- See Also
- Gwern
-
Links
- “Wu’s Method Can Boost Symbolic AI to Rival Silver Medalists and AlphaGeometry to Outperform Gold Medalists at IMO Geometry”, Sinha et al 2024
- “Tokenization Counts: the Impact of Tokenization on Arithmetic in Frontier LLMs”, Singh & Strouse 2024
- “Leveraging Large Language Models to Boost Dafny’s Developers Productivity”, Silva et al 2024
- “Solving Olympiad Geometry without Human Demonstrations”, Trinh et al 2024
- “Generative AI for Math: Part I—MathPile: A Billion-Token-Scale Pretraining Corpus for Math”, Wang et al 2023
- “PRER: Modeling Complex Mathematical Reasoning via Large Language Model Based MathAgent”, Liao et al 2023
- “TinyGSM: Achieving >80% on GSM8k With Small Language Models”, Liu et al 2023
- “Beyond Human Data: Scaling Self-Training for Problem-Solving With Language Models (ReSTEM)”, Singh et al 2023
- “Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning”, Dutta et al 2023
- “Universal Self-Consistency for Large Language Model Generation”, Chen et al 2023
- “Training Chain-Of-Thought via Latent-Variable Inference”, Phan et al 2023
- “Why Won’t OpenAI Say What the Q✱ Algorithm Is? Supposed AI Breakthroughs Are Frequently Veiled in Secrecy, Hindering Scientific Consensus”, Hao 2023
- “Positional Description Matters for Transformers Arithmetic”, Shen et al 2023
- “GPQA: A Graduate-Level Google-Proof Q&A Benchmark”, Rein et al 2023
- “The Impact of Large Language Models on Scientific Discovery: a Preliminary Study Using GPT-4”, AI4Science & Quantum 2023
- “Implicit Chain-Of-Thought Reasoning via Knowledge Distillation”, Deng et al 2023
- “Let Models Speak Ciphers: Multiagent Debate through Embeddings”, Pham et al 2023
- “OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text”, Paster et al 2023
- “Distinct Neuronal Representation of Small and Large Numbers in the Human Medial Temporal Lobe”, Kutter et al 2023
- “Papers With Computer-Checked Proofs”, Bernstein 2023
- “Solving Challenging Math Word Problems Using GPT-4 Code Interpreter With Code-Based Self-Verification”, Zhou et al 2023
- “Testing GPT-4 With Wolfram Alpha and Code Interpreter Plug-Ins on Math and Science Problems”, Davis & Aaronson 2023
- “Teaching Arithmetic to Small Transformers”, Lee et al 2023
- “LeanDojo: Theorem Proving With Retrieval-Augmented Language Models”, Yang et al 2023
- “Let’s Verify Step by Step”, Lightman et al 2023
- “A Chiral Aperiodic Monotile”, Smith et al 2023
- “FERMAT: An Alternative to Accuracy for Numerical Reasoning”, Sivakumar & Moosavi 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 GPT-2 Compute Greater-Than?: Interpreting Mathematical Abilities in a Pre-Trained Language Model”, Hanna et al 2023
- “Evaluating Transformer Language Models on Arithmetic Operations Using Number Decomposition”, Muffo et al 2023
- “The Spinorial Ball: a Macroscopic Object of Spin-1/2”, Bernard-Bernardet et al 2023
- “How Well Do Large Language Models Perform in Arithmetic Tasks?”, Yuan et al 2023
- “ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics”, Azerbayev et al 2023
- “OEIS: A Handbook of Integer Sequences 50 Years Later”, Sloane 2023
- “Solving Math Word Problems With Process & Outcome-Based Feedback”, Uesato et al 2022
- “What Is My Math Transformer Doing? – 3 Results on Interpretability and Generalization”, Charton 2022
- “Broken Neural Scaling Laws”, Caballero et al 2022
- “Dynamic Prompt Learning via Policy Gradient for Semi-Structured 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
- “End-To-End Symbolic Regression With Transformers”, Kamienny et al 2022
- “The Sexes Do Not Differ in General Intelligence, but They Do in Some Specifics”, Reynolds et al 2022
- “PaLM: Scaling Language Modeling With Pathways”, Chowdhery et al 2022
- “Impact of Pretraining Term Frequencies on Few-Shot 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 Cross-System Benchmark for Formal Olympiad-Level 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 Pre-Trained 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 Co-Training 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 Longest-Running 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
- “MMLU: Measuring Massive Multitask Language Understanding”, Hendrycks et al 2020
- “Generative Language Modeling for Automated Theorem Proving”, Polu & Sutskever 2020
- “A Promising Path Towards Autoformalization and General Artificial Intelligence”, Szegedy 2020
- “Lights and Shadows”, Ciechanowski 2020
- “Singing Euclid: the Oral Character of Greek Geometry”, Blåsjö 2020
- “Mathematical Reasoning via Self-Supervised Skip-Tree Training”, Rabe et al 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
- “Do NLP Models Know Numbers? Probing Numeracy in Embeddings”, Wallace et al 2019
- “Ternary Circuits: Why R=3 Is Not the Optimal Radix for Computation”, Etiemble 2019
- “MAWPS: A Math Word Problem Repository”, Koncel-Kedziorski et al 2019
- “Learning to Reason in Large Theories without Imitation”, Bansal et al 2019
- “Analysing Mathematical Reasoning Abilities of Neural Models”, Saxton et al 2019
- “Paul Erdős’s Mathematics As a Social Activity”, Rekvenyi 2019
- “Fancy Euclid’s Elements in TeX”, Slyusarev 2019
- “Reinventing the Wheel: Discovering the Optimal Rolling Shape With PyTorch”, Wiener 2019
- “The First Printed Math Books”, Boardley 2019
- “Making of Byrne’s Euclid”, Rougeux 2018
- “Best Practices: Formal Proofs, the Fine Print and Side Effects”, Murray & Oorschot 2018
- “Mastering Chess and Shogi by Self-Play 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
- “A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory”, Yedidia & Aaronson 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 Gradient-Free 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
- “The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems—Can We Trust in Them?”, Durán et al 2014
- “Neural Networks, Manifolds, and Topology”, Olah 2014
- “Finite Time Blowup for an Averaged Three-Dimensional Navier-Stokes Equation”, Tao 2014
- “Homotopy Groups of Suspended Classifying Spaces: An Experimental Approach”, Romero & Rubio 2013
- “On Unsettleable Arithmetical Problems”, Conway 2013
- “The Algebraic Combinatorial Approach for Low-Rank Matrix Completion”, Király et al 2012
- “Mind Switches in Futurama and Stargate”, Evans & Huang 2012
- “Vividness in Mathematics and Narrative”, Gowers 2012
- “How to Write a 21st Century Proof”, Lamport 2011
- “Jewish Problems”, Khovanova & Radul 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
- “Desperately Seeking Mathematical Proof”, Nathanson 2009
- “The Gödel Letter”, Gödel 2009
- “11858_2008_132_41_1-Web 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 4-Line System for Setting Mathematics”, Rhatigan 2007
- “Maximum Overhang”, Paterson et al 2007
- “Computational Discovery in Pure Mathematics”, Colton 2007
- “Béla Bollobás: Graphs Extremal and Random [Interview of Béla Bollobás by Y. K. Leong]”, Leong & Bollobás 2007
- “Comment on a Paper by Yucai Su On the Jacobian Conjecture (2005-12-30)”, 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 & John-Steiner 1993
- “What in Heaven Is a Digital Sundial?”, stewart 1991
- “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’, Pg83-86 [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
- “The Emergence of Princeton As a World Center for Mathematical Research, 1896--1939”, Aspray 1988
- “The Aesthetic Viewpoint in Mathematics”
- “John Von Neumann As Seen By His Brother”, Vonneuman 1987
- “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
- “Bi-Continuous Extensions of Invertible Combinatorial Functions”, Toffoli 1981
- “The Letter S”, Knuth 1980
- “Some Proposals for Reviving the Philosophy of Mathematics”, Hersh 1979
- “Heaviside's Operational Calculus and the Attempts to Rigorise It”, Lützen 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 Computer-Science 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 Steepest-Ascent 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 Predictor-Corrector 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
- “Non-Cooperative Games”, Nash 1951
- “Principles of the Self-Organizing 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 2024
- spolu
- Wikipedia
- Miscellaneous
- Link Bibliography
See Also
Gwern
“One Man’s Modus Ponens”, Gwern 2012
“Prediction Markets”, Gwern 2009
“Girl Scouts & Good Corporate Governance”, Gwern 2011
“Simulation Inferences”, Gwern 2009
Links
“Wu’s Method Can Boost Symbolic AI to Rival Silver Medalists and AlphaGeometry to Outperform Gold Medalists at IMO Geometry”, Sinha et al 2024
“Tokenization Counts: the Impact of Tokenization on Arithmetic in Frontier LLMs”, Singh & Strouse 2024
Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs
“Leveraging Large Language Models to Boost Dafny’s Developers Productivity”, Silva et al 2024
Leveraging Large Language Models to Boost Dafny’s Developers Productivity
“Solving Olympiad Geometry without Human Demonstrations”, Trinh et al 2024
“Generative AI for Math: Part I—MathPile: A Billion-Token-Scale Pretraining Corpus for Math”, Wang et al 2023
Generative AI for Math: Part I—MathPile: A Billion-Token-Scale Pretraining Corpus for Math
“PRER: Modeling Complex Mathematical Reasoning via Large Language Model Based MathAgent”, Liao et al 2023
PRER: Modeling Complex Mathematical Reasoning via Large Language Model based MathAgent
“TinyGSM: Achieving >80% on GSM8k With Small Language Models”, Liu et al 2023
“Beyond Human Data: Scaling Self-Training for Problem-Solving With Language Models (ReSTEM)”, Singh et al 2023
Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models (ReSTEM)
“Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning”, Dutta et al 2023
Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning
“Universal Self-Consistency for Large Language Model Generation”, Chen et al 2023
Universal Self-Consistency for Large Language Model Generation
“Training Chain-Of-Thought via Latent-Variable Inference”, Phan et al 2023
“Why Won’t OpenAI Say What the Q✱ Algorithm Is? Supposed AI Breakthroughs Are Frequently Veiled in Secrecy, Hindering Scientific Consensus”, Hao 2023
“Positional Description Matters for Transformers Arithmetic”, Shen et al 2023
“GPQA: A Graduate-Level Google-Proof Q&A Benchmark”, Rein et al 2023
“The Impact of Large Language Models on Scientific Discovery: a Preliminary Study Using GPT-4”, AI4Science & Quantum 2023
The Impact of Large Language Models on Scientific Discovery: a Preliminary Study using GPT-4
“Implicit Chain-Of-Thought Reasoning via Knowledge Distillation”, Deng et al 2023
Implicit Chain-of-Thought Reasoning via Knowledge Distillation
“Let Models Speak Ciphers: Multiagent Debate through Embeddings”, Pham et al 2023
Let Models Speak Ciphers: Multiagent Debate through Embeddings
“OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text”, Paster et al 2023
OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text
“Distinct Neuronal Representation of Small and Large Numbers in the Human Medial Temporal Lobe”, Kutter et al 2023
Distinct neuronal representation of small and large numbers in the human medial temporal lobe
“Papers With Computer-Checked Proofs”, Bernstein 2023
“Solving Challenging Math Word Problems Using GPT-4 Code Interpreter With Code-Based Self-Verification”, Zhou et al 2023
“Testing GPT-4 With Wolfram Alpha and Code Interpreter Plug-Ins on Math and Science Problems”, Davis & Aaronson 2023
Testing GPT-4 with Wolfram Alpha and Code Interpreter plug-ins on math and science problems
“Teaching Arithmetic to Small Transformers”, Lee et al 2023
“LeanDojo: Theorem Proving With Retrieval-Augmented Language Models”, Yang et al 2023
LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
“Let’s Verify Step by Step”, Lightman et al 2023
“A Chiral Aperiodic Monotile”, Smith et al 2023
“FERMAT: An Alternative to Accuracy for Numerical Reasoning”, Sivakumar & Moosavi 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 GPT-2 Compute Greater-Than?: Interpreting Mathematical Abilities in a Pre-Trained 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
“The Spinorial Ball: a Macroscopic Object of Spin-1/2”, Bernard-Bernardet et al 2023
“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 Undergraduate-Level Mathematics”, Azerbayev et al 2023
ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics
“OEIS: A Handbook of Integer Sequences 50 Years Later”, Sloane 2023
“Solving Math Word Problems With Process & Outcome-Based Feedback”, Uesato et al 2022
Solving math word problems with process & outcome-based 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
“Broken Neural Scaling Laws”, Caballero et al 2022
“Dynamic Prompt Learning via Policy Gradient for Semi-Structured Mathematical Reasoning”, Lu et al 2022
Dynamic Prompt Learning via Policy Gradient for Semi-structured 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
“End-To-End Symbolic Regression With Transformers”, Kamienny et al 2022
“The Sexes Do Not Differ in General Intelligence, but They Do in Some Specifics”, Reynolds et al 2022
The sexes do not differ in general intelligence, but they do in some specifics
“PaLM: Scaling Language Modeling With Pathways”, Chowdhery et al 2022
“Impact of Pretraining Term Frequencies on Few-Shot Reasoning”, Razeghi et al 2022
Impact of Pretraining Term Frequencies on Few-Shot Reasoning
“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
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 Cross-System Benchmark for Formal Olympiad-Level Mathematics”, Zheng et al 2021
MiniF2F: a cross-system benchmark for formal Olympiad-level 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 Pre-Trained Model for Mathematical Formula Understanding”, Peng et al 2021
MathBERT: A Pre-Trained 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 Co-Training for Theorem Proving With Language Models”, Han et al 2021
Proof Artifact Co-training 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 Longest-Running 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
“MMLU: Measuring Massive Multitask Language Understanding”, Hendrycks et al 2020
“Generative Language Modeling for Automated Theorem Proving”, Polu & Sutskever 2020
“A Promising Path Towards Autoformalization and General Artificial Intelligence”, Szegedy 2020
A Promising Path Towards Autoformalization and General Artificial Intelligence
“Lights and Shadows”, Ciechanowski 2020
“Singing Euclid: the Oral Character of Greek Geometry”, Blåsjö 2020
“Mathematical Reasoning via Self-Supervised Skip-Tree Training”, Rabe et al 2020
Mathematical Reasoning via Self-supervised Skip-tree Training
“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
“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
“Do NLP Models Know Numbers? Probing Numeracy in Embeddings”, Wallace et al 2019
“Ternary Circuits: Why R=3 Is Not the Optimal Radix for Computation”, Etiemble 2019
Ternary circuits: why R=3 is not the Optimal Radix for Computation
“MAWPS: A Math Word Problem Repository”, Koncel-Kedziorski et al 2019
“Learning to Reason in Large Theories without Imitation”, Bansal et al 2019
“Analysing Mathematical Reasoning Abilities of Neural Models”, Saxton et al 2019
“Paul Erdős’s Mathematics As a Social Activity”, Rekvenyi 2019
“Fancy Euclid’s Elements in TeX”, Slyusarev 2019
“Reinventing the Wheel: Discovering the Optimal Rolling Shape With PyTorch”, Wiener 2019
Reinventing the Wheel: Discovering the Optimal Rolling Shape with PyTorch
“The First Printed Math Books”, Boardley 2019
“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
“Mastering Chess and Shogi by Self-Play With a General Reinforcement Learning Algorithm”, Silver et al 2017
Mastering Chess and Shogi by Self-Play 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
“A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory”, Yedidia & Aaronson 2016
A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory
“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 Gradient-Free 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
“The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems—Can We Trust in Them?”, Durán et al 2014
The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems—Can We Trust in Them?
“Neural Networks, Manifolds, and Topology”, Olah 2014
“Finite Time Blowup for an Averaged Three-Dimensional Navier-Stokes Equation”, Tao 2014
Finite time blowup for an averaged three-dimensional Navier-Stokes equation
“Homotopy Groups of Suspended Classifying Spaces: An Experimental Approach”, Romero & Rubio 2013
Homotopy groups of suspended classifying spaces: An experimental approach
“On Unsettleable Arithmetical Problems”, Conway 2013
“The Algebraic Combinatorial Approach for Low-Rank Matrix Completion”, Király et al 2012
The Algebraic Combinatorial Approach for Low-Rank Matrix Completion
“Mind Switches in Futurama and Stargate”, Evans & Huang 2012
“Vividness in Mathematics and Narrative”, Gowers 2012
“How to Write a 21st Century Proof”, Lamport 2011
“Jewish Problems”, Khovanova & Radul 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
“Desperately Seeking Mathematical Proof”, Nathanson 2009
“The Gödel Letter”, Gödel 2009
“11858_2008_132_41_1-Web 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 4-Line System for Setting Mathematics”, Rhatigan 2007
“Maximum Overhang”, Paterson et al 2007
“Computational Discovery in Pure Mathematics”, Colton 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]:
View PDF:
“Comment on a Paper by Yucai Su On the Jacobian Conjecture (2005-12-30)”, Moh 2006
Comment on a Paper by Yucai Su On the Jacobian Conjecture (2005-12-30)
“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
View PDF:
“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 & John-Steiner 1993
A visit to Hungarian mathematics:
View PDF:
“What in Heaven Is a Digital Sundial?”, stewart 1991
What in Heaven Is a Digital Sundial?:
View PDF:
“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’, Pg83-86 [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
“The Emergence of Princeton As a World Center for Mathematical Research, 1896--1939”, Aspray 1988
The Emergence of Princeton as a World Center for Mathematical Research, 1896--1939
“The Aesthetic Viewpoint in Mathematics”
“John Von Neumann As Seen By His Brother”, Vonneuman 1987
John von Neumann As Seen By His Brother:
View PDF:
“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
“Bi-Continuous Extensions of Invertible Combinatorial Functions”, Toffoli 1981
Bi-continuous extensions of invertible combinatorial functions
“The Letter S”, Knuth 1980
“Some Proposals for Reviving the Philosophy of Mathematics”, Hersh 1979
Some Proposals for Reviving the Philosophy of mathematics:
View PDF:
“Heaviside's Operational Calculus and the Attempts to Rigorise It”, Lützen 1979
Heaviside's Operational Calculus and the Attempts to Rigorise It
“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 Computer-Science 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?:
View PDF:
“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 Steepest-Ascent Method for Solving Optimum Programming Problems”, Bryson & Denham 1962
A Steepest-Ascent 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 Predictor-Corrector Methods for Ordinary Differential Equations”, Hamming 1959
Stable Predictor-Corrector 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
“Non-Cooperative Games”, Nash 1951
“Principles of the Self-Organizing 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
Cutting a Round Cake on Scientific Principles:
View PDF:
“On Operators in Physical Mathematics. Part I”, Heaviside 1892
On Operators in Physical Mathematics. Part I:
View PDF:
“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 2024
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Wikipedia
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All horses are the same color:
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Journal of Integer Sequences:
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On-Line Encyclopedia of Integer Sequences § Self-referential sequences:
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Miscellaneous
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http://math.andrej.com/2007/09/28/seemingly-impossible-functional-programs/ -
https://bldgblog.com/2007/12/adventures-in-stacking/:View External Link:
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https://eli.thegreenplace.net/2023/demystifying-tuppers-formula/ -
https://marckhoury.github.io/blog/counterintuitive-properties-of-high-dimensional-space/ -
https://math.dartmouth.edu/~matc/MathDrama/reading/Hamming.html -
https://mathoverflow.net/questions/19930/writing-papers-in-pre-latex-era -
https://nunosempere.com/blog/2023/01/30/an-in-progress-experiment-to-test-how-laplace-s-rule-of/: -
https://pershmail.substack.com/p/questions-and-answers-about-multiplication -
https://pro.univ-lille.fr/fileadmin/user_upload/pages_pros/lorenzo_ramero/CoursAG.pdf -
https://publicdomainreview.org/collection/chladni-figures-1787/ -
https://publicdomainreview.org/collection/the-geometric-landscapes-of-lorenz-stoer-1567/ -
https://publicdomainreview.org/collection/william-hogarth-satire-on-false-perspective/ -
https://terrytao.wordpress.com/2023/06/19/ai-anthology/#comment-678803 -
https://terrytao.wordpress.com/about/ai-generated-versions-of-the-ai-anthology-article/ -
https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ -
https://thehighergeometer.wordpress.com/2023/08/09/no-order-10-projective-planes-via-sat/ -
https://thepalindrome.org/p/how-does-the-japanese-multiplication-work -
https://thonyc.wordpress.com/2021/11/04/renaissance-science-xxii/: -
https://twitter.com/AlexKontorovich/status/1678772963183820801 -
https://twitter.com/AlexKontorovich/status/1678772964836397056 -
https://twitter.com/gmchariszhang/status/1620150392326864898 -
https://twitter.com/mezaoptimizer/status/1725512396901433575 -
https://worksinprogress.co/issue/how-mathematics-built-the-modern-world/ -
https://writings.stephenwolfram.com/2023/03/chatgpt-gets-its-wolfram-superpowers/ -
https://www.amazon.com/Turings-Cathedral-Origins-Digital-Universe/dp/1400075998/ -
https://www.kroneckerwallis.com/product/euclids-elements-completing-oliver-byrnes-work/ -
https://www.lesswrong.com/posts/ZwshvqiqCvXPsZEct/the-learning-theoretic-agenda-status-2023 -
https://www.nytimes.com/2022/03/22/science/geometry-math-brain-primmates.html -
https://www.nytimes.com/2023/12/29/science/puzzles-mechanical-miller.html -
https://www.quantamagazine.org/a-new-agenda-for-low-dimensional-topology-20240222/ -
https://www.quantamagazine.org/how-isaac-newton-discovered-the-binomial-power-series-20220831/ -
https://www.quantamagazine.org/how-mathematical-curves-power-cryptography-20220919/ -
https://www.quantamagazine.org/in-new-math-proofs-artificial-intelligence-plays-to-win-20220307/ -
https://www.quantamagazine.org/the-mysterious-math-of-billiards-tables-20240215/ -
https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-famed-fractal-20240126/ -
https://www.stephenwolfram.com/publications/mathematical-notation-past-future/ -
https://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/426855/ -
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https://xenaproject.wordpress.com/2022/09/12/beyond-the-liquid-tensor-experiment/
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