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Annoying Precision
Personal blog · qchu.wordpress.commathphilosophy
Annoying Precision is a personal blog at qchu.wordpress.com about math and philosophy. Since 2012, 13 different Hacker News readers have linked it 14 times, most often “The type system of mathematics”. The last post was in 2020, but the archive is still widely read.
"A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one." - Paul Halmos
Most-linked posts?
- The type system of mathematics4 people · 4 mentions · first linked 2015-11-23
- What’s a fire, and why does it burn?2 people · 2 mentions · first linked 2017-01-10
What Hacker News says?
One of my current favorite things: categorification of linear algebra via higher category theory: https://qchu.wordpress.com/2016/05/31/higher-linear-algebra/
Comment linking /2016/05/31/higher-linear-algebra/
on “Computational Linear Algebra”Submitted What’s a fire, and why does it burn? as a story · 276 points
HN discussionI'm no expert but I think one of the big ones is Grothendieck's identification of affine schemes with the dual (categorical opposite) of commutative rings. That is, a "space" is just a commutative ring (of functions on it), but you think about it backwards. So a map of "spaces" A->B, is a map of commutative rings A<-B. John Baez has a bunch of TWF's about this stuff that I highly recommend. Also [1]. [1] https://qch…
Comment linking /2009/11/24/spectra-of-rings-of-continuous-functions/
on “Grothendieck's Approach to Equality [pdf]”Submitted What’s a fire and why does it burn? (2016) as a story · 147 points
HN discussionSee also [1], where Terence Tao suggests that 2 pi i may be even more fundamental than both 2 pi and pi , and [2] for some explanation on why. [1] http://blog.computationalcomplexity.org/2007/08/is-pi-define... [2] http://qchu.wordpress.com/2011/03/14/pi-is-still-wrong/
Comment linking /2011/03/14/pi-is-still-wrong/
on “Pi Is Wrong”Submitted The type system of mathematics as a story · 3 points
HN discussionThis is pretty good, although I am always a bit worried that it is difficult for people to internalize this stuff without a real drive to get into abstract algebra. As a side note, I think a really nice way to go (dovetailing off of the ending group actions section) is to use group actions and this lemma ( https://qchu.wordpress.com/2013/07/09/the-p-group-fixed-poin... ) to prove a bunch of cool stuff. It really uni…
Comment linking /2013/07/09/the-p-group-fixed-point-theorem/
on “Groups: A Primer (2012)”Submitted The type systems of mathematics (2013) as a story · 3 points
HN discussionSubmitted The type system of mathematics (2013) as a story · 2 points
HN discussionSubmitted The Type System of Mathematics as a story · 2 points
HN discussionSubmitted Cantor’s theorem, the prisoner’s dilemma, and the halting problem as a story · 2 points
HN discussionSubmitted The type system of mathematics (2013) as a story · 1 points
HN discussionSubmitted Cantor’s theorem, the prisoner’s dilemma, and the halting problem as a story · 1 points
HN discussionSubmitted Ramsey theory and Fermat's Last Theorem as a story · 1 points
HN discussion
