Top all-time · #1404
Joel David Hamkins
Personal blog · jdh.hamkins.orgmathphilosophy
Joel David Hamkins's personal blog at jdh.hamkins.org covers math and philosophy. Since 2014, 50 different Hacker News readers have linked it 72 times, most often “Math for eight-year-olds: graph theory and the Euler characteristic”. It is still writing: the last post was on 2026-10-21, and you can follow it by feed.
Too few sampled comments (22) to say how often HN recommends it.?
Why HN links it
HN readers link Joel David Hamkins's blog for math written for children (graph theory, coloring, Eulerian paths) and logic puzzles, especially the transfinite version of Cheryl's birthday puzzle.
- Recommended for · 7 comments
- Kids enjoyed the math posts; a favourite version of Cheryl's puzzle; a fun transfinite puzzle that takes logic puzzles to an extreme; a Nim strategy post that m
Summarised by Claude from a sample of 22 HN comments that link here. Each comment is marked recommending, critical or neutral (citing without judging); how this works.
mathematics and philosophy of the infinite
Most-linked posts?
- Math for eight-year-olds: graph theory and the Euler characteristic6 people · 6 mentions · first linked 2015-04-09
- Transfinite epistemic logic puzzle challenge: Cheryl's birthday on steroids4 people · 4 mentions · first linked 2015-04-19
- Transfinite game values in infinite chess (2013)3 people · 3 mentions · first linked 2016-03-26
- Math for seven-year-olds3 people · 3 mentions · first linked 2014-06-13
- A poster about: How to count to infinity and beyond2 people · 3 mentions · first linked 2021-09-02
- Infinite chess -– bishop cannon gun battery fires out bishop cannonballs2 people · 3 mentions · first linked 2015-10-29
- Pop culture quotes written in first-order logic – can you figure them out?2 people · 3 mentions · first linked 2016-03-17
- Sudoku for two players and its strategies2 people · 2 mentions · first linked 2018-04-17
- /cheryls-rational-gifts/2 people · 2 mentions · first linked 2022-05-09
- /category/math-for-kids/2 people · 2 mentions · first linked 2014-06-13
What Hacker News says?
> And Hamkins shows it can go all the way down to eight-year-olds. At the bottom he mentions his previous visit - Math for seven-year-olds: graph coloring, chromatic numbers, and Eulerian paths and circuits http://jdh.hamkins.org/math-for-seven-year-olds-graph-colori...
Comment linking /math-for-seven-year-olds-graph-coloring-chromatic-numbers-eulerian-paths/
on “Math for eight-year-olds: graph theory for kids”Submitted Math for eight-year-olds: graph theory for kids as a story · 350 points
HN discussionI like Cheryl's transfinite logic puzzle, which takes logic puzzles to a ridiculous extreme. http://jdh.hamkins.org/transfinite-epistemic-logic-puzzle-ch... The puzzle is inspired by Cantor's transfinite ordinal numbers, which are pretty cool. You don't need to know anything about transfinite numbers to solve the puzzle, but they are interesting in their own right. The simplified idea is suppose you count 1, 2, 3, .…
Comment linking /transfinite-epistemic-logic-puzzle-challenge/
on “Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]”Submitted Math for seven-year-olds as a story · 262 points
HN discussionMy kids enjoyed this: http://jdh.hamkins.org/math-for-eight-year-olds/
Comment linking /math-for-eight-year-olds/
on “A Coloring Book about Group Theory”Submitted The propagation of error in classical geometry constructions (2018) as a story · 88 points
HN discussionUnfortunately no, ZFC isn't good enough to capture arithmetical truth. The problem is that there are nonstandard models of ZFC where every single model of second-order PA within is itself nonstandard. There are even models of ZFC where a certain specific computer program, known as the "universal algorithm" [1], solves the halting problem for all standard Turing machines. https://jdh.hamkins.org/the-universal-algorit…
Comment linking /the-universal-algorithm-a-new-simple-proof-of-woodins-theorem/
on “BusyBeaver(6) Is Quite Large”Submitted A program that accepts exactly any desired finite set, in the right universe as a story · 87 points
HN discussionAll of this looks awesome: http://jdh.hamkins.org/category/math-for-kids/
Comment linking /category/math-for-kids/
on “Math for seven-year-olds”Submitted How the continuum hypothesis could have been a fundamental axiom as a story · 72 points
HN discussionFor the more mathematically minded readers, here's a harder version of the problem: http://jdh.hamkins.org/transfinite-epistemic-logic-puzzle-ch...
Comment linking /transfinite-epistemic-logic-puzzle-challenge/
on “When Is Cheryl's Birthday?”Submitted Coming to Agreement, a logic puzzle for Oxford admissions interviews as a story · 63 points
HN discussionThis puzzle also exists in a transfinite version, where the two players converge on the correct solution but require longer than infinity for the process: http://jdh.hamkins.org/cheryls-rational-gifts/
Comment linking /cheryls-rational-gifts/
on ““I don't know the numbers”: a math puzzle”Submitted Transfinite NIM (the game, not the programming language) as a story · 62 points
HN discussionMy favorite version of this is a real mind fuck. http://jdh.hamkins.org/cheryls-rational-gifts/ Two people are told rational numbers of a particular form. They want to know whose number is larger: > Albert I don’t know. > Bernard Neither do I. > Albert Indeed, I still do not know. > Bernard And still neither do I. > Cheryl Well, it is no use to continue that way! I can tell you that no matter how long you continue t…
Comment linking /cheryls-rational-gifts/
on ““I don't know the numbers”: a math puzzle”Submitted Transfinite game values in infinite chess (2013) as a story · 32 points
HN discussionMy favourite trivia about "On Computable Numbers" is that Alan Turing got the definition of computable reals wrong! The way he defines them - namely that a computable real is a Turing machine that generates the sequence of digits of the real - has severe issues, because addition and other basic operations are incomputable due to subtle diagonalisation arguments (see https://jdh.hamkins.org/alan-turing-on-computable-…
Comment linking /alan-turing-on-computable-numbers/
on “Turing Machines”Submitted The lattice of sets of natural numbers is rich as a story · 13 points
HN discussionThese are great problems the first two seem to have obvious modes of proof at first sight ... What I particularly like is that the Erdos-Strauss problem is one that's accessible to a junior schooler - once you know fractions you can investigate. I could see it forming part of a project like the graph theory investigations posted formerly, http://jdh.hamkins.org/math-for-eight-year-olds/ .
Comment linking /math-for-eight-year-olds/
on “Famous Unsolved Math Problems as Homework”Submitted The rule-making game as a story · 11 points
HN discussionThis too, http://jdh.hamkins.org/category/math-for-kids/ , which featured on HN a couple of months ago.
Comment linking /category/math-for-kids/
on “Most Math Problems Do Not Have a Unique Right Answer”Submitted Transfinite Nim as a story · 9 points
HN discussion> Far better to show them the most effective technique, let them practice it, and move on. This can work for the base levels of what most folks think as mathematics, namely arithmetic and algebra. But it starts falling apart as students get to more advanced algebra and mathematical topics. Memorizing a particular algorithm does not lend to understanding mathematics. In particular, the parallels between algebra (and…
Comment linking /math-for-eight-year-olds/
on “How to Remove Obstacles to Learning Math”Submitted Proof and the Art of Mathematics as a story · 7 points
HN discussionThe author's previous post on winning strategies for regular Nim may be more interesting to people here: https://jdh.hamkins.org/win-at-nim-the-secret-mathematical-s...
Comment linking /win-at-nim-the-secret-mathematical-strategy/
on “Transfinite NIM (the game, not the programming language)”Submitted Every function can be computable as a story · 4 points
HN discussionhttp://jdh.hamkins.org/lectures-on-the-philosophy-of-mathema...
Comment linking /lectures-on-the-philosophy-of-mathematics/
on “Ask HN: What are your favorite books/courses of 2022? Why?”Submitted Nondegenerate regular polygons in the integer lattice as a story · 4 points
HN discussionAnother interesting one in the style of the Singaporean puzzle that's been making the rounds recently: http://jdh.hamkins.org/transfinite-epistemic-logic-puzzle-ch... (knowledge of transfinite ordinals is useful)
Comment linking /transfinite-epistemic-logic-puzzle-challenge/
on “The Hardest Logic Puzzle Ever”Submitted A position in infinite chess with game value Omega^4 as a story · 3 points
HN discussion
