Bibliography:

doc tag
‘STEM humor’ tag
‘Transformer matrix optimizations’ tag
‘algorithms’ tag
‘computability’ tag
‘T_eX’ tag
‘Fermi problems’ tag
Number Search Engine via NN Embeddings
One Man’s Modus Ponens
Prediction Markets
Girl Scouts & Good Corporate Governance
Simulation Inferences
Fermat’s Last Theorem—How It’s Going
Math’s ‘Bunkbed Conjecture’ Has Been Debunked
Mixture of Parrots: Experts improve memorization more than reasoning
Industrious Dice [Minimizing Pip Counts on Still-Functional Dice]
Can OpenAI’s o1-Preview Ace the 2023 Putnam Exam?
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
To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning
I Have Played a Little Bit With OpenAI’s New Iteration, GPT-4 O1
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‘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
Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process
Learning Formal Mathematics From Intrinsic Motivation
MCTSr: Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMA-3-8B
AI Will Become Mathematicians’ ‘Co-Pilot’: Fields Medalist Terence Tao explains how proof checkers and AI programs are dramatically changing mathematics
OmegaPRM: Improve Mathematical Reasoning in Language Models by Automated Process Supervision
MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark
The Lessons of Hermann Grassmann and the Nature of Abstractions
8b226cb9ce8ab9549c0a7498d447eab00d2c7f9f.html#the-lessons-of-hermann-grassmann-and-the-nature-of-abstractions
Crows ‘count’ the number of self-generated vocalizations
DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data
Verified Neural Compressed Sensing
GSM1k: A Careful Examination of Large Language Model Performance on Grade School Arithmetic
Wu’s Method can Boost Symbolic AI to Rival Silver Medalists and AlphaGeometry to Outperform Gold Medalists at IMO Geometry
Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap
Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs
Autonomous Data Selection with Language Models for Mathematical Texts
Hamiltonicity of expanders: optimal bounds and applications
Leveraging Large Language Models to Boost Dafny’s Developers Productivity
Solving olympiad geometry without human demonstrations
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
TinyGSM: achieving >80% on GSM8k with small language models
Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models (ReST^EM)
Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning
Universal Self-Consistency for Large Language Model Generation
Training Chain-of-Thought via Latent-Variable Inference
Why Won’t OpenAI Say What the Q^✱ Algorithm Is? Supposed AI breakthroughs are frequently veiled in secrecy, hindering scientific consensus
Positional Description Matters for Transformers Arithmetic
GPQA: A Graduate-Level Google-Proof Q&A Benchmark
The Impact of Large Language Models on Scientific Discovery: a Preliminary Study using GPT-4
Implicit Chain-of-Thought Reasoning via Knowledge Distillation
Llemma: An Open Language Model For Mathematics
Let Models Speak Ciphers: Multiagent Debate through Embeddings
OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text
Distinct neuronal representation of small and large numbers in the human medial temporal lobe
MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models
FIMO: A Challenge Formal Dataset for Automated Theorem Proving
Papers with computer-checked proofs
Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification
Testing GPT-4 with Wolfram Alpha and Code Interpreter plug-ins on math and science problems
Solid-body trajectoids shaped to roll along desired pathways
Teaching Arithmetic to Small Transformers
Length Generalization in Arithmetic Transformers
LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
Let’s Verify Step by Step
A chiral aperiodic monotile
FERMAT: An Alternative to Accuracy for Numerical Reasoning
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)
How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model
Evaluating Transformer Language Models on Arithmetic Operations Using Number Decomposition
The spinorial ball: a macroscopic object of spin-1/2
How well do Large Language Models perform in Arithmetic tasks?
ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics
OEIS: A Handbook of Integer Sequences 50 Years Later
Solving math word problems with process & outcome-based feedback
What is my math transformer doing? – 3 results on interpretability and generalization
Broken Neural Scaling Laws
Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning
Mathematical Proof Between Generations
Connecting the Scientific and Industrial Revolutions: The Role of Practical Mathematics
NaturalProver: Grounded Mathematical Proof Generation with Language Models
HTPS: HyperTree Proof Search for Neural Theorem Proving
End-to-end symbolic regression with transformers
The sexes do not differ in general intelligence, but they do in some specifics
PaLM: Scaling Language Modeling with Pathways
Impact of Pretraining Term Frequencies on Few-Shot Reasoning
Exact Number Concepts Are Limited to the Verbal Count Range
Formal Mathematics Statement Curriculum Learning
Deep Symbolic Regression for Recurrent Sequences
Counting and the ontogenetic origins of exact equality
A Neural Network Solves and Generates Mathematics Problems by Program Synthesis: Calculus, Differential Equations, Linear Algebra, and More
What is the point of computers? A question for pure mathematicians
Scaling Language Models: Methods, Analysis & Insights from Training Gopher
Linear algebra with transformers
Training Verifiers to Solve Math Word Problems
MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics
A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers
SymbolicGPT: A Generative Transformer Model for Symbolic Regression
Basins with tentacles
Behavioral and Neuronal Representation of Numerosity Zero in the Crow
MathBERT: A Pre-Trained Model for Mathematical Formula Understanding
Constructions in combinatorics via neural networks
NaturalProofs: Mathematical Theorem Proving in Natural Language
Are NLP Models really able to Solve Simple Math Word Problems?
Measuring Mathematical Problem Solving With the MATH Dataset
TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning
Proof Artifact Co-training for Theorem Proving with Language Models
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
The Empirical Metamathematics of Euclid and Beyond
MMLU: Measuring Massive Multitask Language Understanding
Generative Language Modeling for Automated Theorem Proving
A Promising Path Towards Autoformalization and General Artificial Intelligence
Lights and Shadows
Singing Euclid: the oral character of Greek geometry
Mathematical Reasoning via Self-supervised Skip-tree Training
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
Learning to Prove Theorems by Learning to Generate Theorems
Transformers as Soft Reasoners over Language
Neural Arithmetic Units
Generative Language Modeling for Automated Theorem Proving § Experiments
Deep Learning for Symbolic Mathematics
The Lean mathematical library
Talent Search versus Talent Development
Do NLP Models Know Numbers? Probing Numeracy in Embeddings
Ternary circuits: why R=3 is not the Optimal Radix for Computation
MAWPS: A Math Word Problem Repository
Learning to Reason in Large Theories without Imitation
Analysing Mathematical Reasoning Abilities of Neural Models
Paul Erdős’s Mathematics As a Social Activity
Fancy Euclid’s Elements in T_eX
A randomized controlled trial of interleaved mathematics practice
Reinventing the Wheel: Discovering the Optimal Rolling Shape With PyTorch
The First Printed Math Books
1fad52b71b998e788c985ab0b0b2c9dd0eb8cc82.html
Making of Byrne’s Euclid
Best Practices: Formal Proofs, the Fine Print and Side Effects
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
Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems
The Reinhardt Conjecture as an Optimal Control Problem
The Doodle Theorem, and Beyond: Colin Wright Juggles Euler, Doodling and Millennium Problems
Solving General Arithmetic Word Problems
DeepMath: Deep Sequence Models for Premise Selection
A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory
The LEGO Counting Problem
Too good to be true: when overwhelming evidence fails to convince
Probabilistic Integration: A Role in Statistical Computation?
Random Gradient-Free Minimization of Convex Functions
Prizes and Productivity: How Winning the Fields Medal Affects Scientific Output
Is There a Curse of the Fields Medal?
The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems—Can We Trust in Them?
Interleaved Practice Improves Mathematics Learning
The case of the Case of Benny: Elucidating the influence of a landmark study in mathematics education
Neural Networks, Manifolds, and Topology
Finite time blowup for an averaged three-dimensional Navier-Stokes equation
Homotopy groups of suspended classifying spaces: An experimental approach
Mathematics in the Age of the Turing Machine
On Unsettleable Arithmetical Problems
The Algebraic Combinatorial Approach for Low-Rank Matrix Completion
How Did Software Get So Reliable Without Proof? [Blog]
Mind Switches in Futurama and Stargate
On the distribution of time-to-proof of mathematical conjectures
Vividness in Mathematics and Narrative
How to Write a 21^st Century Proof
Jewish Problems
The Cosmic Distance Ladder
Coolex: The coolest way to generate combinations
Packing Unit Squares in Squares: A Survey and New Results
Desperately seeking mathematical proof
The Gödel Letter
Physics, Topology, Logic and Computation: A Rosetta Stone
11858_2008_132_41_1-Web 45..60
Probing the Improbable: Methodological Challenges for Risks with Low Probabilities and High Stakes
The Epic Story of Maximum Likelihood
Overhang
The Monotype 4-Line System for Setting Mathematics
Maximum overhang
Computational Discovery in Pure Mathematics
Béla Bollobás: Graphs Extremal and Random [Interview of Béla Bollobás by Y. K. Leong]
How abstract is symbolic thought?
Comment on a Paper by Yucai Su On the Jacobian Conjecture (2005-12-30)
Proof of Two Dimensional Jacobian Conjecture
Monstrous Moonshine: The first 25 years
Online Convex Programming and Generalized Infinitesimal Gradient Ascent
EWD1300: The Notational Conventions I Adopted, and Why
Philosophical Problems in Logic § Ultrafinitism
Hymne to Hymen
The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen
Making Mathematics: The Coffee Connection
An Editor Recalls Some Hopeless Papers
How did software get so reliable without proof?
Light Shadows: Remembrances of Yale in the Early Fifties
Ten Lessons I Wish I Had Been Taught
Riemann zeta function is a fractal
A Visit to Hungarian Mathematics
Mathematics for Little Ones
Everything About Kolmogorov Was Unusual.
What in Heaven Is a Digital Sundial?
How I Was Led to the Frequency Approach
On the computational complexity of the Jones and Tutte polynomials
Factors and primes: a specific numerical ability
Envisioning Information: chapter 5, ‘Color and Information’, pg83-86 [on Oliver Byrne’s color diagram version of Euclid’s Elements]
Discussion: John von Neumann—A Case Study of Scientific Creativity
In Memory of Henry J. Kelley
Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems
The Printing of Mathematics
The Emergence of Princeton As a World Center for Mathematical Research, 1896--1939
8a85ac1a003826664827022e225240cccf621019.pdf
The Aesthetic Viewpoint in Mathematics
John Von Neumann As Seen By His Brother
The Back of the Envelope Returns
Review of Yuri I. Manin Yu, A Course in Mathematical Logic 1997
Terence Tao
The Back of the Envelope
Discrete Hartley transform
Are impossible figures possible?
On Number Numbness
Bi-continuous extensions of invertible combinatorial functions
Bouvet and Leibniz: A Scholarly Correspondence
The Letter S
Monstrous Moonshine
Some Proposals for Reviving the Philosophy of Mathematics
Heaviside's Operational Calculus and the Attempts to Rigorise It
Social Processes and Proofs of Theorems and Programs
Life at low Reynolds number
Randomness and Mathematical Proof
Constructing the sunflower head
The Legend of John Von Neumann
Benny’s conception of rules and answers in IPI mathematics
The Dangers of Computer-Science Theory
Nonstandard Analysis
Fidelity in Mathematical Discourse: Is One and One Really Two?
The Humble Programmer [EWD340]
Two-Circle Roller
Assigning Probabilities to Logical Formulas
Creativity in Science through Visualization
Singular Extremals In Lawden’s Problem Of Optimal Rocket Flight
A Steepest-Ascent Method for Solving Optimum Programming Problems
Method of Gradients
An Exceptional Talent For Calculative Thinking
Gradient Theory of Optimal Flight Paths
Toward Mechanical Mathematics
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
Non-Cooperative Games
Principles of the Self-Organizing Dynamic System
An Essay On The Psychology Of Invention In The Mathematical Field
A More Symmetrical Fourier Analysis Applied to Transmission Problems
Leonhard Euler's Elastic Curves
On a Problem of Formal Logic
Operational Methods in Mathematical Physics
The Foundations of Mathematics
Cutting a Round Cake on Scientific Principles
On Operators in Physical Mathematics. Part I
Packomania
Sculptures
ebb8482917bf213bcbb2c3f911f96d6e04149558.html
Adventures in Stacking
Extreme D&D DIY: Adventures in Hypergeometry, Procedural Generation, and Software Development (part 1)
Spaced Repetition for Mathematics
Why Momentum Really Works
1972 Talk at CERN on Scientific Research
How Should Mathematics Be Taught to Non-Mathematicians?
393f0df1d9a3d8a1800ccd5ccff8415fcc2184e2.html
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
3d8370396e0f4cb558594895101c9dfc4ba1bf3f.html
Oliver Byrne’s edition of Euclid’s Elements [Scans]
Chladni Figures (1787)
Solid Objects: 16^th-Century Geometric and Perspective Drawings
The Geometric Landscapes of Lorenz Stoer (1567)
William Hogarth’s Satire on False Perspective (1754)
The Spiralist
Differentiable Programming from Scratch
Renaissance Science – XXII
0785505553951c11a14f9e894d3cb7a15e62d659.html
Optimized, Individualized Spaced Repetition in Hierarchical Knowledge Structures
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Best-Of-n With Misaligned Reward Models for Math Reasoning
A Mentor Challenged Bright Math Students And Changed Their Lives
Trajectoid
Mathematical Notation: Past and Future
9f00052c868b2fd2504ca0cb6cf3d80baae4a5a6.html#frequency
GPT-3 calculating derivatives
The Examples Are Indeed Extremely Simple on Purpose (otherwise It’s Hard to Communicate Efficiently What’s Happening to Non-Metamath Experts). That Being Said, We’re Still Pretty Far Away from IMOs; but This Is Definitely a Goal for Us, and One We’re Actively Working Towards!
design#future-tag-features

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GSM1k: A Careful Examination of Large Language Model Performance on Grade School Arithmetic
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Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap
https%253A%252F%252Farxiv.org%252Fabs%252F2402.19450.html
Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs
https%253A%252F%252Farxiv.org%252Fabs%252F2402.14903.html
Autonomous Data Selection with Language Models for Mathematical Texts
https%253A%252F%252Farxiv.org%252Fabs%252F2402.07625.html
PRER: Modeling Complex Mathematical Reasoning via Large Language Model based MathAgent
https%253A%252F%252Farxiv.org%252Fabs%252F2312.08926.html
Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models (ReST^EM)
Abhishek Kumar
Igor Mordatch
Behnam Neyshabur
Jascha Sohl-Dickstein
https%253A%252F%252Farxiv.org%252Fabs%252F2312.06585%2523deepmind.html
Training Chain-of-Thought via Latent-Variable Inference
https%253A%252F%252Farxiv.org%252Fabs%252F2312.02179.html
OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text
https%253A%252F%252Farxiv.org%252Fabs%252F2310.06786.html
MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models
https%253A%252F%252Farxiv.org%252Fabs%252F2309.12284.html
Papers with computer-checked proofs
https%253A%252F%252Fcr.yp.to%252Fpapers%252Fpwccp-20230907.pdf.html
Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification
https%253A%252F%252Farxiv.org%252Fabs%252F2308.07921.html
Teaching Arithmetic to Small Transformers
https%253A%252F%252Farxiv.org%252Fabs%252F2307.03381.html
LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
https%253A%252F%252Farxiv.org%252Fabs%252F2306.15626.html
Let’s Verify Step by Step
Jan Leike
John Schulman’s Homepage
https%253A%252F%252Farxiv.org%252Fabs%252F2305.20050%2523openai.html
How well do Large Language Models perform in Arithmetic tasks?
https%253A%252F%252Farxiv.org%252Fabs%252F2304.02015%2523alibaba.html
ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics
https%253A%252F%252Farxiv.org%252Fabs%252F2302.12433.html
OEIS: A Handbook of Integer Sequences 50 Years Later
http%253A%252F%252Fneilsloane.com%252Fdoc%252FHIS50.pdf.html
NaturalProver: Grounded Mathematical Proof Generation with Language Models
Hannaneh Hajishirzi—University of Washington
https%253A%252F%252Farxiv.org%252Fabs%252F2205.12910%2523allen.html
HTPS: HyperTree Proof Search for Neural Theorem Proving
https%253A%252F%252Farxiv.org%252Fabs%252F2205.11491%2523facebook.html
The sexes do not differ in general intelligence, but they do in some specifics
%252Fdoc%252Fiq%252F2022-reynolds.pdf.html
PaLM: Scaling Language Modeling with Pathways
Yi Tay
https://x.com/jekbradbury
Vedant Misra
Barret Zoph
Jason Wei
https%253A%252F%252Farxiv.org%252Fabs%252F2204.02311%2523google.html
Formal Mathematics Statement Curriculum Learning
https%253A%252F%252Farxiv.org%252Fabs%252F2202.01344%2523openai.html
Counting and the ontogenetic origins of exact equality
%252Fdoc%252Fmath%252F2022-schneider.pdf.html
A Neural Network Solves and Generates Mathematics Problems by Program Synthesis: Calculus, Differential Equations, Linear Algebra, and More
https%253A%252F%252Farxiv.org%252Fabs%252F2112.15594.html
Scaling Language Models: Methods, Analysis & Insights from Training Gopher
Karen Simonyan
https://x.com/jekbradbury
Koray Kavukcuoglu
https%253A%252F%252Farxiv.org%252Fabs%252F2112.11446%2523deepmind.html
Training Verifiers to Solve Math Word Problems
Jacob Hilton's Homepage
John Schulman’s Homepage
https%253A%252F%252Farxiv.org%252Fabs%252F2110.14168%2523openai.html
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
https%253A%252F%252Fwww.quantamagazine.org%252Fhow-the-slowest-computer-programs-illuminate-maths-fundamental-limits-20201210%252F.html
MMLU: Measuring Massive Multitask Language Understanding
https://people.eecs.berkeley.edu/~hendrycks/
Steven's Web Thoughts
Andy Zou
Mantas Mazeika
Jacob Steinhardt
https%253A%252F%252Farxiv.org%252Fabs%252F2009.03300.html
Generative Language Modeling for Automated Theorem Proving
https%253A%252F%252Farxiv.org%252Fabs%252F2009.03393%2523openai.html
A randomized controlled trial of interleaved mathematics practice
Doug Rohrer
%252Fdoc%252Fpsychology%252Fspaced-repetition%252F2019-rohrer.pdf.html
Making of Byrne’s Euclid
https%253A%252F%252Fwww.c82.net%252Fblog%252F%253Fid%253D79.html
Homotopy groups of suspended classifying spaces: An experimental approach
%252Fdoc%252Fmath%252F2013-romero.pdf.html
On Unsettleable Arithmetical Problems
%252Fdoc%252Fcs%252Fcomputable%252F2013-conway.pdf.html
Online Convex Programming and Generalized Infinitesimal Gradient Ascent
%252Fdoc%252Fmath%252F2003-zinkevich.pdf.html
Envisioning Information: chapter 5, ‘Color and Information’, pg83-86 [on Oliver Byrne’s color diagram version of Euclid’s Elements]
%252Fdoc%252Fdesign%252Ftypography%252Frubrication%252F1990-tufte-envisioninginformation-ch5-byrneseuclid.pdf.html
Terence Tao
%252Fdoc%252Fiq%252Fhigh%252Fsmpy%252F1984-clements.pdf.html
Benny’s conception of rules and answers in IPI mathematics
%252Fdoc%252Fmath%252F1973-erlwanger.pdf.html
An Essay On The Psychology Of Invention In The Mathematical Field
https%253A%252F%252Farchive.org%252Fdetails%252Feassayonthepsych006281mbp.html
Wikipedia Bibliography: