Ericson2314on Hacker News • Recommends
On “How a destructive idea paved the way for modern math”
Yes we must take saxioms on faith alone. Embrace pluralism and move on. link to this video by the late great Voedvodvosky is more interesting.
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#vladimirvoevodsky#univalentfoundations#incompletenesstheorem
What if Current Foundations of Mathematics are Inconsistent? | Vladimir Voevodsky
Institute for Advanced Study
161K subscribers • 3 videos on Hallway
- Recommended by 3 people: 3 on Hacker News.
- Presented by Vladimir Voevodsky, Professor of Mathematics at IAS
Advanced. Deep dive for people who know the field.
57K views14 years ago3 recommendations
Computer scienceComputation and complexityFormal methods and verification
Vladimir Voevodsky discusses the potential inconsistency of first-order arithmetic and introduces his vision for computer-checked proofs and univalent foundations.
Vladimir Voevodsky, Professor, School of Mathematics, Institute for Advanced Study ias.edu/people/faculty-and-emeriti/voevodsky In this lecture, Professor Vladimir Voevodsky begins with Gödel's second incompleteness theorem to discuss the possibility that the formal theory of first-order arithmetic may be inconsistent. This lecture was part of the Institute for Advanced Study's celebration of its eightieth anniversary, and took place during the events related to the Schools of Mathematics and Natural Sciences. More videos at video.ias.eduWhy it's here
3 people recommend thisWhat people say. Recommended for its deep exploration of mathematical foundations and the motivation behind computer-verified mathematics.
IngoBlechschmidon Hacker News • Recommends
On “Mystery Math Whiz and Novelist Advance Permutation Problem”
…thematics not only in principle, but also in practice.) The hope is also that with computer-checked proofs, we can advance to new areas of mathematics which are currently inprenetable to our puny human minds. I'm very much looking forward to this future! You can learn more about Voevodsky's vision in slides of him and in a recorded lecture: link link to this video…
ukjon Hacker News • Recommends
On “A Programmer’s Regret: Neglecting Math at University”
Where Hilbert erred was looking for foundations in first-order logic. Univalent foundations are laid on high-order logic. It's the distinction between top-down and bottom-up thinking. If you are into philosophy/epistemology - it's somewhat of an attempt to shift Mathematics from foundationalism towards structuralism. I recommend this video: link to this video Hilbert's dream of Metamathematics has sort of come true in the form of homoiconicity in programming languages.