The latest blog posts to take off on Hacker News. 2,851 posts.
Traditionally, mathematics research projects are conducted by a small number (typically one to five) of expert mathematicians, each of which are familiar enough with all aspects of the project that…
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I discuss various models of biased bit sequences, and how to extract uniform random (or close to it) output bit sequences from them, illustrated with Python code.
By Devine Lu Linvega
Automated reasoning and optimizations specific to CPU microarchitectures improve both performance and assurance of correct implementation.
We are introducing OpenAI o1, a new large language model trained with reinforcement learning to perform complex reasoning. o1 thinks before it answers—it can produce a long internal chain of thought before responding to the user.
In my puzzle collection , there are many games in which you have to connect points together by edges, making a graph, and the puzzle rules say you must avoid making any loop in the graph. Examples are Net , Slant , and some configurations of Bridges (although not the default one). Loopy and Pearl also care about…
The article explains the Bell inequality using Monte Carlo simulations in Python, and shows how non-local action-at-a-distance can be used to break it with entangled qubits.
I got an email the other day from mathematician Bogdan Grechuk, whose book Polynomial Diophantine Equations: A Systematic Approach ( was recently released. This is to my mind a rather remarkable bo…
A few days ago John Graham-Cumming posted about “Steve Ballmer’s incorrect binary search interview question” which drew a lot of attention on Hacker News. The Ballmer’s favorite brain teaser goes like this:
Cosine similarity measures the angle between two vectors — the dot product divided by the product of their magnitudes. Here's what each part of the formula does.
A deep dive into spectral analysis of diffusion models of images, revealing how they implicitly perform a form of autoregression in the frequency domain.
This article is about the Y combinator, a fixed-point combinator that provides a way of using recursion in scenarios and programming languages where symbols are not available. The concept of the Y combinator itself is closely related to lambda calculus (λ-calculus) and functional programming languages. More…
Interactive Mathematical Applets and Animations
Once upon a time I was given the following problem for a technical programming interview:
floating-points-between-zero-and-one - Chad Nauseam Home
I recently learned an interesting fact about Fibonacci numbers while watching a random number theory video on YouTube. Fibonacci numbers can be used to approximately convert from miles to kilometers and back. Here is how. Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No...
EDIT: Be warned that this post is angry. If you’re easily offended when someone goes on a rant, then leave now because I’m very unforgiving in several places below. The tone of my writing is unusually harsh, but the people whose work I’m talking about deserve it, and here’s why. Even though I had been working with…
Visualizations and techniques for different maze generation algorithms.
Stephen Wolfram explores minimal models and their visualizations, aiming to explain the underneath functionality of neural nets and ultimately machine learning.
Pathfinding applied to the software solution domain
1) Foundational math. 2) Classical machine learning. 3) Deep learning. 4) Cutting-edge machine learning.
“Although Abel shared with many mathematicians a complete lack of musical talent, I will not sound absurd if I compare his kind of productivity and his personality with Mozart’s.” — Felix Klein
Personal website of Dr. Peder M. Isager
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
Efficient filtering of polygonal shapes with closed-form solutions based on Green’s theorem with piecewise-polynomial filters (e.g. box/bilinear/bicubic).
Sweep-and-prune is my go-to algorithm when I want to quickly implement collision detection for a game. I think it’s an awesome and elegant algorithm, so I wrote a post about it.
