How real are real numbers? (2004)
Summary
An exploration of the philosophical nature of real numbers, questioning their reality and foundations in mathematics.
Similar Articles
RealMath-Eval: Why SOTA Judges Struggle with Real Human Reasoning
RealMath-Eval is a benchmark of 224 real-world high school math exam responses that reveals a significant 'Evaluation Gap': state-of-the-art LLM judges perform poorly on authentic human reasoning (MSE ~2.96) compared to synthetic LLM-generated solutions (MSE ~1.17), due to higher diversity and surprisal in human error patterns.
The Crisis in Mathematics and the Prospect of AIcademia
A philosopher's essay on how AI reasoning models are disrupting mathematics, solving long-standing conjectures and forcing academia to rethink the future of research.
Revisiting AI consciousness
A philosophical discussion questioning whether humans can objectively prove their consciousness in a way that current AI cannot, highlighting the subjective nature of such proof.
From Geometry to Algebra and Back Again: 4000 Years of Papers (2023) [video]
This video summarizes the 4000-year evolution of mathematics, from ancient geometric reasoning to modern algebraic notation, emphasizing how symbolic systems serve as cognitive tools for thought.
A philosophical reflection on the problem of approximation in mathematics, finance, and AI, discussing how models are imperfect but useful, and the implications for AI safety and machine consciousness
A philosophical reflection on the problem of approximation in mathematics, finance, and AI, discussing how models are imperfect but useful, and the implications for AI safety and machine consciousness.