History
Intuition, Complexity and The Last Paradox
AI since Artistotle (Part 3)
Latest
Differential Equations
The “Well-Posedness” of Differential Equations: the Sense of Hadamard
An overwhelmingly large portion of our modeling of the universe is accomplished by posing and solving differential equations..
Machine Learning
Getting Started with Random Matrices: A Step-by-Step Guide
In the Deep Learning (DL) age, more and more people have encountered and used (knowingly or not) random matrices. Most of the time this use is limited to the initialization of the networks weights, that can be accomplished with a single line of code in your favorite DL framework.
Logic
Logic, Intuition and Paradox
AI since Aristotle (Part 1)
History
The Limit of Logic and The Rise of The Computer
AI since Aristotle (Part 2)
Physics
Inverse-Square Law of Gravitation: The Role of the Apple and the Moon
How Newton confirmed the inverse-square law
Gödel
Gödel’s First Incompleteness Theorem in Simple Symbols and Simple Terms
The following piece explains a particular symbolic expression (or version) of Kurt Gödel’s first incompleteness theorem. It also includes a particular expression (or example) of a Gödel sentence (i.e., “This statement is false”)
Statistics
Maximum Likelihood Estimate
Part 2: Mixture Models
Hardy
G. H. Hardy — Rigorous & Shy
Beauty is the first test: There is no permanent place in the world for ugly mathematics. — GH Hardy in A Mathematician’s Apology
Logic
Only So Much We Can Prove
A Glimpse of Incompleteness
Algebra
The Swirling Power Of Algebra
Equations are more mysterious than we think
Probability Theory
Maximum Likelihood Estimate
Part 1: How to best fit a Gaussian