The latest blog posts to take off on Hacker News. 2,851 posts.
In software programming, the product between two integers is often computed to a fixed number of bits with overflow. Consider 8-bit integers. If you multiply 127 by 127, you get back the number 1 as an 8-bit unsigned integer, with an overflow. The actual full product is 16129. To represent 16129, you typically use 16…
A visual explanation of how threshold secret sharing lets any k of n shares recover a secret.
The following pictures show $n$ unit squares packed inside the smallest known square (of side length $s$). If a pictured packing has multiple numbers in its label above, the picture represents the largest; each smaller is represented by removing any square. For the $n ≤ 324$ not pictured, the trivial packing (with no…
Classical CPU architecture is a poor choice for performing matrix-oriented computations. Developers have to spend much effort to create efficient algorithms even for the problems appearing trivial on the surface. Matrix transpose is probably the most striking representative of such problems. It exposes numerous…
Chess is a lot trickier than it looks. It has so many rules: castling, en passant, pawn promotion, pinning, the discovered check, and the de...
An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.
If you have ever tried to minimize a function with gradient descent, you probably noticed that some functions are a joy to optimize and others are a nightmare. The difference often boils down to two properties: strong convexity and L-smoothness. These two concepts define a “sandwich” of quadratic bounds around your…
ratios will be ratios
We are all having to keep revising upwards our assessments of the mathematical capabilities of large language models. I have just made a fairly large revision as a result of ChatGPT 5.5 Pro, to whi…
A deep dive on flow maps.
Where noise hides when deep neural networks generalize.
Studying brain scan data from individuals — not group averages — reveals key brain-function differences in children who struggle with goal-oriented tasks, a Stanford Medicine study found.
Practice machine learning engineering with hands-on coding challenges. Implement neural network components, backprop, and more — from scratch.
We sometimes have to look for a value in a sorted array. The simplest algorithm consists in just going through the values We sometimes have to look for a value in a sorted array. The simplest algorithm consists in just going through the values one by one, until we encounter the value, or exhaust the … Continue reading…
I have been told that when proposing to formalise mathematics these days, you have to explain why you are not using Lean. And that reminds me why I left the dependent-typed world 40 years ago: its cultism, insularity and conformity. Lean is a great language with good tools, a large library and a huge, enthusiastic…
Each mini-demo below covers one concept used later. Skip the ones you already know.
Learn about the real-life scientific applications of GeoNodes in Cosmology research.
When developing software to run in a Unix environment, you will often be able to use the same system features and benefit from good developer tools, regardless of the particular platform you're working on, as most processors will provide a rich instruction set and virtual memory, among other things.
There is no need to update symmetric key sizes as part of the post-quantum transition, due to the details of how Grover's algorithm scales. Most authorities agree.
Given a set of objects, there can be numerous criteria, based on which to order them (depending on the objects themselves) — size, weight, age, alphabetical order etc.
An exotic data structure and a whole lot of JOINs.
How does the geometry of a road unfold?
a personal blog
NB: The title of this post is an intentional clickbait. Even though I do stand for its statement, a more honest one would be something like: It's NOT OK to compare floating-points using epsilons.
AI agents are getting very good at finding vulnerabilities in large-scale software systems.
On your computer graphics journey, you will eventually run into some paper or code mentioning spherical harmonic functions. They are indeed a very useful tool: with just a few coefficients, they allow us to approximate a given function defined on a sphere. This can be very useful for modeling complex lighting.
<img src="http://stevehanov.ca/blog/images/acer.jpg"/> If you have a web site with a search function, you will rapidly realize that most mortals are terrible typists. Many searches contain mispelled words, and users will expect these searches to magically work. This magic is often done using levenshtein distance. In…
The graph, the viewer, and the verification tooling all live in the WeakC4 repository on GitHub .
