Reasoning With Limited Resources And Assigning Probabilities to Arithmetical Statements
Mathematics, Queen and Servant of Science
https://www.amazon.com/World-Mathematics-Four--Set/dp/0486432688/
Social Processes and Proofs of Theorems and Programs
1986-tymoczko-newdirectionsphilosophymathematics.pdf
The Replication Crisis: Flaws in Mainstream Science
Knuth: Frequently Asked Questions
https://www.lesswrong.com/posts/q79vYjHAE9KHcAjSs/rationalist-fiction?commentId=pqHEg8gKZ5B8mLdQL
Probing the Improbable: Methodological Challenges for Risks with Low Probabilities and High Stakes
Too good to be true: when overwhelming evidence fails to convince
The Apologist and the Revolutionary
https://www.amazon.com/Organic-Psychiatry-Psychological-Consequences-Cerebral/dp/0865428204/
Mathematics in the Age of the Turing Machine
Mathematics on a Distant Planet
Los Alamos
Widely Accepted Mathematical Results That Were Later Shown to Be Wrong
What Do I Know? A Study of Mathematical Self-Awareness
https://rjlipton.com/2010/06/19/guessing-the-truth/
https://rjlipton.com/2009/09/27/surprises-in-mathematics-and-theory/
Widely Accepted Mathematical Results That Were Later Shown to Be Wrong?
1994-anosov-theriemannhilbertproblem.pdf
https://www.amazon.com/Honors-Class-Hilberts-Problems-Solvers/dp/1568812167/
Von Neumann: "The Mathematician"
Computational Knowledge and the Future of Pure Mathematics
Desperately seeking mathematical proof
https://www.math.uvic.ca/faculty/diacu/diacuNbody.pdf
https://maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/Saari.pdf
2008-auslander.pdf
Note on Euler's Φ-Function
Computational Discovery in Pure Mathematics
Homotopy groups of suspended classifying spaces: An experimental approach
Poincaré on Intuition in Mathematics
Isaac Newton As a Probabilist
The Epic Story of Maximum Likelihood
https://web.archive.org/web/20170419194138/https://www.princeton.edu/mudd/finding_aids/mathoral/pmcxrota.htm
1996-04-20-rota-tenlessonsiwishihadbeentaught.html#mistakes
1973-jech-pg118-errorfootnotes.png
1973-jech-theaxiomofchoice.pdf
‘Carleson's Theorem’, Tom Leinster
This Page Collects Links around Papers That Try to Settle the ‘P versus NP’ Question (In Either Way).
Widely Accepted Mathematical Results That Were Later Shown to Be Wrong?
Comment on a Paper by Yucai Su On the Jacobian Conjecture (2005-12-30)
Inside/Outside View
Flaws in the Perfection
https://digital.lib.washington.edu/server/api/core/bitstreams/995f5bb9-3b6a-472f-9cc7-8252ad7992be/content
https://www.amazon.com/gp/product/B007BP3ATU/
Fermat's Proof of His Last Theorem
Fermat's Last Theorem
Edge: GÖDEL AND THE NATURE OF MATHEMATICAL TRUTH
11858_2008_132_41_1-Web 45..60
https://www.amazon.com/Best-Writing-Mathematics-2010/dp/0691148414/
The Aesthetic Viewpoint in Mathematics
Mathematical Creation
1999-whiteley.pdf
1990-wells.pdf
https://www.amazon.com/Mathematicians-Enquirers-Learning-Mathematics-Education/dp/1402078595/
Monte-Carlo Planning in Large POMDPs
Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm
https://rjlipton.com/2010/06/19/guessing-the-truth/#comment-3711
On the distribution of time-to-proof of mathematical conjectures
2013-hisano.pdf
Resolutions of Mathematical Conjectures over Time
Does incubation enhance problem solving? A meta-analytic review
https://www.amazon.com/Fascinating-Mathematical-People-Interviews-Memoirs/dp/0691148295
https://www.amazon.com/Turings-Cathedral-Origins-Digital-Universe/dp/1400075998/
Do Philosophers Dream of Saving Electric Cats?
1990-thomason.pdf
An Essay On The Psychology Of Invention In The Mathematical Field
1993-lamport.pdf
How to Write a 21st Century Proof
Diseconomies of Scale and Lines of Code
SLOCCount Web for Debian Lenny - Statistics
The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems—Can We Trust in Them?
An Empirical Study on the Correctness of Formally Verified Distributed Systems
How did software get so reliable without proof?
Mathematicians Solve 45-Year-Old Kervaire Invariant Puzzle
https://www2.math.upenn.edu/~kazdan/proof/notes/parallel-postulateGrabiner2009.pdf
http://eulerarchive.maa.org/docs/translations/E149tr.pdf
Why We Lose Sleep Some Nights
One Man’s Modus Ponens
Confidence Levels inside and outside an Argument
https://math.dartmouth.edu/~matc/MathDrama/reading/Hamming.html
https://www.sciencemadness.org/lanl1_a/lib-www/la-pubs/00329010.pdf
LA-602 versus RHIC Review
https://news.ycombinator.com/item?id=6500577
https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/
Bounding the Impact of AGI
Mathematical Proofs Improve But Don't Guarantee Security, Safety, and Friendliness
The Probabilistic Heuristic Justification of the ABC Conjecture
https://rjlipton.com/2014/03/15/could-we-have-felt-evidence-for-sdp-p/
Have Any Long-Suspected Irrational Numbers Turned out to Be Rational?
Mathematical "Urban Legends"
Soft Question - Examples of Falsified (Or Currently Open) Long-Standing Conjectures Leading to Large Bodies of Incorrect Results
What Mistakes Did the Italian Algebraic Geometers Actually Make?
Soft Question - Why Doesn't Mathematics Collapse Even Though Humans Quite Often Make Mistakes in Their Proofs?
Most Interesting Mathematics Mistake?
In Mathematics, Mistakes Aren’t What They Used to Be
Cosmic Rays: What Is the Probability They Will Affect a Program?
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
Articles
Best Practices: Formal Proofs, the Fine Print and Side Effects
https://arxiv.org/ftp/arxiv/papers/1609/1609.00331.pdf
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.300.2572&rep=rep1&type=pdf
https://cpilab.org/pubs/Dasgupta2017hypotheses.pdf
2017.07.23: Fast-Key-Erasure Random-Number Generators An Effort to Clean up Several Messes Simultaneously. #rng #forwardsecrecy #urandom #cascade #hmac #rekeying #proofs
https://www.antiquark.com/blogimg/fasc4b.pdf
Soft Question - Proofs Shown to Be Wrong After Formalization With Proof Assistant
Michael Polanyi
Bloom Filters Debunked: Dispelling 30 Years of Bad Math With Coq!
https://www.quantamagazine.org/how-close-are-computers-to-automating-mathematical-reasoning-20200827/
When Extrapolation Fails Us: Incorrect Mathematical Conjectures
Patterns That Eventually Fail
Some Remarkable Properties of Sinc and Related Integrals
borweinintegral-2cost.jpg
Two Curious Integrals and a Graphic Proof
https://www.youtube.com/watch?v=NOCsdhzo6Jg
https://www.quantamagazine.org/new-math-book-rescues-landmark-topology-proof-20210909/
https://jaydaigle.net/blog/replication-crisis-math/
Mathematical Proof Between Generations
Programming as Theory Building
https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-famed-fractal-20240126/
Fermat’s Last Theorem—How It’s Going
What Makes Mathematicians Believe Unproven Mathematical Statements?
1998-dales-truthinmathematics.pdf
Lessons from the Debian/OpenSSL Fiasco
The 3-Page Paper That Shook Philosophy: Gettiers in Software Engineering
Cores that don’t count
Silent Data Corruptions at Scale
Detecting silent data corruptions in the wild