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Complex Projective 4-Space

cp4space.hatsya.com

Where exciting things happen

Math

’15’20’25
Posts
390 from 22 Aug 2012 to 3 May 2026
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now and then (1 in the last year)
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personal blog
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2026 1

  1. Schanuel’s conjecture and the semantics of FPSan

2025 1

  1. Charles Corderman’s computer

2024 2

  1. The minimal infinite threeld
  2. Every finite phoenix has period 2

2023 6

  1. Miscellaneous discoveries
  2. Aperiodic monotile
  3. The Osmiumlocks Prime
  4. Searching for optimal Boolean chains
  5. The ordered partial partition polytope
  6. Tensor rank paper

2022 8

  1. Matrix multiplication update
  2. Updates and errata
  3. A combinatorial proof of Houston’s identity
  4. Tetrational machines
  5. Infinitely many rational dodecahedra
  6. Threelds
  7. 29-year-old Conway conjecture settled
  8. Training a random Gaussian generator

2021 13

  1. Involutions on a finite set
  2. Hamming backups: a 2-of-3 variant of SeedXOR
  3. An efficient prime for number-theoretic transforms
  4. Hamming cube of primes
  5. Determinacy
  6. One-way permutations
  7. Cyclotomic fields
  8. Urbit for mathematicians
  9. A curious construction of the Mathieu group M11
  10. Assorted topics
  11. Meagre sets and null sets
  12. Keep your public keys private
  13. The neural network of the Stockfish chess engine

2020 20

  1. Rigid heptagon linkage
  2. Barreto-Naehrig curves and cryptographic pairings
  3. Shallow trees with heavy leaves
  4. Let the circumcentre be your origin
  5. An attempt to understand the Monster group
  6. The exceptional Jordan algebra
  7. Closed-form numbers
  8. The Barnes-Wall lattices
  9. Subsumptions of regular polytopes
  10. Relocation
  11. Associative universal gates
  12. Another two rational dodecahedra
  13. Banach-Tarski and the Axiom of Choice
  14. Rational dodecahedron inscribed in unit sphere
  15. Fast-growing functions revisited
  16. 4-input 2-output Boolean circuits
  17. That group of order 348364800
  18. More quantum gates and lattices
  19. Minimalistic quantum computation
  20. Nested lattices

2019 4

  1. Self-replicator caught on video
  2. Five-input Boolean circuits
  3. (W^2 + X^2) / (W^2 + X^2 + Y^2 + Z^2)
  4. Complexity of integer multiplication almost solved

2018 13

  1. Fully self-directed replication
  2. 6-colourings of subsets of the plane
  3. Atiyah’s problem
  4. Sorting networks
  5. Eurozone’s Lemma
  6. Royal Wedding and Polymath16
  7. Assorted news
  8. Cubical Type Theory
  9. Diamonds
  10. Happy Noethday
  11. Serge Vlăduţ : Lattices with exponentially large kissing numbers
  12. A rather satisfying winter
  13. Olympiad news

2017 4

  1. Generalised Riemann Hypothesis
  2. AlphaGo Zero
  3. Undecidability of contractibility
  4. Homotopy Type Theory

2016 6

  1. Wallis Workshop
  2. Is Craig Wright?
  3. March miscellany
  4. Presidential endorsement paradox
  5. Deep Learning with the Analytical Engine
  6. Lovelace hackathon: results

2015 6

  1. Ada Lovelace Day: 10th December 2015
  2. Superflip composed with fourspot
  3. Coverings, convolutions and Corbynatorics
  4. ∂ eclipse
  5. Proto-Penrose tilings
  6. Oligomath 2: When are polylogarithms integers?

2014 56

  1. Oligomath 1: Deletion and duplication
  2. Holyhedron update
  3. Ménage primes
  4. Random circular mazes
  5. Cipher 71: Monoalphabetic II
  6. Tweetable architecture
  7. Tributes to cryptanalysts
  8. Hyperbolic Minecraft
  9. First female Fields medallist
  10. How to do geometry properly
  11. I’m still alive
  12. If sunflowers were square
  13. Applications of quaternions
  14. Cipher 70: Wild goose chase
  15. Cavalieri’s principle
  16. Cipher 69: A void
  17. Bounded gaps: one year on…
  18. Liquid mirror telescopes
  19. Meteor shower
  20. Cipher 68: Conjugation
  21. Cipher 67: Dyslexic philosopher
  22. Golyhedron update
  23. Noughts and Crosses
  24. Golygons and golyhedra
  25. Orchestral biography of Turing
  26. Cipher 66: Hash inversion
  27. Poncelet’s porism: the Socratic dialogue
  28. Cipher 65: Melencolia
  29. Lifting the exponent
  30. Cipher 64: Sic transit gloria Monday
  31. Cayley-Menger determinants
  32. Most difficult chess problem
  33. Cipher 62: Also untitled
  34. Denser packing of pound coins discovered
  35. Cipher 61: Discrepancy
  36. Rectangular hyperbolae and the orthocentre
  37. Cipher 60: Tuesday comes between Wednesday and Friday this week
  38. Emergence
  39. Cipher 59: Iterated question-answering
  40. Gears
  41. Schönhage-Strassen algorithm
  42. Cipher 58: Regarding knot theory
  43. Cipher 57: Inadvertent involution
  44. Soddy’s hexlet
  45. Cipher 56: Myrmecological madness
  46. Exotic spheres
  47. Cipher 55: Tantalising
  48. Hurwitz surfaces
  49. Cipher 54: Zero-sum game
  50. Solitons and trains
  51. Cipher 53: Multicoloured
  52. Descartes snark
  53. Cipher 52: Tetragrammaton
  54. Complications of furniturial locomotion
  55. Cipher 51: Wild bee chase
  56. Supercoiling

2013 172

  1. New Year’s Eve
  2. Applications of ultrafilters
  3. Comprehending ultrafilters
  4. Large cardinals
  5. Tarski’s circle-squaring problem
  6. Free commutative monoid on countably many generators
  7. Miscellaneous news and sphere eversion
  8. Brouwer’s fixed-point theorem
  9. Crash course in Gaussian integers
  10. Bounded gaps update
  11. Hearing the shape of a drum
  12. Quantum logic gates
  13. Yf and only Yf?
  14. Gosper’s Pyrominia animation
  15. Cipher 50: Non-trivial evasion
  16. Curves of constant width
  17. Enumerating the rationals
  18. Cipher 49: Feline cartograph
  19. Punting in clearings of arbitrarily small Lebesgue measure
  20. Mathematical innuendo
  21. Mathieu groupoid
  22. MOG results released
  23. What should this group be called?
  24. Cipher 48: Endoplasmic reticulum
  25. Proper classes
  26. Molecular geometry
  27. Cipher 47: Plughole
  28. Lattice gases and conformal maps
  29. The Whetstone of Witte
  30. Mog
  31. Cipher 46: Hellenic Angler Leviathan
  32. Rational approximations to Platonic solids
  33. Desert Island Theorems
  34. W. T. Tutte
  35. Cipher 45: Sisyphean
  36. Perrin sequence
  37. Leech lattice
  38. Category of scones
  39. Cipher 44: Dostin
  40. Ten things you (possibly) didn’t know about the Petersen graph
  41. Exotic continued fractions
  42. Cipher 43: Palindrome
  43. Pappian and Desarguesian planes
  44. Four colour theorem
  45. Comfortably squarefree numbers
  46. Stella octangula
  47. Cipher 42: Sudoku II
  48. A more aperiodic monotile
  49. Block cellular automata
  50. New aperiodic monotile
  51. Gingerbread men
  52. A year of cp4space
  53. Langton’s loops, sexually-transmitted viruses and architecture
  54. Cipher 41: Caesar cipher
  55. Influential mathematicians
  56. Growth of recursive string substitution
  57. Analysing Escher
  58. Polynomials and Hamming weights
  59. Cipher 40: Leversha’s paradise
  60. Symmetric geometry theorems
  61. Kaleidoscopes
  62. Cipher 39: Unknown location
  63. Fair dice
  64. Seven-dimensional cross product
  65. De Bruijn sequences
  66. Cipher 38: 60 percent wordsearch
  67. Further news
  68. Converting problems into elliptic curves
  69. Cipher 37: Honeycomb II
  70. Mathematical Ashes
  71. Von Neumann universe
  72. Cipher 36: Concube cum cerebro
  73. Generalised TFAE
  74. PSL(2,Z)
  75. Cipher 35: Adjacency mania
  76. Lovász conjecture and Devil’s algorithm
  77. Coxeter groups and beyond
  78. Cipher 34: Manual
  79. Competitions
  80. Partition numbers
  81. Cipher 33: Puzzling II
  82. Assorted news
  83. Iterated Aut revisited
  84. Cipher 32: Untitled
  85. How to score 1729 in the IA Tripos
  86. Quasifractals
  87. Plateau
  88. Cipher 31: Polyphasic
  89. Down to 285278
  90. Johnson solids
  91. The Not-Very-Random-At-All Graph
  92. Integral banana
  93. Iterated automorphism groups
  94. IMO team unveiled
  95. Pairwise versus overall
  96. The Universe
  97. Sierpinski triangle
  98. Cipher 30: Finale
  99. Hoffman-Singleton graph
  100. Simultaneous proofs
  101. Cipher 29: Permutation
  102. FRACTRAN
  103. Things that shouldn’t work, but do
  104. Cipher 28: Irrationality II
  105. Words in summation convention
  106. Background Problem I
  107. Cipher 27: Sunflower
  108. Affine spaces over F3
  109. Recent discoveries in Conway’s Life
  110. Cipher 26: Spaced out
  111. Ring of periods
  112. The n-body problem
  113. Cipher 25: My dear Watson
  114. EGMO synopsis
  115. Efficient computational matchings and lax sexual morality
  116. One-dimensional noughts and crosses
  117. Gamma(1/4)
  118. Cipher 24: ADFGVX
  119. Don’t do it!
  120. 3D chess is Turing-complete
  121. BMO training
  122. Circuitry in 3D chess
  123. Cipher 23: Orthogonal boustrophedons
  124. New prime-generating algorithm
  125. Three-dimensional chess
  126. Urinals
  127. Cipher 22: There be dragons
  128. Rational distance problem
  129. Holyhedra
  130. Cipher 21: Sudoku
  131. Generalising Erdős’ conjecture
  132. Three directions
  133. Antoine’s necklace
  134. Cipher 20: Ulam
  135. Permanent-determinant method
  136. Eilenberg-Mazur swindle
  137. Cipher 19: Corrupted
  138. Assorted news
  139. Radical Tauism
  140. Cipher 18: Enigma
  141. 27 lines on a cubic
  142. The torus
  143. Cipher 17: Hallucinogen
  144. What constitutes an explicit example?
  145. Tournament dice
  146. Magic squares of squares
  147. Cipher 16: The scenic route
  148. BMO2 marked
  149. Langton’s ant revisited
  150. New perfect number discovered
  151. Cipher 15: Shuffled
  152. |cp4space| = 100
  153. Sphere packings, lattices and fruits
  154. Cipher 14: Remorse
  155. Visualising complex functions
  156. Ordinal music
  157. Origami
  158. Cipher 13: Intercardinal
  159. Cayley-Bacharach applications
  160. Non-trivial mutual friends
  161. Assorted stuff
  162. Projective Cranch geometry
  163. Cipher 12: Knot homophonic
  164. Graph minors
  165. Alexandroff line
  166. Generalised Truchet tiles
  167. Cipher 11: Musical mayhem
  168. Bombers and Basilisks
  169. The Ξ function
  170. Topological tacks
  171. Egmohedron
  172. Cipher 10: 2013

2012 78

  1. Recapping 2012
  2. Busy beavers
  3. The inadequacy of SCLT
  4. Cipher 9: Christmas cryptography
  5. The world still exists
  6. Dissecting the disc
  7. TREE(3) and impartial games
  8. Cipher 8: Honeycomb
  9. Pictures of matchstick graphs
  10. Fast-growing functions
  11. Infinite monkey theorem
  12. Treefoil
  13. Cipher 7: Generalised RSA
  14. BMO1 marked
  15. Things go wrong eventually
  16. Triangling the square
  17. Bolzano-Weierstrass
  18. Cipher 6: Puzzling
  19. Adenovirus
  20. Fat Cantor set
  21. Geomagic squares
  22. Cipher 5: 99 problems or 23?
  23. Miscellany
  24. Outer automorphism of S6
  25. Hyperboloid of one sheet
  26. Betts revisited
  27. Cipher 4: Think rationally
  28. Spin groups
  29. Field with one element
  30. Mouse-astrophe
  31. Self-replication
  32. Wire tetrahedra
  33. The Betts problem
  34. Responses
  35. Final chapter of MODA
  36. NP-triv
  37. Happy Hallowe’en
  38. Fusible numbers
  39. MODA: Diophantine equations
  40. Gmt
  41. Borromean strings
  42. Markov basket-weaving
  43. Cipher 3: Chess cipher
  44. MODA: Inversion
  45. Combinatorial cake
  46. Surfaces
  47. MODA: Barycentric stuff
  48. Campanology
  49. Spinning around
  50. Projective polyhedra
  51. Antikythera revisited
  52. MODA: Geometry bashing
  53. Combinatorial game theory
  54. A slice of π
  55. MODA: Projective geometry
  56. Hiatus interruptus
  57. Good fibrations
  58. Cipher 2: Labyrinth
  59. MODA: Inequalities
  60. One hundred and sixty three
  61. Antikythera mechanism
  62. MODA: Sequences and Polynomials
  63. Lizard and Spock dice
  64. Linear-bounded automata
  65. Lunisolar calendars
  66. Second and third chapters
  67. Big Mandelbrots
  68. Dürer’s square
  69. Digest
  70. MODA ready for review
  71. Closed-form bijections
  72. Activities with golden rhombi
  73. Sexy symmetrical starfish
  74. Elliptic curve calculator
  75. Cipher 1: Puzzle Hybridisation
  76. Conway polyhedron notation
  77. Are you Ready?
  78. Pathological functions