William Thurston

By

William Thurston

Cornell Conference on William Thurston (2014)

Polyhedra

Shapes of Polyhedra and Triangulations of the Sphere

John Baez: Triangulations of the Sphere

Richard Schwarz: Notes on Shapes of Polyhedra

Proof and Progress

On Proof and Progress in Mathematics 

YouTube





Comments

Post a Comment

Popular posts from this blog

Computing and the Linguistic Turn

By
Image
Enigma (Wikipedia) Symbolic analysis and statistical analysis were both approaches codebreakers took in breaking Enigma. The development of AI has also incorporated both approaches. One historical question for AI is why the dominance of Symbolic AI, associated here with the linguistic turn, from 1950 to 1990? Note the development of AI out of the Dartmouth Workshop and especially the contributions of one of its attendees,  Ray Solomonoff , to the statistical approach, an approach taken up by Marcus Hutter , a DeepMind  researcher, and of course, others. Note that a history of AI outside the linguistic turn from Moritz Hardt and Ben Recht is in Patterns, Predictions, and Actions . And note too that along with the difference between the symbolic and the statistical is the difference between language learning and computer vision, which tends to be a history outside the linguistic turn. And the turn Richard Sutton takes is to push learning outside the context of language, which ...
Read more

How Does AI Solve Erdős Problems? - AI

By
Image
Erd ő s Problems List of Conjectures Erd ő s Problems On ChatGPT as Solver On Liam Price Terence Tao Tao AI AI solves Erdős problems through a combination of Large Language Models (LLMs) for generating creative proofs and formal verification tools like Lean 4 to ensure mathematical correctness . [ 1 , 2 , 3 ] Recent breakthroughs, such as the resolution of Erdős Problem #728 and #1196 , have used specialized workflows where AI acts as a "junior co-author" to discover novel connections that human mathematicians had previously overlooked. [ 1 , 2 , 3 , 4 , 5 ] The Core Solving Process Solving these open conjectures typically involves a "loop" between a reasoning model and a formal verifier: Creative Brainstorming : A model (like GPT-5.2 or GPT-5.4) is prompted to research the problem and brainstorm novel mathematical strategies. Generating informal Proofs : The AI writes a mathematical paper in LaTeX, often discovering "elegant" methods, such as using th...
Read more

A Heidegger - Bayes Hybrid Model

By
Image
A Conjecture for a Hybrid Model Bayesian epistemology concerns modelling and specifically, belief, but a Bayesian belief does not need to be fully formed to emerge alongside the Heideggerian to-hand. The Heideggerian to-hand thereby becomes the interaction that generates this further, which is, with this interaction, a certain realization of being in the world. Bayesian selection now concerns available beliefs as well as any to-hand [belief(s)]. How Heidegger Can Make You a Better Guitarist Bayesian Philosophy Bayesian Philosophy Bayesian Epistemology Bayesian Epistemology Bayesian Modelling Bayesian Modelling Bayesian Model Selection David Deutsch on Bayesian Epistemology Bayesian Philosophy of Science Bayesian Philosophy of Science A Bayesian Approach to the Philosophy of Science On Sean Carroll on an Application of Bayes The Heideggerian To-Hand On Heidegger On Heidegger Flipping Descartes Ready-to-Hand and Present-at-Hand Presence-at-Hand Ready-to-Hand and Unready-to-Hand Does Hei...
Read more