Category: Mathematics

The Case for Artisanal Programming
“How to Make $100/hr as a Freelance Software Developer (No Degree Required)” a YouTube video title reads — with a quartermillion views to boot. “Turning code to cash — How to make money as a Web Developer” is the title of a Medium article published by freeCodeCamp. It’s obvious that programming is hot right now — with […]

Gödel’s Second Incompleteness Theorem for Programmers
In the previous blog post in this series, we looked at Gödel’s First Incompleteness Theorem, and came to the amazing conclusion that we can’t compute certain kinds of functions in formal systems (like Javascript). Specifically, we looked at a special function, , which turned out to be noncomputable. In case we forgot, the first incompleteness […]

Gödel’s First Incompleteness Theorem for Programmers
Gödel’s incompleteness theorems have been hailed as “the greatest mathematical discoveries of the 20th century” — indeed, the theorems apply not only to mathematics, but all formal systems and have deep implications for science, logic, computer science, philosophy, and so on. In this post, I’ll give a simple but rigorous sketch of Gödel’s First Incompleteness […]

Confusing Math with Morality
This essay is in response to Counterintuitive problem: Everyone in a room keeps giving dollars to random others. You’ll never guess what happens next. Dan Goldstein attributes the problem to Uri Wilensky, of Northwestern, who formulates it thusly: Imagine a room full of 100 people with 100 dollars each. With every tick of the clock, […]

How to prove there is no Universe
Years ago, when I first read Paul Halmos’ seminal Naive Set Theory, I was blown away by how easy it was to prove that there is no universe. In fact, not even three sections in, he drops this italicized bombshell: $$nothing\text{ }contains\text{ }everything$$ or, “more spectacularly,” he continues $$there\text{ }is\text{ }no\text{ }universe$$ Luckily, we only […]