The Curious Engineer

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Gowers's Weblog

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Mathematics related discussions

Math

’10’15’20’25
Posts
338 from 6 Sep 2007 to 16 Oct 2026
Posting
monthly (6 in the last year)
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personal blog
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2026 6

  1. How worried should we be about extinction risk from AI?
  2. Why I didn’t sign the Fields medallists’ letter
  3. What sort of maths are LLMs good at?
  4. Thoughts about the Leiden Declaration
  5. A recent experience with ChatGPT 5.5 Pro
  6. Group and semigroup puzzles and a possible Polymath project

2025 1

  1. Creating a database of motivated proofs

2022 1

  1. Announcing an automatic theorem proving project

2021 1

  1. Leicester mathematics under threat again

2020 2

  1. Mathematical Research Reports: a “new” mathematics journal is launched
  2. How long should a lockdown-relaxation cycle last?

2019 3

  1. Advances in Combinatorics fully launched
  2. The fate of combinatorics at Strathclyde
  3. Voting tactically in the EU elections

2018 7

  1. How Craig Barton wishes he’d taught maths
  2. Taylor and Francis doing Trump’s dirty work for him
  3. Worrying news from Turkey
  4. A quasirandomness implication
  5. Additional thoughts on the Ted Hill paper
  6. Has an uncomfortable truth been suppressed?
  7. A new journal in combinatorics

2017 10

  1. Two infinities that are surprisingly equal
  2. Intransitive dice VII — aiming for further results
  3. Another journal flips
  4. Intransitive dice VI: sketch proof of the main conjecture for the balanced-sequences model
  5. Intransitive dice V: we want a local central limit theorem
  6. Intransitive dice IV: first problem more or less solved?
  7. Intransitive dice III
  8. Intransitive dice II
  9. A potential new Polymath project: intransitive dice
  10. Timothy Chow starts Polymath12

2016 15

  1. Time for Elsexit?
  2. Call for nominations for the 2018 Chern Medal
  3. Quick update on Leicester
  4. Discrete Analysis one year on
  5. In case you haven’t heard what’s going on in Leicester …
  6. ∈
  7. Reflections on the recent solution of the cap-set problem I
  8. The L-functions and modular forms database
  9. Should I have bet on Leicester City?
  10. Discrete Analysis launched
  11. FUNC4 — further variants
  12. FUNC3 — further strengthenings and variants
  13. FUNC2 — more examples
  14. FUNC1 — strengthenings, variants, potential counterexamples
  15. Frankl’s union-closed conjecture — a possible Polymath project?

2015 7

  1. Entropy and Sidorenko’s conjecture — after Szegedy
  2. Interesting times in academic publishing
  3. Gil Kalai starts Polymath10
  4. EDP28 — problem solved by Terence Tao!
  5. Discrete Analysis — an arXiv overlay journal
  6. Is Nick Clegg a Liberal Democrat?
  7. USS changes — don’t be fooled

2014 26

  1. Sums of kth powers
  2. ICM2014 — Bhargava, Gentry, Sanders
  3. ICM2014 — Kollár, Conlon, Katz, Krivelevich, Milnor
  4. ICM2014 — Jim Arthur plenary lecture
  5. ICM2014 — Barak, Guralnick, Brown
  6. ICM2014 — Emmanuel Candès plenary lecture
  7. ICM2014 — Ian Agol plenary lecture
  8. ICM2014 — Khot laudatio
  9. ICM2014 — Mirzakhani laudatio
  10. ICM2014 — Hairer laudatio
  11. ICM2014 — Bhargava laudatio
  12. ICM2014 — Avila laudatio
  13. ICM2014 — opening ceremony
  14. ICM2014 — first impressions
  15. ICM2014 — introductory post
  16. Mini-monomath
  17. ECM2016 — your chance to influence the programme
  18. Elsevier journals — some facts
  19. A few analysis resources
  20. How do the power-series definitions of sin and cos relate to their geometrical interpretations?
  21. Differentiating power series
  22. Recent news concerning the Erdos discrepancy problem
  23. Taylor’s theorem with the Lagrange form of the remainder
  24. How to work out proofs in Analysis I
  25. Introduction to Cambridge IA Analysis I 2014
  26. DBD2 — success of a kind

2013 26

  1. A little paradox
  2. DBD1 — initial post
  3. What I did in my summer holidays
  4. Holding a country to ransom
  5. Razborov and Rudich’s natural proofs argument
  6. How not to prove that P is not equal to NP
  7. Preprint about theorem-proving program up on arXiv
  8. Determinacy of Borel games V
  9. Determinacy of Borel games IV
  10. Determinacy of Borel games III
  11. Determinacy of Borel games II
  12. Determinacy of Borel games I
  13. The selected-papers network
  14. Elsevier journals: has anything changed?
  15. Answers, results of polls, and a brief description of the program
  16. A second experiment concerning mathematical writing.
  17. Another test
  18. An experiment concerning mathematical writing
  19. Test
  20. Pierre Deligne wins the 2013 Abel Prize
  21. The work of Endre Szemerédi
  22. Whither Polymath?
  23. Ted Odell
  24. The Elsevier boycott one year on
  25. Why I’ve also joined the good guys
  26. Why I’ve joined the bad guys

2012 41

  1. What maths A-level doesn’t necessarily give you
  2. What actually happened
  3. Mathematics meets real life
  4. EDP27 — the modular version of Roth’s AP-discrepancy theorem
  5. EDP26 — three generalizations
  6. EDP25 — third guest post by Gil Kalai
  7. EDP24 — an attempt to get back into the diagonal-decomposition approach
  8. EDP23 — second guest post by Gil Kalai
  9. EDP22 — first guest post by Gil Kalai
  10. EDP: a possible revival
  11. What are dense Sidon subsets of {1,2,…,n} like?
  12. A trip to Watford Grammar School for Boys
  13. A new open-access venture from Cambridge University Press
  14. How should mathematics be taught to non-mathematicians?
  15. EPSRC update update
  16. A look at a few Tripos questions X
  17. A look at a few Tripos questions IX
  18. A look at a few Tripos questions VIII
  19. Have you signed the open-access petition?
  20. A look at a few Tripos questions VII
  21. Horizon 2020 to promote open access
  22. A look at a few Tripos questions VI
  23. A look at a few Tripos questions V
  24. The mathematics department at TU Munich cancels its subscriptions to Elsevier journals
  25. Elsevier’s recent update to its letter to the mathematical community
  26. A look at a few Tripos questions IV
  27. A look at a few Tripos questions III
  28. A look at a few Tripos questions II
  29. A look at a few Tripos questions I
  30. Polymath paper published
  31. A brief EPSRC update
  32. Endre Szemeredi wins the 2012 Abel Prize
  33. It’s that time of year again
  34. Elsevier withdraws support for the Research Works Act
  35. Elsevier’s open letter point by point, and some further arguments
  36. A more formal statement about mathematical publishing
  37. Abstract thoughts about online review systems
  38. What’s wrong with electronic journals?
  39. http://thecostofknowledge.com
  40. Elsevier — my part in its downfall
  41. SOPA — my part in its downfall

2011 40

  1. Farewell to a pen-friend
  2. Group actions IV: intrinsic actions
  3. A short post on countability and uncountability
  4. Group actions III — what’s the point of them?
  5. Normal subgroups and quotient groups
  6. Proving the fundamental theorem of arithmetic
  7. Why isn’t the fundamental theorem of arithmetic obvious?
  8. Group actions II: the orbit-stabilizer theorem
  9. Group actions I
  10. A more modest proposal
  11. How might we get to a new model of mathematical publishing?
  12. Equivalence relations
  13. Alternative definitions
  14. Definitions
  15. Permutations
  16. Domains, codomains, ranges, images, preimages, inverse images
  17. Injections, surjections and all that
  18. Basic logic — summary
  19. Basic logic — tips for handling variables
  20. Basic logic — relationships between statements — converses and contrapositives
  21. Basic logic — relationships between statements — negation
  22. Basic logic — quantifiers
  23. Basic logic — connectives — IMPLIES
  24. Basic logic — connectives — NOT
  25. Basic logic — connectives — AND and OR
  26. Welcome to the Cambridge Mathematical Tripos
  27. Results and explanation
  28. Which is easier?
  29. A message from our sponsors
  30. To cut or not to cut?
  31. Some post-referendum consolations
  32. AV vs FPTP — the short(er) version
  33. AV vs FPTP — a supplementary post
  34. Is AV better than FPTP?
  35. April 1st comes a few days early
  36. Milnor wins 2011 Abel Prize
  37. A new way of proving sumset estimates
  38. Polymath6: A is to B as C is to ???
  39. More on the cap-set problem
  40. What is difficult about the cap-set problem?

2010 67

  1. Finding Cantor’s proof that there are transcendental numbers
  2. Status update
  3. A little physics problem
  4. Online mathematics finally takes off …
  5. Polymath3 now active
  6. Is the Tricki dead?
  7. EDP21 — restrictions on possible proofs
  8. Are these the same proof?
  9. EDP20 — squares and fly traps
  10. A Disappearing Number on in London
  11. EDP19 — removing some vagueness
  12. EDP18 — apparently P does not equal NP
  13. ICM2010 — final post
  14. ICM2010 — fourth day
  15. ICM2010 — rest of day three
  16. ICM2010 — Spielman, Csornyei, Lurie
  17. ICM2010 — Avila, Dinur, plenary lectures
  18. ICM2010 — rest of second day
  19. ICM2010 — Nirenberg and Meyer laudationes
  20. ICM2010 — Chern prize inauguration
  21. ICM2010 — rest of day one
  22. ICM2010 — Spielman laudatio
  23. ICM2010 — Villani laudatio
  24. ICM2010 — Smirnov laudatio
  25. ICM2010 — Ngô laudatio
  26. ICM2010 — Lindenstrauss laudatio
  27. ICM2010 — Opening ceremony, continued
  28. ICM2010 — more on the opening ceremony
  29. ICM2010 — opening ceremony in brief
  30. ICM2010 — first impressions
  31. A possible answer to my objection
  32. Could anything like Deolalikar’s strategy work?
  33. My pennyworth about Deolalikar
  34. EDP17 — are we nearly there?
  35. Polymath news
  36. EDP16 — from AP-discrepancy to HAP-discrepancy?
  37. A mathematician watches tennis II
  38. EDP15 — finding a diagonal matrix
  39. If politicians were mathematicians
  40. A little experiment IV
  41. A little experiment III
  42. Is the British voting system fair?
  43. A little experiment II
  44. EDP14 — strategic questions
  45. A little experiment
  46. Use of mathematics II
  47. When is proof by contradiction necessary?
  48. EDP13 — quick summary
  49. “Hello World!”
  50. EDP12 — representing diagonal maps
  51. EDP11 — the search continues
  52. EDP10 — a new and very promising approach
  53. EDP9 — a change of focus
  54. EDP8 — what next?
  55. DHJ latest
  56. EDP7 — emergency post
  57. EDP6 — what are the chances of success?
  58. EDP5 — another very brief summary
  59. EDP4 — focusing on multiplicative functions
  60. EDP3 — a very brief report on where we are
  61. EDP2 — a few lessons from EDP1
  62. EDP1 — the official start of Polymath5
  63. The Erdős discrepancy problem V
  64. The Erdős discrepancy problem IV
  65. The Erdős discrepancy problem III
  66. Erdős discrepancy problem, continued
  67. Erdős’s discrepancy problem as a forthcoming Polymath project

2009 52

  1. The next Polymath project on this blog: some polls
  2. Wiles meets his match
  3. Erdős’s discrepancy problem
  4. Problems related to Littlewood’s conjecture
  5. The first unknown case of polynomial DHJ
  6. A conversation about complexity lower bounds, X
  7. Polymath and the origin of life
  8. A conversation about complexity lower bounds, IX
  9. A conversation about complexity lower bounds, VIII
  10. Triple negatives and Conservapedia’s support for Hitler
  11. A conversation about complexity lower bounds, VII
  12. Miscellaneous matters
  13. A conversation about complexity lower bounds, VI
  14. A conversation about complexity lower bounds, V
  15. A conversation about complexity lower bounds, IV
  16. A conversation about complexity lower bounds, III
  17. A conversation about complexity lower bounds, continued
  18. A conversation about complexity lower bounds
  19. Possible future Polymath projects
  20. PCM errata III
  21. The next phase of Polymath
  22. Help — I’m stuck in my ivory tower!
  23. A mathematician watches tennis
  24. DHJ write-up and other matters
  25. Why aren’t all functions well-defined?
  26. Swine flu and British public health policy
  27. What is Wolfram Alpha good for?
  28. A solution to an exposition problem
  29. When normality is abnormal
  30. Cohomology for amateurs—by an amateur
  31. Tricki now fully live
  32. Tricki available for viewing
  33. Can Polymath be scaled up?
  34. PCM errata II
  35. DHJ(3) and related results: 1050-1099
  36. Polymath1 and open collaborative mathematics
  37. Problem solved (probably)
  38. DHJ(3): 851-899
  39. Brief review of polymath1
  40. To thread or not to thread
  41. Must an “explicitly defined” Banach space contain c_0 or ell_p?
  42. DHJ — possible proof strategies
  43. DHJ — quasirandomness and obstructions to uniformity
  44. A remarkable recent result in Banach space theory
  45. DHJ — the triangle-removal approach
  46. Quick question
  47. Why this particular problem?
  48. A combinatorial approach to density Hales-Jewett
  49. Questions of procedure
  50. Background to a Polymath project
  51. Is massively collaborative mathematics possible?
  52. A Tricki issue

2008 19

  1. How can one equivalent statement be stronger than another?
  2. Very brief Tricki update
  3. The possible merger of the LMS and the IMA
  4. The forthcoming launch of the Tricki
  5. Princeton Companion errata
  6. Princeton Companion latest
  7. Just-do-it proofs
  8. How to use Zorn’s lemma
  9. A small countability question
  10. Dimension arguments in combinatorics
  11. Recognising countable sets
  12. More quasi-automatic theorem proving
  13. What is deep mathematics?
  14. Punctuation question
  15. Open problems concerning card games
  16. Probability paradox II
  17. Removing the magic from Stirling’s formula
  18. A paradox in probability
  19. General news—February 2008

2007 14

  1. General news — December 2007
  2. Examples first II
  3. My favourite pedagogical principle: examples first!
  4. A paper on the ArXiV
  5. When are two proofs essentially the same?
  6. The exchange lemma and Gaussian elimination
  7. One way of looking at Cauchy’s theorem
  8. About this blog
  9. Discovering a formula for the cubic
  10. Alternative maths reviews
  11. How should vector spaces be introduced?
  12. How should logarithms be taught?
  13. What might an expository mathematical wiki be like?
  14. The Princeton Companion to Mathematics