 See Also

Links
 “Papers With Computerchecked Proofs”, Bernstein 2023
 “Solving Challenging Math Word Problems Using GPT4 Code Interpreter With Codebased SelfVerification”, Zhou et al 2023
 “Testing GPT4 With Wolfram Alpha and Code Interpreter Plugins on Math and Science Problems”, Davis & Aaronson 2023
 “Teaching Arithmetic to Small Transformers”, Lee et al 2023
 “LeanDojo: Theorem Proving With RetrievalAugmented Language Models”, Yang et al 2023
 “Let’s Verify Step by Step”, Lightman et al 2023
 “A Chiral Aperiodic Monotile”, Smith et al 2023
 “What Number Comes Next? The Encyclopedia of Integer Sequences Knows. The ‘mathematical Equivalent to the FBI’s Voluminous Fingerprint Files’ Turns 50 This Year, With 362,765 Entries (and Counting)”, Roberts 2023
 “How Does GPT2 Compute Greaterthan?: Interpreting Mathematical Abilities in a Pretrained Language Model”, Hanna et al 2023
 “Evaluating Transformer Language Models on Arithmetic Operations Using Number Decomposition”, Muffo et al 2023
 “How Well Do Large Language Models Perform in Arithmetic Tasks?”, Yuan et al 2023
 “ProofNet: Autoformalizing and Formally Proving UndergraduateLevel Mathematics”, Azerbayev et al 2023
 “OEIS: A Handbook of Integer Sequences 50 Years Later”, Sloane 2023
 “Solving Math Word Problems With Process & Outcomebased Feedback”, Uesato et al 2022
 “What Is My Math Transformer Doing? – 3 Results on Interpretability and Generalization”, Charton 2022
 “Dynamic Prompt Learning via Policy Gradient for Semistructured Mathematical Reasoning”, Lu et al 2022
 “Mathematical Proof Between Generations”, Bayer et al 2022
 “Connecting the Scientific and Industrial Revolutions: The Role of Practical Mathematics”, Kelly & Gráda 2022
 “NaturalProver: Grounded Mathematical Proof Generation With Language Models”, Welleck et al 2022
 “HTPS: HyperTree Proof Search for Neural Theorem Proving”, Lample et al 2022
 “Endtoend Symbolic Regression With Transformers”, Kamienny et al 2022
 “PaLM: Scaling Language Modeling With Pathways”, Chowdhery et al 2022
 “Impact of Pretraining Term Frequencies on FewShot Reasoning”, Razeghi et al 2022
 “Exact Number Concepts Are Limited to the Verbal Count Range”, Pitt et al 2022
 “Formal Mathematics Statement Curriculum Learning”, Polu et al 2022
 “Deep Symbolic Regression for Recurrent Sequences”, d’Ascoli et al 2022
 “Counting and the Ontogenetic Origins of Exact Equality”, Schneider et al 2022
 “A Neural Network Solves and Generates Mathematics Problems by Program Synthesis: Calculus, Differential Equations, Linear Algebra, and More”, Drori et al 2021
 “What Is the Point of Computers? A Question for Pure Mathematicians”, Buzzard 2021
 “Scaling Language Models: Methods, Analysis & Insights from Training Gopher”, Rae et al 2021
 “Linear Algebra With Transformers”, Charton 2021
 “Training Verifiers to Solve Math Word Problems”, Cobbe et al 2021
 “MiniF2F: a Crosssystem Benchmark for Formal Olympiadlevel Mathematics”, Zheng et al 2021
 “A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers”, Miao et al 2021
 “SymbolicGPT: A Generative Transformer Model for Symbolic Regression”, Valipour et al 2021
 “Basins With Tentacles”, Zhang & Strogatz 2021
 “Behavioral and Neuronal Representation of Numerosity Zero in the Crow”, Kirschhock et al 2021
 “MathBERT: A PreTrained Model for Mathematical Formula Understanding”, Peng et al 2021
 “Constructions in Combinatorics via Neural Networks”, Wagner 2021
 “NaturalProofs: Mathematical Theorem Proving in Natural Language”, Welleck et al 2021
 “Are NLP Models Really Able to Solve Simple Math Word Problems?”, Patel et al 2021
 “Measuring Mathematical Problem Solving With the MATH Dataset”, Hendrycks et al 2021
 “TacticZero: Learning to Prove Theorems from Scratch With Deep Reinforcement Learning”, Wu et al 2021
 “Proof Artifact Cotraining for Theorem Proving With Language Models”, Han et al 2021
 “LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning”, Wu et al 2021
 “How the Slowest Computer Programs Illuminate Math’s Fundamental Limits: The Goal of the ‘busy Beaver’ Game Is to Find the Longestrunning Computer Program. Its Pursuit Has Surprising Connections to Some of the Most Profound Questions and Concepts in Mathematics”, Pavlus 2020
 “The Empirical Metamathematics of Euclid and Beyond”, Wolfram 2020
 “Generative Language Modeling for Automated Theorem Proving”, Polu & Sutskever 2020
 “Lights and Shadows”, Ciechanowski 2020
 “Singing Euclid: the Oral Character of Greek Geometry”, Blåsjö 2020
 “Remembering John Conway’s FRACTRAN, a Ridiculous, yet Surprisingly Deep Language”, Braithwaite 2020
 “Radical Solutions: French Mathematician Évariste Galois Lived a Full Life. When He Wasn’t Trying to Overthrow the Government, He Was Reinventing Algebra”, Brook & Macfarlane 2020
 “Learning to Prove Theorems by Learning to Generate Theorems”, Wang & Deng 2020
 “Transformers As Soft Reasoners over Language”, Clark et al 2020
 “Neural Arithmetic Units”, Madsen & Johansen 2020
 “Generative Language Modeling for Automated Theorem Proving § Experiments”, Polu & Sutskever 2020 (page 11 org openai)
 “Deep Learning for Symbolic Mathematics”, Lample & Charton 2019
 “MAWPS: A Math Word Problem Repository”, KoncelKedziorski et al 2019
 “Analysing Mathematical Reasoning Abilities of Neural Models”, Saxton et al 2019
 “Fancy Euclid’s Elements in T_{e}X”, Slyusarev 2019
 “The First Printed Math Books”, Boardley 2019
 “Reinventing the Wheel: Discovering the Optimal Rolling Shape With PyTorch”, Wiener 2019
 “Making of Byrne’s Euclid”, Rougeux 2018
 “Best Practices: Formal Proofs, the Fine Print and Side Effects”, Murray & Oorschot 2018
 “Neural Arithmetic Logic Units”, Trask et al 2018
 “Mastering Chess and Shogi by SelfPlay With a General Reinforcement Learning Algorithm”, Silver et al 2017
 “From Boiling Lead and Black Art: An Essay on the History of Mathematical Typography”, Smith 2017
 “Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems”, Ling et al 2017
 “Solving General Arithmetic Word Problems”, Roy & Roth 2016
 “DeepMath—Deep Sequence Models for Premise Selection”, Alemi et al 2016
 “The LEGO Counting Problem”, Eilers 2016
 “Too Good to Be True: When Overwhelming Evidence Fails to Convince”, Gunn et al 2016
 “Probabilistic Integration: A Role in Statistical Computation?”, Briol et al 2015
 “Random GradientFree Minimization of Convex Functions”, Nesterov & Spokoiny 2015
 “Prizes and Productivity: How Winning the Fields Medal Affects Scientific Output”, Borjas & Doran 2015
 “Is There a Curse of the Fields Medal?”, Kollár 2015
 “Neural Networks, Manifolds, and Topology”, Olah 2014
 “Finite Time Blowup for an Averaged Threedimensional NavierStokes Equation”, Tao 2014
 “On Unsettleable Arithmetical Problems”, Conway 2013
 “The Algebraic Combinatorial Approach for LowRank Matrix Completion”, Király et al 2012
 “One Man’s Modus Ponens”, Gwern 2012
 “Vividness in Mathematics and Narrative”, Gowers 2012
 “How to Write a 21^{st} Century Proof”, Lamport 2011
 “Jewish Problems”, Khovanova & Radul 2011
 “Charity Is Not about Helping”, Gwern 2011
 “Girl Scouts & Good Corporate Governance”, Gwern 2011
 “The Cosmic Distance Ladder”, Tao 2010
 “Coolex: The Coolest Way to Generate Combinations”, Ruskey & Williams 2009
 “Packing Unit Squares in Squares: A Survey and New Results”, Friedman 2009
 “Simulation Inferences”, Gwern 2009
 “Desperately Seeking Mathematical Proof”, Nathanson 2009
 “The Gödel Letter”, Gödel 2009
 “Prediction Markets”, Gwern 2009
 “11858_2008_132_41_1web 45..60”
 “Probing the Improbable: Methodological Challenges for Risks With Low Probabilities and High Stakes”, Ord et al 2008
 “The Epic Story of Maximum Likelihood”, Stigler 2007
 “Overhang”, Paterson & Zwick 2007
 “The Monotype 4Line System for Setting Mathematics”, Rhatigan 2007
 “Maximum Overhang”, Paterson et al 2007
 “Béla Bollobás: Graphs Extremal and Random [Interview of Béla Bollobás by Y. K. Leong]”, Leong & Bollobás 2007
 “Computational Discovery in Pure Mathematics”, Colton 2007
 “Comment on a Paper by Yucai Su On the Jacobian Conjecture (20051230)”, Moh 2006
 “Proof of Two Dimensional Jacobian Conjecture”, Su 2005
 “Online Convex Programming and Generalized Infinitesimal Gradient Ascent”, Zinkevich 2003
 “EWD1300: The Notational Conventions I Adopted, and Why”, Dijkstra 2002
 “Hymne to Hymen”, Descartes & Smith 2002
 “The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen”, Dalen 2001
 “Making Mathematics: The Coffee Connection”, Wieschenberg 1999
 “An Editor Recalls Some Hopeless Papers”, Hodges 1998
 “How Did Software Get so Reliable without Proof?”, Hoare 1996
 “Light Shadows: Remembrances of Yale in the Early Fifties”, Rota 1996
 “Ten Lessons I Wish I Had Been Taught”, Rota 1996
 “Riemann Zeta Function Is a Fractal”, Woon 1994
 “A Visit to Hungarian Mathematics”, Hersh & JohnSteiner 1993
 “How I Was Led to the Frequency Approach”, Hamming 1991
 “On the Computational Complexity of the Jones and Tutte Polynomials”, Jaeger et al 1990
 “Factors and Primes: a Specific Numerical Ability”, Hermelin & O’Connor 1990
 “Envisioning Information: Chapter 5, ‘Color and Information’, Pg8386 [on Oliver Byrne’s Color Diagram Version of Euclid’s Elements]”, Tufte 1990
 “In Memory of Henry J. Kelley”, Cliff 1989
 “Dynamical Systems That Sort Lists, Diagonalize Matrices and Solve Linear Programming Problems”, Brockett 1988
 “The Printing of Mathematics”, Wishart 1988
 “John Von Neumann As Seen By His Brother”, Vonneuman 1987
 “The Aesthetic Viewpoint in Mathematics”
 “Review of Yuri I. Manin Yu, A Course in Mathematical Logic 1997”, Boolos 1986
 “Discrete Hartley Transform”, Bracewell 1983
 “Are Impossible Figures Possible?”, Kulpa 1983
 “Bicontinuous Extensions of Invertible Combinatorial Functions”, Toffoli 1981
 “The Letter S”, Knuth 1980
 “Heaviside's Operational Calculus and the Attempts to Rigorise It”, Lützen 1979
 “Some Proposals for Reviving the Philosophy of Mathematics”, Hersh 1979
 “Social Processes and Proofs of Theorems and Programs”, Millo et al 1979
 “Life at Low Reynolds Number”, Purcell 1977
 “Randomness and Mathematical Proof”, Chatin 1975
 “The Dangers of ComputerScience Theory”, Knuth 1973
 “Fidelity in Mathematical Discourse: Is One and One Really Two?”, Davis 1972
 “The Humble Programmer [EWD340]”, Dijkstra 1972
 “Assigning Probabilities to Logical Formulas”, Scott & Krauss 1966
 “Singular Extremals In Lawden’s Problem Of Optimal Rocket Flight”, Kelley 1963
 “A SteepestAscent Method for Solving Optimum Programming Problems”, Bryson & Denham 1962
 “Method of Gradients”, Kelley 1962
 “Gradient Theory of Optimal Flight Paths”, Kelley 1960
 “Toward Mechanical Mathematics”, Wang 1960
 “Stable PredictorCorrector Methods for Ordinary Differential Equations”, Hamming 1959
 “The Printing of Mathematics: Aids for Authors and Editors and Rules for Compositors and Readers at the University Press, Oxford”, Chaundy et al 1954
 “NonCooperative Games”, Nash 1951
 “Principles of the SelfOrganizing Dynamic System”, Ashby 1947
 “An Essay On The Psychology Of Invention In The Mathematical Field”, Hadamard 1945
 “A More Symmetrical Fourier Analysis Applied to Transmission Problems”, Hartley 1942
 “Leonhard Euler's Elastic Curves”
 “On a Problem of Formal Logic”, Ramsey 1930
 “Operational Methods in Mathematical Physics”, Carslaw 1928
 “The Foundations of Mathematics”, Ramsey 1926b
 “Cutting a Round Cake on Scientific Principles”, Galton 1906
 “On Operators in Physical Mathematics. Part I”, Heaviside 1892
 “Why Momentum Really Works”
 “Math: OpenAI API Can Do Some Math out of the Gate, but Most Math It Seems It Has to Learn. Many Times, the Numbers That It Spits out Are Just Random. However, including Different Priming Prompts Can Result in Decent Results.”
 “Oliver Byrne’s Edition of Euclid [Scans]”, Casselman 2023
 Sort By Magic
 Wikipedia
 Miscellaneous
 Link Bibliography
See Also
Links
“Papers With Computerchecked Proofs”, Bernstein 2023
“Solving Challenging Math Word Problems Using GPT4 Code Interpreter With Codebased SelfVerification”, Zhou et al 2023
“Testing GPT4 With Wolfram Alpha and Code Interpreter Plugins on Math and Science Problems”, Davis & Aaronson 2023
“Testing GPT4 with Wolfram Alpha and Code Interpreter plugins on math and science problems”
“Teaching Arithmetic to Small Transformers”, Lee et al 2023
“LeanDojo: Theorem Proving With RetrievalAugmented Language Models”, Yang et al 2023
“LeanDojo: Theorem Proving with RetrievalAugmented Language Models”
“Let’s Verify Step by Step”, Lightman et al 2023
“A Chiral Aperiodic Monotile”, Smith et al 2023
“What Number Comes Next? The Encyclopedia of Integer Sequences Knows. The ‘mathematical Equivalent to the FBI’s Voluminous Fingerprint Files’ Turns 50 This Year, With 362,765 Entries (and Counting)”, Roberts 2023
“How Does GPT2 Compute Greaterthan?: Interpreting Mathematical Abilities in a Pretrained Language Model”, Hanna et al 2023
“Evaluating Transformer Language Models on Arithmetic Operations Using Number Decomposition”, Muffo et al 2023
“Evaluating Transformer Language Models on Arithmetic Operations Using Number Decomposition”
“How Well Do Large Language Models Perform in Arithmetic Tasks?”, Yuan et al 2023
“How well do Large Language Models perform in Arithmetic tasks?”
“ProofNet: Autoformalizing and Formally Proving UndergraduateLevel Mathematics”, Azerbayev et al 2023
“ProofNet: Autoformalizing and Formally Proving UndergraduateLevel Mathematics”
“OEIS: A Handbook of Integer Sequences 50 Years Later”, Sloane 2023
“Solving Math Word Problems With Process & Outcomebased Feedback”, Uesato et al 2022
“Solving math word problems with process & outcomebased feedback”
“What Is My Math Transformer Doing? – 3 Results on Interpretability and Generalization”, Charton 2022
“What is my math transformer doing? – 3 results on interpretability and generalization”
“Dynamic Prompt Learning via Policy Gradient for Semistructured Mathematical Reasoning”, Lu et al 2022
“Dynamic Prompt Learning via Policy Gradient for Semistructured Mathematical Reasoning”
“Mathematical Proof Between Generations”, Bayer et al 2022
“Connecting the Scientific and Industrial Revolutions: The Role of Practical Mathematics”, Kelly & Gráda 2022
“Connecting the Scientific and Industrial Revolutions: The Role of Practical Mathematics”
“NaturalProver: Grounded Mathematical Proof Generation With Language Models”, Welleck et al 2022
“NaturalProver: Grounded Mathematical Proof Generation with Language Models”
“HTPS: HyperTree Proof Search for Neural Theorem Proving”, Lample et al 2022
“Endtoend Symbolic Regression With Transformers”, Kamienny et al 2022
“PaLM: Scaling Language Modeling With Pathways”, Chowdhery et al 2022
“Impact of Pretraining Term Frequencies on FewShot Reasoning”, Razeghi et al 2022
“Impact of Pretraining Term Frequencies on FewShot Reasoning”
“Exact Number Concepts Are Limited to the Verbal Count Range”, Pitt et al 2022
“Exact Number Concepts Are Limited to the Verbal Count Range”
“Formal Mathematics Statement Curriculum Learning”, Polu et al 2022
“Deep Symbolic Regression for Recurrent Sequences”, d’Ascoli et al 2022
“Counting and the Ontogenetic Origins of Exact Equality”, Schneider et al 2022
“A Neural Network Solves and Generates Mathematics Problems by Program Synthesis: Calculus, Differential Equations, Linear Algebra, and More”, Drori et al 2021
“What Is the Point of Computers? A Question for Pure Mathematicians”, Buzzard 2021
“What is the point of computers? A question for pure mathematicians”
“Scaling Language Models: Methods, Analysis & Insights from Training Gopher”, Rae et al 2021
“Scaling Language Models: Methods, Analysis & Insights from Training Gopher”
“Linear Algebra With Transformers”, Charton 2021
“Training Verifiers to Solve Math Word Problems”, Cobbe et al 2021
“MiniF2F: a Crosssystem Benchmark for Formal Olympiadlevel Mathematics”, Zheng et al 2021
“MiniF2F: a crosssystem benchmark for formal Olympiadlevel mathematics”
“A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers”, Miao et al 2021
“A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers”
“SymbolicGPT: A Generative Transformer Model for Symbolic Regression”, Valipour et al 2021
“SymbolicGPT: A Generative Transformer Model for Symbolic Regression”
“Basins With Tentacles”, Zhang & Strogatz 2021
“Behavioral and Neuronal Representation of Numerosity Zero in the Crow”, Kirschhock et al 2021
“Behavioral and Neuronal Representation of Numerosity Zero in the Crow”
“MathBERT: A PreTrained Model for Mathematical Formula Understanding”, Peng et al 2021
“MathBERT: A PreTrained Model for Mathematical Formula Understanding”
“Constructions in Combinatorics via Neural Networks”, Wagner 2021
“NaturalProofs: Mathematical Theorem Proving in Natural Language”, Welleck et al 2021
“NaturalProofs: Mathematical Theorem Proving in Natural Language”
“Are NLP Models Really Able to Solve Simple Math Word Problems?”, Patel et al 2021
“Are NLP Models really able to Solve Simple Math Word Problems?”
“Measuring Mathematical Problem Solving With the MATH Dataset”, Hendrycks et al 2021
“Measuring Mathematical Problem Solving With the MATH Dataset”
“TacticZero: Learning to Prove Theorems from Scratch With Deep Reinforcement Learning”, Wu et al 2021
“TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning”
“Proof Artifact Cotraining for Theorem Proving With Language Models”, Han et al 2021
“Proof Artifact Cotraining for Theorem Proving with Language Models”
“LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning”, Wu et al 2021
“LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning”
“How the Slowest Computer Programs Illuminate Math’s Fundamental Limits: The Goal of the ‘busy Beaver’ Game Is to Find the Longestrunning Computer Program. Its Pursuit Has Surprising Connections to Some of the Most Profound Questions and Concepts in Mathematics”, Pavlus 2020
“The Empirical Metamathematics of Euclid and Beyond”, Wolfram 2020
“Generative Language Modeling for Automated Theorem Proving”, Polu & Sutskever 2020
“Generative Language Modeling for Automated Theorem Proving”
“Lights and Shadows”, Ciechanowski 2020
“Singing Euclid: the Oral Character of Greek Geometry”, Blåsjö 2020
“Remembering John Conway’s FRACTRAN, a Ridiculous, yet Surprisingly Deep Language”, Braithwaite 2020
“Remembering John Conway’s FRACTRAN, a ridiculous, yet surprisingly deep language”
“Radical Solutions: French Mathematician Évariste Galois Lived a Full Life. When He Wasn’t Trying to Overthrow the Government, He Was Reinventing Algebra”, Brook & Macfarlane 2020
“Learning to Prove Theorems by Learning to Generate Theorems”, Wang & Deng 2020
“Learning to Prove Theorems by Learning to Generate Theorems”
“Transformers As Soft Reasoners over Language”, Clark et al 2020
“Neural Arithmetic Units”, Madsen & Johansen 2020
“Generative Language Modeling for Automated Theorem Proving § Experiments”, Polu & Sutskever 2020 (page 11 org openai)
“Generative Language Modeling for Automated Theorem Proving § Experiments”
“Deep Learning for Symbolic Mathematics”, Lample & Charton 2019
“MAWPS: A Math Word Problem Repository”, KoncelKedziorski et al 2019
“Analysing Mathematical Reasoning Abilities of Neural Models”, Saxton et al 2019
“Analysing Mathematical Reasoning Abilities of Neural Models”
“Fancy Euclid’s Elements in T_{e}X”, Slyusarev 2019
“The First Printed Math Books”, Boardley 2019
“Reinventing the Wheel: Discovering the Optimal Rolling Shape With PyTorch”, Wiener 2019
“Reinventing the Wheel: Discovering the Optimal Rolling Shape with PyTorch”
“Making of Byrne’s Euclid”, Rougeux 2018
“Best Practices: Formal Proofs, the Fine Print and Side Effects”, Murray & Oorschot 2018
“Best Practices: Formal Proofs, the Fine Print and Side Effects”
“Neural Arithmetic Logic Units”, Trask et al 2018
“Mastering Chess and Shogi by SelfPlay With a General Reinforcement Learning Algorithm”, Silver et al 2017
“Mastering Chess and Shogi by SelfPlay with a General Reinforcement Learning Algorithm”
“From Boiling Lead and Black Art: An Essay on the History of Mathematical Typography”, Smith 2017
“From boiling lead and black art: An essay on the history of mathematical typography”
“Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems”, Ling et al 2017
“Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems”
“Solving General Arithmetic Word Problems”, Roy & Roth 2016
“DeepMath—Deep Sequence Models for Premise Selection”, Alemi et al 2016
“The LEGO Counting Problem”, Eilers 2016
“Too Good to Be True: When Overwhelming Evidence Fails to Convince”, Gunn et al 2016
“Too good to be true: when overwhelming evidence fails to convince”
“Probabilistic Integration: A Role in Statistical Computation?”, Briol et al 2015
“Probabilistic Integration: A Role in Statistical Computation?”
“Random GradientFree Minimization of Convex Functions”, Nesterov & Spokoiny 2015
“Prizes and Productivity: How Winning the Fields Medal Affects Scientific Output”, Borjas & Doran 2015
“Prizes and Productivity: How Winning the Fields Medal Affects Scientific Output”
“Is There a Curse of the Fields Medal?”, Kollár 2015
“Neural Networks, Manifolds, and Topology”, Olah 2014
“Finite Time Blowup for an Averaged Threedimensional NavierStokes Equation”, Tao 2014
“Finite time blowup for an averaged threedimensional NavierStokes equation”
“On Unsettleable Arithmetical Problems”, Conway 2013
“The Algebraic Combinatorial Approach for LowRank Matrix Completion”, Király et al 2012
“The Algebraic Combinatorial Approach for LowRank Matrix Completion”
“One Man’s Modus Ponens”, Gwern 2012
“Vividness in Mathematics and Narrative”, Gowers 2012
“How to Write a 21^{st} Century Proof”, Lamport 2011
“Jewish Problems”, Khovanova & Radul 2011
“Charity Is Not about Helping”, Gwern 2011
“Girl Scouts & Good Corporate Governance”, Gwern 2011
“The Cosmic Distance Ladder”, Tao 2010
“Coolex: The Coolest Way to Generate Combinations”, Ruskey & Williams 2009
“Packing Unit Squares in Squares: A Survey and New Results”, Friedman 2009
“Simulation Inferences”, Gwern 2009
“Desperately Seeking Mathematical Proof”, Nathanson 2009
“The Gödel Letter”, Gödel 2009
“Prediction Markets”, Gwern 2009
“11858_2008_132_41_1web 45..60”
“Probing the Improbable: Methodological Challenges for Risks With Low Probabilities and High Stakes”, Ord et al 2008
“Probing the Improbable: Methodological Challenges for Risks with Low Probabilities and High Stakes”
“The Epic Story of Maximum Likelihood”, Stigler 2007
“Overhang”, Paterson & Zwick 2007
“The Monotype 4Line System for Setting Mathematics”, Rhatigan 2007
“Maximum Overhang”, Paterson et al 2007
“Béla Bollobás: Graphs Extremal and Random [Interview of Béla Bollobás by Y. K. Leong]”, Leong & Bollobás 2007
“Béla Bollobás: Graphs Extremal and Random [Interview of Béla Bollobás by Y. K. Leong]”
“Computational Discovery in Pure Mathematics”, Colton 2007
“Comment on a Paper by Yucai Su On the Jacobian Conjecture (20051230)”, Moh 2006
“Comment on a Paper by Yucai Su On the Jacobian Conjecture (20051230)”
“Proof of Two Dimensional Jacobian Conjecture”, Su 2005
“Online Convex Programming and Generalized Infinitesimal Gradient Ascent”, Zinkevich 2003
“Online Convex Programming and Generalized Infinitesimal Gradient Ascent”
“EWD1300: The Notational Conventions I Adopted, and Why”, Dijkstra 2002
“Hymne to Hymen”, Descartes & Smith 2002
“The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen”, Dalen 2001
“The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen”
“Making Mathematics: The Coffee Connection”, Wieschenberg 1999
“An Editor Recalls Some Hopeless Papers”, Hodges 1998
“How Did Software Get so Reliable without Proof?”, Hoare 1996
“Light Shadows: Remembrances of Yale in the Early Fifties”, Rota 1996
“Ten Lessons I Wish I Had Been Taught”, Rota 1996
“Riemann Zeta Function Is a Fractal”, Woon 1994
“A Visit to Hungarian Mathematics”, Hersh & JohnSteiner 1993
“How I Was Led to the Frequency Approach”, Hamming 1991
“On the Computational Complexity of the Jones and Tutte Polynomials”, Jaeger et al 1990
“On the computational complexity of the Jones and Tutte polynomials”
“Factors and Primes: a Specific Numerical Ability”, Hermelin & O’Connor 1990
“Envisioning Information: Chapter 5, ‘Color and Information’, Pg8386 [on Oliver Byrne’s Color Diagram Version of Euclid’s Elements]”, Tufte 1990
“In Memory of Henry J. Kelley”, Cliff 1989
“Dynamical Systems That Sort Lists, Diagonalize Matrices and Solve Linear Programming Problems”, Brockett 1988
“Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems”
“The Printing of Mathematics”, Wishart 1988
“John Von Neumann As Seen By His Brother”, Vonneuman 1987
“The Aesthetic Viewpoint in Mathematics”
“Review of Yuri I. Manin Yu, A Course in Mathematical Logic 1997”, Boolos 1986
“Review of Yuri I. Manin Yu, A course in mathematical logic 1997”
“Discrete Hartley Transform”, Bracewell 1983
“Are Impossible Figures Possible?”, Kulpa 1983
“Bicontinuous Extensions of Invertible Combinatorial Functions”, Toffoli 1981
“Bicontinuous extensions of invertible combinatorial functions”
“The Letter S”, Knuth 1980
“Heaviside's Operational Calculus and the Attempts to Rigorise It”, Lützen 1979
“Heaviside's Operational Calculus and the Attempts to Rigorise It”
“Some Proposals for Reviving the Philosophy of Mathematics”, Hersh 1979
“Social Processes and Proofs of Theorems and Programs”, Millo et al 1979
“Life at Low Reynolds Number”, Purcell 1977
“Randomness and Mathematical Proof”, Chatin 1975
“The Dangers of ComputerScience Theory”, Knuth 1973
“Fidelity in Mathematical Discourse: Is One and One Really Two?”, Davis 1972
“Fidelity in Mathematical Discourse: Is One and One Really Two?”
“The Humble Programmer [EWD340]”, Dijkstra 1972
“Assigning Probabilities to Logical Formulas”, Scott & Krauss 1966
“Singular Extremals In Lawden’s Problem Of Optimal Rocket Flight”, Kelley 1963
“Singular Extremals In Lawden’s Problem Of Optimal Rocket Flight”
“A SteepestAscent Method for Solving Optimum Programming Problems”, Bryson & Denham 1962
“A SteepestAscent Method for Solving Optimum Programming Problems”
“Method of Gradients”, Kelley 1962
“Gradient Theory of Optimal Flight Paths”, Kelley 1960
“Toward Mechanical Mathematics”, Wang 1960
“Stable PredictorCorrector Methods for Ordinary Differential Equations”, Hamming 1959
“Stable PredictorCorrector Methods for Ordinary Differential Equations”
“The Printing of Mathematics: Aids for Authors and Editors and Rules for Compositors and Readers at the University Press, Oxford”, Chaundy et al 1954
“NonCooperative Games”, Nash 1951
“Principles of the SelfOrganizing Dynamic System”, Ashby 1947
“An Essay On The Psychology Of Invention In The Mathematical Field”, Hadamard 1945
“An Essay On The Psychology Of Invention In The Mathematical Field”
“A More Symmetrical Fourier Analysis Applied to Transmission Problems”, Hartley 1942
“A More Symmetrical Fourier Analysis Applied to Transmission Problems”
“Leonhard Euler's Elastic Curves”
“On a Problem of Formal Logic”, Ramsey 1930
“Operational Methods in Mathematical Physics”, Carslaw 1928
“The Foundations of Mathematics”, Ramsey 1926b
“Cutting a Round Cake on Scientific Principles”, Galton 1906
“On Operators in Physical Mathematics. Part I”, Heaviside 1892
“Why Momentum Really Works”
“Math: OpenAI API Can Do Some Math out of the Gate, but Most Math It Seems It Has to Learn. Many Times, the Numbers That It Spits out Are Just Random. However, including Different Priming Prompts Can Result in Decent Results.”
“Oliver Byrne’s Edition of Euclid [Scans]”, Casselman 2023
Sort By Magic
Annotations sorted by machine learning into inferred 'tags'. This provides an alternative way to browse: instead of by date order, one can browse in topic order. The 'sorted' list has been automatically clustered into multiple sections & autolabeled for easier browsing.
Beginning with the newest annotation, it uses the embedding of each annotation to attempt to create a list of nearestneighbor annotations, creating a progression of topics. For more details, see the link.
proofs
mathematics
mathematicalreasoning
Wikipedia
Miscellaneous

/doc/psychology/20201026dyqzrdataisbeautifuliasked16kpeoplehowmanyholescertainobjectshave.html

/doc/math/1986tymoczkonewdirectionsphilosophymathematics.pdf

/doc/math/1985tukeytheprincetonmathematicscommunityinthe1930spmc41interview.html

/doc/math/1980eulerrationalmechanicsflexibleelasticbodies16381788.pdf

/doc/math/1931ramseyfoundationsofmathematicsandotherlogicalessays.epub

https://blog.ploeh.dk/2017/10/04/fromdesignpatternstocategorytheory/

https://cronokirby.com/posts/2021/02/spacedrepetitionformathematics/

https://eli.thegreenplace.net/2023/demystifyingtuppersformula/

https://marckhoury.github.io/blog/counterintuitivepropertiesofhighdimensionalspace/

https://mathoverflow.net/questions/19930/writingpapersinprelatexera

https://nunosempere.com/blog/2023/01/30/aninprogressexperimenttotesthowlaplacesruleof/

https://pershmail.substack.com/p/questionsandanswersaboutmultiplication

https://publicdomainreview.org/collection/chladnifigures1787/

https://publicdomainreview.org/collection/thegeometriclandscapesoflorenzstoer1567/

https://publicdomainreview.org/collection/williamhogarthsatireonfalseperspective/

https://terrytao.wordpress.com/2023/06/19/aianthology/#comment678803

https://terrytao.wordpress.com/careeradvice/theresmoretomathematicsthanrigourandproofs/

https://thehighergeometer.wordpress.com/2023/08/09/noorder10projectiveplanesviasat/

https://thepalindrome.org/p/howdoesthejapanesemultiplicationwork

https://thonyc.wordpress.com/2021/11/04/renaissancesciencexxii/

https://twitter.com/AlexKontorovich/status/1678772963183820801

https://twitter.com/AlexKontorovich/status/1678772964836397056

https://twitter.com/gmchariszhang/status/1620150392326864898

https://www.amazon.com/TuringsCathedralOriginsDigitalUniverse/dp/1400075998/

https://www.kroneckerwallis.com/product/euclidselementscompletingoliverbyrneswork/

https://www.nytimes.com/2022/03/22/science/geometrymathbrainprimmates.html

https://www.quantamagazine.org/howisaacnewtondiscoveredthebinomialpowerseries20220831/

https://www.quantamagazine.org/howmathematicalcurvespowercryptography20220919/

https://www.quantamagazine.org/innewmathproofsartificialintelligenceplaystowin20220307/

https://www.theatlantic.com/magazine/archive/2016/03/themathrevolution/426855/

https://xenaproject.wordpress.com/2022/09/12/beyondtheliquidtensorexperiment/
Link Bibliography

https://cr.yp.to/papers/pwccp20230907.pdf
: “Papers With Computerchecked Proofs”, Daniel J. Bernstein 
https://arxiv.org/abs/2308.07921
: “Solving Challenging Math Word Problems Using GPT4 Code Interpreter With Codebased SelfVerification”, 
https://arxiv.org/abs/2307.03381
: “Teaching Arithmetic to Small Transformers”, Nayoung Lee, Kartik Sreenivasan, Jason D. Lee, Kangwook Lee, Dimitris Papailiopoulos 
https://arxiv.org/abs/2304.02015#alibaba
: “How Well Do Large Language Models Perform in Arithmetic Tasks?”, Zheng Yuan, Hongyi Yuan, Chuanqi Tan, Wei Wang, Songfang Huang 
https://arxiv.org/abs/2302.12433
: “ProofNet: Autoformalizing and Formally Proving UndergraduateLevel Mathematics”, Zhangir Azerbayev, Bartosz Piotrowski, Hailey Schoelkopf, Edward W. Ayers, Dragomir Radev, Jeremy Avigad 
http://neilsloane.com/doc/HIS50.pdf
: “OEIS: A Handbook of Integer Sequences 50 Years Later”, Neil Sloane 
https://arxiv.org/abs/2205.12910#allen
: “NaturalProver: Grounded Mathematical Proof Generation With Language Models”, Sean Welleck, Jiacheng Liu, Ximing Lu, Hannaneh Hajishirzi, Yejin Choi 
https://arxiv.org/abs/2205.11491#facebook
: “HTPS: HyperTree Proof Search for Neural Theorem Proving”, 
https://arxiv.org/abs/2204.02311#google
: “PaLM: Scaling Language Modeling With Pathways”, 
https://arxiv.org/abs/2202.01344#openai
: “Formal Mathematics Statement Curriculum Learning”, Stanislas Polu, Jesse Michael Han, Kunhao Zheng, Mantas Baksys, Igor Babuschkin, Ilya Sutskever 
2022schneider.pdf
: “Counting and the Ontogenetic Origins of Exact Equality”, Rose M. Schneider, Erik Brockbank, Roman Feiman, David Barner 
https://arxiv.org/abs/2112.11446#deepmind
: “Scaling Language Models: Methods, Analysis & Insights from Training Gopher”, 
https://www.quantamagazine.org/thebusybeavergameilluminatesthefundamentallimitsofmath20201210/
: “How the Slowest Computer Programs Illuminate Math’s Fundamental Limits: The Goal of the ‘busy Beaver’ Game Is to Find the Longestrunning Computer Program. Its Pursuit Has Surprising Connections to Some of the Most Profound Questions and Concepts in Mathematics”, John Pavlus 
https://arxiv.org/abs/2009.03393#openai
: “Generative Language Modeling for Automated Theorem Proving”, Stanislas Polu, Ilya Sutskever 
https://www.c82.net/blog/?id=79
: “Making of Byrne’s Euclid”, Nicholas Rougeux 
2013conway.pdf
: “On Unsettleable Arithmetical Problems”, John H. Conway 
modus
: “One Man’s Modus Ponens”, Gwern 
charityisnotabouthelping
: “Charity Is Not about Helping”, Gwern 
girlscouts
: “Girl Scouts & Good Corporate Governance”, Gwern 
simulationinference
: “Simulation Inferences”, Gwern 
predictionmarket
: “Prediction Markets”, Gwern 
2003zinkevich.pdf
: “Online Convex Programming and Generalized Infinitesimal Gradient Ascent”, Martin Zinkevich 
1990tufteenvisioninginformationch5byrneseuclid.pdf
: “Envisioning Information: Chapter 5, ‘Color and Information’, Pg8386 [on Oliver Byrne’s Color Diagram Version of Euclid’s Elements]”, Edward Tufte 
https://archive.org/details/eassayonthepsych006281mbp
: “An Essay On The Psychology Of Invention In The Mathematical Field”, Jacques Hadamard