Gödel Research Prize Fellowships 2008 and 2011: http://videolectures.net/godelfellowship2011_vienna/ Speaker: Harvey Friedman, Department of Mathematics, Ohio State University License: Creative Commons CC BY-NC-ND 3.0 More information at http://videolectures.net/site/about/ More talks at http://videolectures.net/ 1:16 Agenda 2:13 The foundational life 4:40 Foundational life 6:35 Philosophical life 9:10 Mathematical life, scientific life 10:20 An ambition 11:50 Foundations of mathematics foundations of physical science 12:45 Foundations of applied mathematics 14:33 Profound uneasiness - 1 16:13 Profound uneasiness - 2 17:01 First main step epsilon delta 17:33 Number systems 18:38 Real number system multiple definitions 20:17 Infinite upper shift Kernel theorem 21:05 Rationals and integers 22:30 Grand unification 23:59 Pure set theory immutable objects 25:41 Exploding universe 27:21 Assertions and proofs 28:07 Logical structure 29:27 Proof assistants 30:40 Understanding trivialities 32:03 Strict reverse mathematics 33:45 Fundamental foundation moves: consistency, completeness, incompleteness 34:32 Incosistent systems useful? 36:10 Gödel's second incompleteness Theorem 37:04 Four completeness theorems 38:09 Gödel's first incompleteness theorem 39:16 First mathematically natural incompleteness 40:03 Consistency, and the incorporation of new notions 42:25 Concept calculus 44:33 Completeness, and delicate choice of fragments 45:21 0 - Minimality - 1 45:21 0 - Minimality - 2 47:47 Incompleteness, and concreteness, simplicity, naturalness 48:59 Maximal clique embedding

Video Information

Views
5.7K

Total views since publication

Likes
54

User likes and reactions

Duration
01:09:51

Video length

Published
Dec 11, 2012

Release date

Quality
sd

Video definition

Tags and Topics

This video is tagged with the following topics. Click any tag to explore more related content and discover similar videos:

Tags help categorize content and make it easier to find related videos. Browse our collection to discover more content in these categories.