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What if Current Foundations of Mathematics are Inconsistent? | Vladimir Voevodsky

Institute for Advanced Study · lecture · Watch on YouTube

Logic & formal methodsPure mathematics

What it is

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

Why Hacker News recommends it

Recommended as a thought-provoking lecture from a Fields medalist on the foundations of mathematics and formal proof verification.

  • 3 people recommended it
  • 3 different months
  • 0 strong recommendations
  • first 2017, last 2019

What HN commenters said

  1. “by the late great Voedvodvosky is more interesting.”

    Voevodsky's talk on possible inconsistency of mathematical foundations

    Ericson2314, 2017-11 · Recommendation · in “How a destructive idea paved the way for modern math”

  2. “You can learn more about Voevodsky's vision in slides of him and in a recorded lecture”

    Voevodsky's vision for computer-checked proofs

    IngoBlechschmid, 2018-11 · Recommendation · in “Mystery Math Whiz and Novelist Advance Permutation Problem”

  3. “I recommend this video”

    Explains univalent foundations and shift toward structuralism

    ukj, 2019-07 · Recommendation · in “A Programmer’s Regret: Neglecting Math at University”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: voevodsky, incompleteness, univalent foundations, proof assistants, logic

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