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The most popular blog posts about math & algorithms on Hacker News. 266 posts.
Ever wondered how the ^.?$|^(..+?)\1+$ regular expression can tell you if a number is not prime? In this blog post you'll learn how and why it works. Code examples in Java, JavaScript, Python and Perl are provided.
Hugo Hadfield - Cross stack robotics engineer and computer vision researcher specializing in deep learning, sensor fusion, geometric algebra and applications in self-driving cars and robotic manipulation.
While reading Real-World Cryptography , I came across the "million message attack" . This is an attack that Daniel Bleichenbacher demonstrated in 1998, which effectively broke RSA with a particular encoding function called PKCS #1 . It was only mentioned briefly, so I dug in and decided to try to understand the…
Compute this limit more accurately with one weird trick!
The boolean satisfiability problem (“SAT” for short) is arguably the most famous NP-complete problem in theoretical computer science. According to Wikipedia, it is “the problem of determining if there exists an interpretation that satisfies a given Boolean formula ”; or, in simpler terms, if there is at least one…
Visualizations and techniques for different maze generation algorithms.
Database queries are a pretty surprisingly powerful tool that can solve seemingly intractable problems.
The **Gaussian distribution**, or **normal distribution** is a key subject in statistics, machine learning, physics, and pretty much any other field that deals with data and probability.
Using transformed ellipses to estimate perspective transformations of text.
“If you look at zero you see nothing; but look through it and you will see the world.”
1) Foundational math. 2) Classical machine learning. 3) Deep learning. 4) Cutting-edge machine learning.
Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think
The enduring success of her early 19th century novels are in large part due to their persistent relevance
We estimate the magnitude of speed improvement for optimization solvers and computer hardware in the 35 years from 1989 to 2024.
There's been a fair bit of buzz about Kolmogorov-Arnold networks online lately. Some research papers were posted around claiming that they offer better accuracy or faster training compared to traditional neural networks/MLPs for the same parameter count.
Web site content explains the modern view of entropy change and the dispersal of energy in a process (at a specific temperature). It has been selected for instructors in general and physical chemistry by Dr. Frank L. Lambert, Professor Emeritus (Chemistry) of Occidental College, Los Angeles.
Can I make math operations run 100x faster on really, really big numbers?
Yesterday John Graham-Cumming posted about “Steve Ballmer’s incorrect binary search interview question,” and in the Hacker News discussion, among the predictable “interview culture is flawed!!” complaints, there was some discussion of whether binary search was even the right way to solve Ballmer’s puzzle. Here’s a…
Important new study from Apple
One weird hobby of mine is reasonable properties of cryptographic schemes that nobody promised they do or don’t have. Whether that’s invisible salamanders or binding through shared secr…
Lambda Screen allows you to draw images using terms of pure lambda calculus. By using fixed-point combinators, you can even create infinitely detailed fractals.
This is a tale of two approaches to regular expression matching. One of them is in widespread use in the standard interpreters for many languages, including Perl. The other is used only in a few places, notably most implementations of awk and grep. The two approaches have wildly different performance characteristics:
Goodhart's Law is useless. It tells you about a phenomenon, but it doesn't tell you how to solve it. We look at how organisations actually prevent Goodhart's Law, and illustrate this with Amazon's Weekly Business Review as an example.
(I've been editing this post on and off for almost a year. I'm not really happy with it, but I suspect I never will be.)
Wolfram tech and its dedicated website now easily predict eclipses. A look at advances in understanding and science from ancient eclipse data thousands of years old through current eclipse calculations.
A useful theorem attributed to the probably first mathematician ever, Thales of Miletus (ca. 624 BC-ca. 546 BC) is one of most elementary and intuitive ever stated.
In many large-scale web services, multiple layers of stateless and stateful services are seperated by load balancers. Load balancing can be done with dedicated hardware, with dedicated software load balancers, using DNS trickery or through a load-balancing mechanism in the client. In large systems, the resources and…
