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

Why HN readers recommended it

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

This is a summary from the source dataset, not an endorsement by Hacker News or the video creator.

Video & recommendation details

Creator / channel

Institute for Advanced Study

Topic

foundations of mathematics

Format

lecture

Level

advanced

HN recommenders in dataset

3

HN mentions in dataset

3

Recommendation years in dataset

2017–2019

These counts and years describe the included Hacker News records; they are not YouTube views or the video’s publication date.

From the original HN conversations

Excerpts from the recorded comments. Follow each source for the full comment and surrounding discussion.

• Yes we must take saxioms on faith alone. Embrace pluralism and move on. [VIDEO] by the late great Voedvodvosky is more interesting.

• > And indeed, this will likely always be the case, as the true purpose of proving a mathematical result is almost never to actually get the boolean true/false output, but to illustrate how to solve the problem in the first place and what methods were …

• 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 …