AI Advancements and Analysis
We track real AI advancements each week, with independent benchmarks and step by step guides. Clear takeaways, no fluff.
Featured AI Research & Essential Guides
Making sense of it all: explore our research explainers, AI benchmarks and practical guides.
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Number theory
Catalan’s Constant: OpenAI’s Irrationality Argument
Why a familiar constant resisted proof, and how the proposed argument works.
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Formal proofs
Fermat’s Last Theorem: What Claude Formalized in Lean
The difference between solving a theorem and making its proof machine-checkable.
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Algorithms
OpenAI Matrix Multiplication: The 2.25 Bound
The mathematical strategy behind the proposed exponent bound and its practical limits.
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Number theory
The Irrationality Exponent of Pi: OpenAI’s Claim of 2
What rational approximations reveal about pi, and what the manuscript claims.
More Research, Benchmarks & Practical Guides
- Hilbert’s 10th Problem over the RationalsResearch
- Discrete Fourier Transform: The n log n BarrierResearch
- Integer Multiplication below n log nResearch
- Quasi-Riemann Hypothesis: Understanding the 7/8 ClaimResearch
- Kaplansky’s Zero Divisor Conjecture: The CounterexampleResearch
- Cannon’s Conjecture: Groups Meet 3D GeometryResearch
- Mahler’s Conjecture: The Geometry behind the ClaimResearch
- Exponential Time Hypothesis: The Proposed 3-SAT AlgorithmResearch
- Hilbert’s 16th Problem: Uniform Bounds for Limit CyclesResearch
- Derandomization of Logarithmic Space: L = RL = BPLResearch
- Partition Principle versus the Axiom of ChoiceResearch
- Unique Games Conjecture: Approximation Limits ExplainedResearch
- AI IQ Test: Compare Model Reasoning and IntelligenceLeaderboard
- Best LLM for Coding: Benchmarks and Model ComparisonBenchmark
- LLM Math Benchmarks: Compare Mathematical ReasoningBenchmark
- How to Use OpenAI Codex: Setup and Practical WorkflowsGuide
- OpenRouter: Models, Pricing, API and Usage GuideReview
- LLM Pricing Comparison: Understand Model CostsComparison
- AgentKit: Pricing, Access and Agent SetupGuide
- MedGemma 1.5: A Practical Local Medical AI GuideHealthcare
- AI Accelerators: GPUs, TPUs and Specialized ChipsHardware
- AlphaEarth: Google’s Planetary AI ExplainedEarth science
- AI Textbooks: How Learn Your Way Changes StudyingEducation
- Psychology of AI: Understanding the PsAIch EvaluationPsychology
