Top all-time · #5817
Michael Harris
Personal blog · mathematicswithoutapologies.wordpress.commathphilosophy
Michael Harris's personal blog at mathematicswithoutapologies.wordpress.com covers math and philosophy. Since 2015, 14 different Hacker News readers have linked it 16 times, most often “Univalent Foundations: No Comment”. The last post was in 2023, but the archive is still widely read.
Too few sampled comments (11) to say how often HN recommends it.?
Why HN links it
Essays by mathematician Michael Harris on foundations of mathematics, critiquing homotopy type theory and category-theory approaches, plus posts on Lurie, Scholze and related debates.
Summarised by Claude from a sample of 11 HN comments that link here. Each comment is marked recommending, critical or neutral (citing without judging); how this works.
An unapologetic guided tour of the mathematical life
Most-linked posts?
- Univalent Foundations: No Comment4 people · 4 mentions · first linked 2015-05-19
- Univalent Foundations: “No Comment.”2 people · 2 mentions · first linked 2015-05-20
What Hacker News says?
Univalent Foundations is apparently controversial. It appeared to come to a head a couple years ago when a lively debate played out in the comments of a blog (including a comment by Voevodsky himself): https://mathematicswithoutapologies.wordpress.com/2015/05/13...
Comment linking /2015/05/13/univalent-foundations-no-comment/
on “Vladimir Voevodsky has died”Submitted Univalent Foundations: “No Comment.” as a story · 54 points
HN discussionIn the comments of a recent mathematics-without-apologies blog post[1], there was a back-and-forth between Jacob Lurie and Urs Schreiber (the author of the OP article on nLab). I've been trying to parse the material on nLab for years, good to know I'm not the only one who seems to have trouble with it. A refreshingly blunt discussion, not to be missed! 1. https://mathematicswithoutapologies.wordpress.com/2015/05/13.…
Comment linking /2015/05/13/univalent-foundations-no-comment/comment-page-1/
on “Relation Between Type Theory, Category Theory and Logic”Submitted Global warming equations in the Paris metro (2015) as a story · 1 points
HN discussionI wouldn't say it "challenges" set theory. For this to be the case there have to demonstrable advantages over working with set theory. The main attraction of HoTT is that it allows people to do homotopy theory on computers using theorem provers. It is still a very open question whether this is an improvement over pen and paper math. It's still not clear if HoTT is just some neat technical gimmick that allows one to…
Comment linking /2015/05/13/univalent-foundations-no-comment/
on “The Foundations of Mathematics (2007) [pdf]”Submitted Univalent Foundations – No Comment as a story · 1 points
HN discussionLurie's "On Infinity Topoi"[0] preceded the book and is, I quote[1], > 50 pages of pure cake, beautifully and informally written. The book is 1000 pages long. There is some new cake there, but not 20 times as much. [0] https://arxiv.org/abs/math/0306109 [1] https://mathematicswithoutapologies.wordpress.com/2015/05/13...
Comment linking /2015/05/13/univalent-foundations-no-comment/comment-page-1/
on “Physics, Topology, Logic and Computation: A Rosetta Stone (2009) [pdf]”Submitted Univalent Foundations: No Comment as a story · 1 points
HN discussionI agree with you that this is really about the foundations of algebraic topology, but what makes you say that these are not the foundations of mathematics? In the community of computer-aided formalization, a lot of interest in modern type theory arose, because some things in algebraic topology just couldn't easily be done in the old First-order-logic + ZFC framework: For example, Kevin Buzzard once asked if Isabelle…
Comment linking /2015/05/13/univalent-foundations-no-comment/comment-page-1/
on “With Category Theory, Mathematics Escapes from Equality (2019)”> evinces a misunderstanding of what people who work on foundations actually want out of a foundation of mathematics This is still gatekeeping who gets to use the word "foundations". I will go read https://mathematicswithoutapologies.wordpress.com/2015/05/13 but my hopes are not high for a sudden breakthrough.
Comment linking /2015/05/13
on “With Category Theory, Mathematics Escapes from Equality (2019)”First, I'm not a set theorist. Second, one of the major motivations for introducing type theory in mathematics was to assist with computer-aided formalization efforts, which has had some success and has a promising future (e.g. the stuff the Lean community has been doing lately). This is great! I'm not complaining at all. But I do think trumpeting HoTT as a new, improved foundation of mathematics evinces a misunders…
Comment linking /2015/05/13/univalent-foundations-no-comment/comment-page-1/
on “With Category Theory, Mathematics Escapes from Equality (2019)”This is not "foundational mathematics." This is about the foundations of algebraic topology. The experts in the foundations of mathematics as a whole (set theorists, logicians, model theorists, etc.) don't care about homotopy type theory. It's sort of pointless for the study of the foundations of mathematics. That is, they really just care about ZF or ZFC, because those are already formulated so that they are maxima…
Comment linking /2015/05/18/jacob-lurie-explains-and-elaborates-on-his-no-comment/
on “With Category Theory, Mathematics Escapes from Equality (2019)”In 2013, a consortium of the greatest mathematicians published a massive volume which reboots our conception of mathematics. Ok, here's a rant by a frustrated student who's spent way too much time drinking the cool-aid. None of the authors, except for Voevodsky, is widely known among professional mathematicians. And Voevodsky is not known because of his work on HoTT. In fact, most mathematicians regard homotopy type…
Comment linking /2015/05/13/univalent-foundations-no-comment
on “Homotopy Type Theory and Higher Inductive Types”Some additions to this profile: Scholze won 3 gold medals at the International Mathematical Olympiad [1], refused the Milner and Zuckerberg's Millenium Prize (without justification, afaik) [2], answers once in a while on mathoverflow [3] and has played the bass in a rock band, obviously. [4] [1] http://imo-official.org/participant_r.aspx?id=7867 [2] https://mathematicswithoutapologies.wordpress.com/2015/11/09... [3]…
Comment linking /2015/11/09/working-the-red-carpet-part-2/
on “The Oracle of Arithmetic”Learning mathematics had been incredibly useful to me. If that hasn't been the case for you, I'm sorry. Your claim that HoTT is "broadly regarded as an exciting and important new area of mathematics" is simply wrong. I suggest talking to a wider variety of mathematicians. In particular, concerning "well-regarded and prominent mathematicians," Steve Simpson and Harvey Friedman are on record on the Foundations of Math…
Comment linking /2015/05/13/univalent-foundations-no-comment/
on “Homotopy Type Theory (2012) [pdf]”This is caused by the realigning of university administrative structures along the philosophical lines of neoliberalism [0]. It's hard to find a definition of neoliberalim outside of technical political theory, but I think this source is a good overview and I've seen it cited by academics [1], for example this guy who contextualizes it within academia (some of his writing was accused of being neoliberal ideology) [2…
Comment linking /2015/05/08/how-to-brand-mathematics/
on “Public universities have “really lost our focus””
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