“‘Math’ Tag”,2019-08-28

Bibliography for tag math, most recent first: 6 related tags, 262 annotations, & 108 links (parent).

• See Also
• Gwern
  • “Number Search Engine via NN Embeddings”, Gwern2024
  • “One Man’s Modus Ponens”, Gwern2012
  • “Prediction Markets”, Gwern2009
  • “Girl Scouts & Good Corporate Governance”, Gwern2011
  • “Simulation Inferences”, Gwern2009
• Links
  • “Math’s ‘Bunkbed Conjecture’ Has Been Debunked”
  • “Mixture of Parrots: Experts Improve Memorization More Than Reasoning”, Jelassi et al 2024
  • “Industrious Dice [Minimizing Pip Counts on Still-Functional Dice]”
  • “Can OpenAI’s o1-Preview Ace the 2023 Putnam Exam?”, Kabasares2024
  • “An Intuitive Explanation of Black-Scholes: I Explain the Black-Scholes Formula Using Only Basic Probability Theory and Calculus, With a Focus on the Big Picture and Intuition over Technical Details”, Gundersen2024
  • “To CoT or Not to CoT? Chain-Of-Thought Helps Mainly on Math and Symbolic Reasoning”, Sprague et al 2024
  • “I Have Played a Little Bit With OpenAI’s New Iteration, GPT-4 O1”, Tao2024
  • “‘He Was in Mystic Delirium’: Was This Hermit Mathematician Alexander Grothendieck a Forgotten Genius Whose Ideas Could Transform AI—Or a Lonely Madman?”
  • “Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature”, Constantin et al 2024
  • “Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process”, Ye et al 2024
  • “MCTSr: Accessing GPT-4 Level Mathematical Olympiad Solutions via Monte Carlo Tree Self-Refine With LLaMA-3-8B”, Zhang et al 2024
  • “AI Will Become Mathematicians’ ‘Co-Pilot’: Fields Medalist Terence Tao Explains How Proof Checkers and AI Programs Are Dramatically Changing Mathematics”, Drösser & Tao2024
  • “OmegaPRM: Improve Mathematical Reasoning in Language Models by Automated Process Supervision”, Luo et al 2024
  • “MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark”, Wang et al 2024
  • “The Lessons of Hermann Grassmann and the Nature of Abstractions”, Emanual2024
  • “Crows ‘Count’ the Number of Self-Generated Vocalizations”, Liao et al 2024
  • “DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data”, Xin et al 2024
  • “Verified Neural Compressed Sensing”, Bunel et al 2024
  • “GSM1k: A Careful Examination of Large Language Model Performance on Grade School Arithmetic”, Zhang et al 2024
  • “Wu’s Method Can Boost Symbolic AI to Rival Silver Medalists and AlphaGeometry to Outperform Gold Medalists at IMO Geometry”, Sinha et al 2024
  • “Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap”, Srivastava et al 2024
  • “Tokenization Counts: the Impact of Tokenization on Arithmetic in Frontier LLMs”, Singh & Strouse2024
  • “Autonomous Data Selection With Language Models for Mathematical Texts”, Zhang et al 2024
  • “Hamiltonicity of Expanders: Optimal Bounds and Applications”, Draganić et al 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 (ReST^EM)”, 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”, Hao2023
  • “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 & Quantum2023
  • “Implicit Chain-Of-Thought Reasoning via Knowledge Distillation”, Deng et al 2023
  • “Llemma: An Open Language Model For Mathematics”, Azerbayev 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
  • “MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models”, Yu et al 2023
  • “FIMO: A Challenge Formal Dataset for Automated Theorem Proving”, Liu et al 2023
  • “Papers With Computer-Checked Proofs”, Bernstein2023
  • “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 & Aaronson2023
  • “Teaching Arithmetic to Small Transformers”, Lee et al 2023
  • “Length Generalization in Arithmetic Transformers”, Jelassi 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 & Moosavi2023
  • “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)”, Roberts2023
  • “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”, Sloane2023
  • “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”, Charton2022
  • “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 & Gráda2022
  • “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”, Buzzard2021
  • “Scaling Language Models: Methods, Analysis & Insights from Training Gopher”, Rae et al 2021
  • “Linear Algebra With Transformers”, Charton2021
  • “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 & Strogatz2021
  • “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”, Wagner2021
  • “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”, Pavlus2020
  • “The Empirical Metamathematics of Euclid and Beyond”, Wolfram2020
  • “MMLU: Measuring Massive Multitask Language Understanding”, Hendrycks et al 2020
  • “Generative Language Modeling for Automated Theorem Proving”, Polu & Sutskever2020
  • “A Promising Path Towards Autoformalization and General Artificial Intelligence”, Szegedy2020
  • “Lights and Shadows”, Ciechanowski2020
  • “Singing Euclid: the Oral Character of Greek Geometry”, Blåsjö2020
  • “Mathematical Reasoning via Self-Supervised Skip-Tree Training”, Rabe et al 2020
  • “Remembering John Conway’s FRACTRAN, a Ridiculous, yet Surprisingly Deep Language”, Braithwaite2020
  • “Radical Solutions: French Mathematician Évariste Galois Lived a Full Life. When He Wasn’t Trying to Overthrow the Government, He Was Reinventing Algebra”, Brook & Macfarlane2020
  • “Learning to Prove Theorems by Learning to Generate Theorems”, Wang & Deng2020
  • “Transformers As Soft Reasoners over Language”, Clark et al 2020
  • “Neural Arithmetic Units”, Madsen & Johansen2020
  • “Generative Language Modeling for Automated Theorem Proving § Experiments”, Polu & Sutskever2020 (page 11 org openai)
  • “Deep Learning for Symbolic Mathematics”, Lample & Charton2019
  • “The Lean Mathematical Library”, Community2019
  • “Talent Search versus Talent Development”, Berzsenyi2019
  • “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”, Etiemble2019
  • “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”, Rekvenyi2019
  • “Fancy Euclid’s Elements in T_eX”, Slyusarev2019
  • “A Randomized Controlled Trial of Interleaved Mathematics Practice”, Rohrer et al 2019
  • “Reinventing the Wheel: Discovering the Optimal Rolling Shape With PyTorch”, Wiener2019
  • “The First Printed Math Books”, Boardley2019
  • “Making of Byrne’s Euclid”, Rougeux2018
  • “Best Practices: Formal Proofs, the Fine Print and Side Effects”, Murray & Oorschot2018
  • “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”, Smith2017
  • “Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems”, Ling et al 2017
  • “The Reinhardt Conjecture As an Optimal Control Problem”, Hales2017
  • “The Doodle Theorem, and Beyond: Colin Wright Juggles Euler, Doodling and Millennium Problems”, Wright2016
  • “Solving General Arithmetic Word Problems”, Roy & Roth2016
  • “DeepMath: Deep Sequence Models for Premise Selection”, Alemi et al 2016
  • “A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory”, Yedidia & Aaronson2016
  • “The LEGO Counting Problem”, Eilers2016
  • “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 & Spokoiny2015
  • “Prizes and Productivity: How Winning the Fields Medal Affects Scientific Output”, Borjas & Doran2015
  • “Is There a Curse of the Fields Medal?”, Kollár2015
  • “The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems—Can We Trust in Them?”, Durán et al 2014
  • “Interleaved Practice Improves Mathematics Learning”, Rohrer et al 2014b
  • “The Case of the Case of Benny: Elucidating the Influence of a Landmark Study in Mathematics Education”, Leatham & Winiecke2014
  • “Neural Networks, Manifolds, and Topology”, Olah2014
  • “Finite Time Blowup for an Averaged Three-Dimensional Navier-Stokes Equation”, Tao2014
  • “Homotopy Groups of Suspended Classifying Spaces: An Experimental Approach”, Romero & Rubio2013
  • “Mathematics in the Age of the Turing Machine”, Hales2013
  • “On Unsettleable Arithmetical Problems”, Conway2013
  • “The Algebraic Combinatorial Approach for Low-Rank Matrix Completion”, Király et al 2012
  • “How Did Software Get So Reliable Without Proof? [Blog]”, Regehr2012
  • “Mind Switches in Futurama and Stargate”, Evans & Huang2012
  • “On the Distribution of Time-To-Proof of Mathematical Conjectures”, Hisano & Sornette2012
  • “Vividness in Mathematics and Narrative”, Gowers2012
  • “How to Write a 21^st Century Proof”, Lamport2011
  • “Jewish Problems”, Khovanova & Radul2011
  • “The Cosmic Distance Ladder”, Tao2010
  • “Coolex: The Coolest Way to Generate Combinations”, Ruskey & Williams2009
  • “Packing Unit Squares in Squares: A Survey and New Results”, Friedman2009
  • “Desperately Seeking Mathematical Proof”, Nathanson2009
  • “The Gödel Letter”, Gödel2009
  • “Physics, Topology, Logic and Computation: A Rosetta Stone”, Baez & Stay2009
  • “11858_2008_16ya_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”, Stigler2007
  • “Overhang”, Paterson & Zwick2007
  • “The Monotype 4-Line System for Setting Mathematics”, Rhatigan2007
  • “Maximum Overhang”, Paterson et al 2007
  • “Computational Discovery in Pure Mathematics”, Colton2007
  • “Béla Bollobás: Graphs Extremal and Random [Interview of Béla Bollobás by Y. K. Leong]”, Leong & Bollobás2007
  • “How Abstract Is Symbolic Thought?”, Landy & Goldstone2007
  • “Comment on a Paper by Yucai Su On the Jacobian Conjecture (2005-12-30)”, Moh2006
  • “Proof of Two Dimensional Jacobian Conjecture”, Su2005
  • “Monstrous Moonshine: The First 25 Years”, Gannon2004
  • “Online Convex Programming and Generalized Infinitesimal Gradient Ascent”, Zinkevich2003
  • “EWD1300: The Notational Conventions I Adopted, and Why”, Dijkstra2002
  • “Philosophical Problems in Logic § Ultrafinitism”, Friedman2002 (page 4)
  • “Hymne to Hymen”, Descartes & Smith2002
  • “The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen”, Dalen2001
  • “Making Mathematics: The Coffee Connection”, Wieschenberg1999
  • “An Editor Recalls Some Hopeless Papers”, Hodges1998
  • “How Did Software Get so Reliable without Proof?”, Hoare1996
  • “Light Shadows: Remembrances of Yale in the Early Fifties”, Rota1996
  • “Ten Lessons I Wish I Had Been Taught”, Rota1996
  • “Riemann Zeta Function Is a Fractal”, Woon1994
  • “A Visit to Hungarian Mathematics”, Hersh & John-Steiner1993
  • “Mathematics for Little Ones”, Zvonkin1992
  • “What in Heaven Is a Digital Sundial?”, stewart 1991
  • “How I Was Led to the Frequency Approach”, Hamming1991
  • “On the Computational Complexity of the Jones and Tutte Polynomials”, Jaeger et al 1990
  • “Factors and Primes: a Specific Numerical Ability”, Hermelin & O’Connor1990
  • “Envisioning Information: Chapter 5, ‘Color and Information’, Pg83-86 [On Oliver Byrne’s Color Diagram Version of Euclid’s Elements]”, Tufte1990
  • “Discussion: John Von Neumann—A Case Study of Scientific Creativity”, Aspray et al 1989
  • “In Memory of Henry J. Kelley”, Cliff1989
  • “Dynamical Systems That Sort Lists, Diagonalize Matrices and Solve Linear Programming Problems”, Brockett1988
  • “The Printing of Mathematics”, Wishart1988
  • “The Emergence of Princeton As a World Center for Mathematical Research, 1896^–₄₃1939_85ya”, Aspray1988
  • “The Aesthetic Viewpoint in Mathematics”
  • “John Von Neumann As Seen By His Brother”, Vonneuman1987
  • “The Back of the Envelope Returns”, Bentley1986
  • “Review of Yuri I. Manin Yu, A Course in Mathematical Logic 1997”, Boolos1986
  • “Terence Tao”, Clements1984
  • “The Back of the Envelope”, Bentley1984
  • “Discrete Hartley Transform”, Bracewell1983
  • “Are Impossible Figures Possible?”, Kulpa1983
  • “On Number Numbness”, Hofstadter1982b
  • “Bi-Continuous Extensions of Invertible Combinatorial Functions”, Toffoli1981
  • “Bouvet and Leibniz: A Scholarly Correspondence”, Swiderski1980
  • “The Letter S”, Knuth1980
  • “Monstrous Moonshine”, Conway & Norton1979
  • “Some Proposals for Reviving the Philosophy of Mathematics”, Hersh1979
  • “Heaviside’s Operational Calculus and the Attempts to Rigorise It”, Lützen1979
  • “Social Processes and Proofs of Theorems and Programs”, Millo et al 1979
  • “Life at Low Reynolds Number”, Purcell1977
  • “Randomness and Mathematical Proof”, Chatin1975
  • “Constructing the Sunflower Head”, Mathai & Davis1974
  • “The Legend of John Von Neumann”, Halmos1973
  • “Benny’s Conception of Rules and Answers in IPI Mathematics”, Erlwanger1973
  • “The Dangers of Computer-Science Theory”, Knuth1973
  • “Nonstandard Analysis”, Davis & Hersh1972b
  • “Fidelity in Mathematical Discourse: Is One and One Really Two?”, Davis1972
  • “The Humble Programmer [EWD340]”, Dijkstra1972
  • “Assigning Probabilities to Logical Formulas”, Scott & Krauss1966
  • “Singular Extremals In Lawden’s Problem Of Optimal Rocket Flight”, Kelley1963
  • “A Steepest-Ascent Method for Solving Optimum Programming Problems”, Bryson & Denham1962
  • “Method of Gradients”, Kelley1962
  • “An Exceptional Talent For Calculative Thinking”, Hunter1962
  • “Gradient Theory of Optimal Flight Paths”, Kelley1960
  • “Toward Mechanical Mathematics”, Wang1960
  • “Stable Predictor-Corrector Methods for Ordinary Differential Equations”, Hamming1959
  • 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”, Nash1951
  • “Principles of the Self-Organizing Dynamic System”, Ashby1947
  • An Essay On The Psychology Of Invention In The Mathematical Field, Hadamard1945
  • “A More Symmetrical Fourier Analysis Applied to Transmission Problems”, Hartley1942
  • “Leonhard Euler’s Elastic Curves”
  • “On a Problem of Formal Logic”, Ramsey1930
  • “Operational Methods in Mathematical Physics”, Carslaw1928
  • “The Foundations of Mathematics”, Ramsey1926b
  • “Cutting a Round Cake on Scientific Principles”, Galton1906
  • “On Operators in Physical Mathematics. Part I”, Heaviside1892
  • “Packomania”
  • “Sculptures”, Abel2024
  • “Adventures in Stacking”
  • “Extreme D&D DIY: Adventures in Hypergeometry, Procedural Generation, and Software Development (part 1)”, Achmiz2024
  • “Spaced Repetition for Mathematics”
  • “Why Momentum Really Works”
  • “1972 Talk at CERN on Scientific Research”, Grothendieck2024
  • “How Should Mathematics Be Taught to Non-Mathematicians?”, Gowers2024
  • “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.”
  • “Hamiltonian Cycles on Ammann-Beenker Tilings”
  • “A000108”
  • “Oliver Byrne’s Edition of Euclid’s Elements [Scans]”, Casselman2024
  • “Chladni Figures (1787_237ya)”
  • “Solid Objects: 16^th-Century Geometric and Perspective Drawings”
  • “The Geometric Landscapes of Lorenz Stoer (1567_457ya)”
  • “William Hogarth’s Satire on False Perspective (1754_270ya)”
  • “The Spiralist”
  • “Differentiable Programming from Scratch”
  • “Renaissance Science – XXII”
  • “Optimized, Individualized Spaced Repetition in Hierarchical Knowledge Structures”, Skycak2024
  • “Best-Of-n With Misaligned Reward Models for Math Reasoning”
  • “A Mentor Challenged Bright Math Students And Changed Their Lives”
  • “Mathematical Notation: Past and Future”
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