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SATisfying Solutions to Difficult Problems
This post covers the same material as my !!Con 2024 talk , for which the slides are here .
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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The Busy Beaver Game
This month, a bunch of ‘logic hackers’ have been seeking to determine the precise boundary between the knowable and the unknowable. The challenge has been around for a long time. But on…
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Skip Lists are Fascinating
Skip lists are a fascinating data structure: very simple, and yet have the same asymptotic efficiency as much more complicated AVL trees and red-black trees.
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Decision Table Patterns
Decision tables are easy, simple, and powerful. You can teach them in five minutes and write one in half that time. You can look at a table and understand what it’s saying, see if it matches your problem, and check for design flaws. So it’s kinda weird that there’s basically nothing about them online. I wrote an…
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Abel, the Mozart of Mathematics
“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
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RSA: Theory and Implementation
RSA has been a staple of public key cryptography for over 40 years, and is still being used today for some tasks in the newest TLS 1.3 standard. This post describes the theory behind RSA - the math that makes it work, as well as some practical considerations; it also presents a complete implementation of RSA key…
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Bitwise Binary Search: Elegant and Fast
I recently read the article Beautiful Branchless Binary Search by Malte Skarupke. In it they discuss the merits of the following snippet of C++ code implementing a binary search :
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The Viterbi Algorithm at 50 (2017)
In a noisy world, it allows you to be heard.
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TypeScript and Set Theory
How does set theory help to understand type assignability and resolution in TypeScript?
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You've heard of Markov chains. But who was Markov?
Harvard celebrates the 100th anniversary of a computational principle that was little noticed in its time, but that underlies all of modern science.
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The Single Rotation rule: simple and rich reversible cellular automaton (2013)
See also other posts tagged Single Rotation . In the previous post I have presented the Reversible Cellular Automata simulator , along ...
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A Gentle Introduction to Backpropagation
A gentle introduction to backpropagation, a method of programming neural networks
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An Introduction to Hierarchical Modeling
A visual explanation of multi-level modeling
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Zero-allocation Trie Traversal
As part of a demonstration in an upcoming article , I wrote a simple trie implementation. A trie is a search tree where the keys are a sequence of symbols (i.e. strings). Strings with a common prefix share an initial path down the trie, and the keys themselves are stored implicitly by the structure of the trie. It’s…
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Avoiding visible texture repetition (2015)
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
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Modelling a Basic Income with Python and Monte Carlo Simulation
Basic Income is a popular policy floating around the internet lately. The idea consists of declaring that the government will pay each living adult a fixed amount of money every month - an amount comparable to a minimum wage job. This policy would then replace all current welfare programs - welfare, unemployment …
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The largest number representable in 64 bits
A rewrite of this blog post with many new insights and updates appeared in Jan 2026
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Million Times Million
Is a million times a million a billion or is it a trillion ? For my entire childhood, it was a billion, only for me to grow up and realise, as an adult, that it had better be a trillion!
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Math for kids outside of the Calculus Sequence
The Enrichment side of the "Accelerate vs Enrich" dichotomy in math education for kids who love math.
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Two Workers Are Quadratically Better Than One
For latency, anyway. A common architecture pattern is the “task queue”: tasks enter an ordered queue, workers pop tasks and process them. This pattern is used everywhere from distributed systems to thread pools. It applies just as well to human systems, like waiting in line at a supermarket or a bank. Task queues are…
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Mathematical Jargon Failures
From the highly eclectic blog of Mark Dominus
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Closing the “green gap”: energy savings from the math of the landscape function
I recently returned from the 2025 Annual Meeting of the “Localization of Waves” collaboration (supported by the Simons Foundation, with additional related support from the NSF), where I…