Bibliography (256):

  1. Reasoning With Limited Resources And Assigning Probabilities to Arithmetical Statements

  2. Mathematics, Queen and Servant of Science

  3. https://www.amazon.com/World-Mathematics-Four--Set/dp/0486432688/

  4. Social Processes and Proofs of Theorems and Programs

  5. 1986-tymoczko-newdirectionsphilosophymathematics.pdf

  6. The Replication Crisis: Flaws in Mainstream Science

  7. Knuth: Frequently Asked Questions

  8. https://www.lesswrong.com/posts/q79vYjHAE9KHcAjSs/rationalist-fiction?commentId=pqHEg8gKZ5B8mLdQL

  9. Probing the Improbable: Methodological Challenges for Risks with Low Probabilities and High Stakes

  10. Too good to be true: when overwhelming evidence fails to convince

  11. The Apologist and the Revolutionary

  12. https://www.amazon.com/Organic-Psychiatry-Psychological-Consequences-Cerebral/dp/0865428204/

  13. Mathematics in the Age of the Turing Machine

  14. Mathematics on a Distant Planet

  15. Los Alamos

  16. Widely Accepted Mathematical Results That Were Later Shown to Be Wrong

  17. What Do I Know? A Study of Mathematical Self-Awareness

  18. https://rjlipton.com/2010/06/19/guessing-the-truth/

  19. https://rjlipton.com/2009/09/27/surprises-in-mathematics-and-theory/

  20. Widely Accepted Mathematical Results That Were Later Shown to Be Wrong?

  21. 1994-anosov-theriemannhilbertproblem.pdf

  22. https://www.amazon.com/Honors-Class-Hilberts-Problems-Solvers/dp/1568812167/

  23. Von Neumann: "The Mathematician"

  24. Computational Knowledge and the Future of Pure Mathematics

  25. Desperately seeking mathematical proof

  26. https://www.math.uvic.ca/faculty/diacu/diacuNbody.pdf

  27. https://maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/Saari.pdf

  28. 2008-auslander.pdf

  29. Note on Euler's Φ-Function

  30. Computational Discovery in Pure Mathematics

  31. Homotopy groups of suspended classifying spaces: An experimental approach

  32. Poincaré on Intuition in Mathematics

  33. Isaac Newton As a Probabilist

  34. The Epic Story of Maximum Likelihood

  35. https://web.archive.org/web/20170419194138/https://www.princeton.edu/mudd/finding_aids/mathoral/pmcxrota.htm

  36. 1996-04-20-rota-tenlessonsiwishihadbeentaught.html#mistakes

  37. 1973-jech-pg118-errorfootnotes.png

  38. 1973-jech-theaxiomofchoice.pdf

  39. ‘Carleson's Theorem’, Tom Leinster

  40. This Page Collects Links around Papers That Try to Settle the ‘P versus NP’ Question (In Either Way).

  41. Widely Accepted Mathematical Results That Were Later Shown to Be Wrong?

  42. Comment on a Paper by Yucai Su On the Jacobian Conjecture (2005-12-30)

  43. Inside/Outside View

  44. Flaws in the Perfection

  45. https://digital.lib.washington.edu/server/api/core/bitstreams/995f5bb9-3b6a-472f-9cc7-8252ad7992be/content

  46. https://www.amazon.com/gp/product/B007BP3ATU/

  47. Fermat's Proof of His Last Theorem

  48. Fermat's Last Theorem

  49. Edge: GÖDEL AND THE NATURE OF MATHEMATICAL TRUTH

  50. 11858_2008_132_41_1-Web 45..60

  51. https://www.amazon.com/Best-Writing-Mathematics-2010/dp/0691148414/

  52. The Aesthetic Viewpoint in Mathematics

  53. Mathematical Creation

  54. 1999-whiteley.pdf

  55. 1990-wells.pdf

  56. https://www.amazon.com/Mathematicians-Enquirers-Learning-Mathematics-Education/dp/1402078595/

  57. Monte-Carlo Planning in Large POMDPs

  58. Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm

  59. https://rjlipton.com/2010/06/19/guessing-the-truth/#comment-3711

  60. On the distribution of time-to-proof of mathematical conjectures

  61. 2013-hisano.pdf

  62. Resolutions of Mathematical Conjectures over Time

  63. Does incubation enhance problem solving? A meta-analytic review

  64. https://www.amazon.com/Fascinating-Mathematical-People-Interviews-Memoirs/dp/0691148295

  65. https://www.amazon.com/Turings-Cathedral-Origins-Digital-Universe/dp/1400075998/

  66. Do Philosophers Dream of Saving Electric Cats?

  67. 1990-thomason.pdf

  68. An Essay On The Psychology Of Invention In The Mathematical Field

  69. 1993-lamport.pdf

  70. How to Write a 21st Century Proof

  71. Diseconomies of Scale and Lines of Code

  72. SLOCCount Web for Debian Lenny - Statistics

  73. The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems—Can We Trust in Them?

  74. An Empirical Study on the Correctness of Formally Verified Distributed Systems

  75. How did software get so reliable without proof?

  76. Mathematicians Solve 45-Year-Old Kervaire Invariant Puzzle

  77. https://www2.math.upenn.edu/~kazdan/proof/notes/parallel-postulateGrabiner2009.pdf

  78. http://eulerarchive.maa.org/docs/translations/E149tr.pdf

  79. Why We Lose Sleep Some Nights

  80. One Man’s Modus Ponens

  81. Confidence Levels inside and outside an Argument

  82. https://math.dartmouth.edu/~matc/MathDrama/reading/Hamming.html

  83. https://www.sciencemadness.org/lanl1_a/lib-www/la-pubs/00329010.pdf

  84. LA-602 versus RHIC Review

  85. https://news.ycombinator.com/item?id=6500577

  86. https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/

  87. Bounding the Impact of AGI

  88. Mathematical Proofs Improve But Don't Guarantee Security, Safety, and Friendliness

  89. The Probabilistic Heuristic Justification of the ABC Conjecture

  90. https://rjlipton.com/2014/03/15/could-we-have-felt-evidence-for-sdp-p/

  91. Have Any Long-Suspected Irrational Numbers Turned out to Be Rational?

  92. Mathematical "Urban Legends"

  93. Soft Question - Examples of Falsified (Or Currently Open) Long-Standing Conjectures Leading to Large Bodies of Incorrect Results

  94. What Mistakes Did the Italian Algebraic Geometers Actually Make?

  95. Soft Question - Why Doesn't Mathematics Collapse Even Though Humans Quite Often Make Mistakes in Their Proofs?

  96. Most Interesting Mathematics Mistake?

  97. In Mathematics, Mistakes Aren’t What They Used to Be

  98. Cosmic Rays: What Is the Probability They Will Affect a Program?

  99. When You Start Talking about Numbers As Small As 2−122, You Have to Start Looking More Closely at the Things You Thought Were Zero

  100. Articles

  101. Best Practices: Formal Proofs, the Fine Print and Side Effects

  102. https://arxiv.org/ftp/arxiv/papers/1609/1609.00331.pdf

  103. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.300.2572&rep=rep1&type=pdf

  104. https://cpilab.org/pubs/Dasgupta2017hypotheses.pdf

  105. 2017.07.23: Fast-Key-Erasure Random-Number Generators An Effort to Clean up Several Messes Simultaneously. #rng #forwardsecrecy #urandom #cascade #hmac #rekeying #proofs

  106. https://www.antiquark.com/blogimg/fasc4b.pdf

  107. Soft Question - Proofs Shown to Be Wrong After Formalization With Proof Assistant

  108. Michael Polanyi

  109. Bloom Filters Debunked: Dispelling 30 Years of Bad Math With Coq!

  110. https://www.quantamagazine.org/how-close-are-computers-to-automating-mathematical-reasoning-20200827/

  111. When Extrapolation Fails Us: Incorrect Mathematical Conjectures

  112. Patterns That Eventually Fail

  113. Some Remarkable Properties of Sinc and Related Integrals

  114. borweinintegral-2cost.jpg

  115. Two Curious Integrals and a Graphic Proof

  116. https://www.youtube.com/watch?v=NOCsdhzo6Jg

  117. https://www.quantamagazine.org/new-math-book-rescues-landmark-topology-proof-20210909/

  118. https://jaydaigle.net/blog/replication-crisis-math/

  119. Mathematical Proof Between Generations

  120. Programming as Theory Building

  121. https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-famed-fractal-20240126/

  122. Fermat’s Last Theorem—How It’s Going

  123. What Makes Mathematicians Believe Unproven Mathematical Statements?

  124. 1998-dales-truthinmathematics.pdf

  125. Lessons from the Debian/OpenSSL Fiasco

  126. The 3-Page Paper That Shook Philosophy: Gettiers in Software Engineering

  127. Cores that don’t count

  128. Silent Data Corruptions at Scale

  129. Detecting silent data corruptions in the wild

  130. Wikipedia Bibliography:

    1. Global catastrophic risk

    2. Cotard's syndrome

    3. False memory syndrome  :

    4. Pathological lying

    5. Confabulation

    6. Anosognosia

    7. Ludwig Wittgenstein

    8. Remarks on the Foundations of Mathematics  :

    9. Saul Kripke

    10. Wittgenstein on Rules and Private Language

    11. Richard Hamming

    12. Castle Bravo § High yield  :

    13. Toby Ord

    14. The Precipice: Existential Risk and the Future of Humanity  :

    15. List of conjectures § Disproved (no longer conjectures)  :

    16. Type I and type II errors

    17. Hilbert's problems  :

    18. Continuum hypothesis  :

    19. Georg Kreisel  :

    20. Burnside problem  :

    21. Euler's sum of powers conjecture

    22. Fundamental theorem of algebra  :

    23. Jordan curve theorem  :

    24. Henri Poincaré

    25. Three-body problem  :

    26. Gösta Mittag-Leffler  :

    27. Karl F. Sundman  :

    28. Italian school of algebraic geometry § Collapse of the school  :

    29. Robert Daniel Carmichael  :

    30. Carmichael's totient function conjecture  :

    31. Four color theorem § Early proof attempts  :

    32. Pessimistic induction  :

    33. Dirichlet’s principle  :

    34. Augustus De Morgan  :

    35. Ralph P. Boas Jr

    36. Mathematical Reviews

    37. Gian-Carlo Rota

    38. Olga Taussky-Todd  :

    39. Augustin-Louis Cauchy  :

    40. Richard Dedekind  :

    41. Peter Gustav Lejeune Dirichlet  :

    42. Karl Weierstrass  :

    43. Carl Friedrich Gauss

    44. George Green (mathematician)  :

    45. William Thomson, First Baron Kelvin  :

    46. Bernhard Riemann  :

    47. Michael Faraday

    48. Évariste Galois

    49. Charles Hermite  :

    50. Karl Pearson

    51. Siméon Denis Poisson

    52. Jakob Steiner  :

    53. Jean Baptiste Joseph Delambre  :

    54. Joseph-Louis Lagrange  :

    55. Pafnuty Chebyshev  :

    56. P versus NP problem

    57. Jacobian conjecture  :

    58. Jacobian matrix and determinant

    59. Millennium Prize Problems  :

    60. Fermat's Last Theorem

    61. André Weil

    62. Ferdinand von Lindemann  :

    63. MathWorld  :

    64. Mathematical beauty

    65. Hans Reichenbach  :

    66. Hermann Weyl

    67. A Mathematician's Apology

    68. G. H. Hardy

    69. White-box testing

    70. Monte Carlo method

    71. Sleep and memory

    72. Hippocampal replay  :

    73. Terence Tao

    74. Exponential distribution

    75. Survivorship curve

    76. Incubation (psychology)

    77. Richard K. Guy  :

    78. Chess endgame  :

    79. Stanisław Ulam

    80. George Dyson (science historian)

    81. Leonard Eugene Dickson  :

    82. Jacques Hadamard

    83. Leslie Lamport

    84. Natural deduction  :

    85. Source lines of code

    86. Diseconomies of scale

    87. Debian  :

    88. Tony Hoare  :

    89. Blue screen of death

    90. Norbert Wiener

    91. Kervaire invariant  :

    92. Parallel postulate § History  :

    93. Jean-Baptiste Biot  :

    94. Euclid's Elements

    95. Law of noncontradiction  :

    96. Principle of sufficient reason

    97. Mechanical advantage § Lever  :

    98. Giordano Bruno

    99. Critique of Pure Reason

    100. Johann Heinrich Lambert  :

    101. Giovanni Girolamo Saccheri  :

    102. Hyperbolic geometry

    103. Riemann hypothesis

    104. The Unreasonable Effectiveness of Mathematics in the Natural Sciences

    105. What the Tortoise Said to Achilles  :

    106. Perko pair  :

    107. Borwein integral  :

    108. 3Blue1Brown  :

    109. Counterexamples in Topology  :

    110. Cosmic ray

    111. Soft error § Cosmic rays creating energetic neutrons and protons  :

    112. Hal Abelson

    113. Gerald Sussman  :

    114. Structure And Interpretation of Computer Programs  :

    115. Evaluation strategy § Strict binding strategies  :

    116. Integer overflow

    117. Undefined behavior  :

    118. Arbitrary-precision arithmetic  :

    119. Lazy evaluation

    120. Floating-point arithmetic

    121. NaN

    122. Order of operations § Programming languages  :

    123. Spectre (security vulnerability)

    124. Buffer overflow

    125. Row hammer

    126. ECC memory

    127. Pentium FDIV bug