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The Fast Fourier Transform
It’s often said that the Age of Information began on August 17, 1964 with the publication of Cooley and Tukey’s paper, “An Algorithm for the Machine Calculation of Complex Fourier…
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 82 posts.
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Traveling Salesman: the most misunderstood problem
Whenever people start talking about NP-Complete problems, or even NP problems, one of the first examples they reach for is the classic Traveling Salesperson Problem. TSP makes sense because it int...
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Does one have to be a genius to do maths?
Better beware of notions like genius and inspiration; they are a sort of magic wand and should be used sparingly by anybody who wants to see things clearly. (José Ortega y Gasset, “Notes on t…
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Gödel's Incompleteness Theorem explained
This theorem is one of the most important proven in the twentieth century. Here are a few brief selections that will help you start to understand it. Gödel’s original paper “On Formally Undecidable Propositions” is available in a modernized translation . It’s also in print from Dover in a nice, inexpensive edition …
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What is static program analysis?
The halting problem asks whether the execution of a specific program for a given input will terminate.
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Who Expected That? Extreme close-ups create a Klein Bottle.
Suppose you go around taking extremely close-up black-and-white pictures of randomly chosen natural and unnatural objects (rocks, trees, streams, buildings, etc.). What do they look like? Well, eac…
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Tabasco Sort: a super-optimal merge sort
Paul Khuong's personal blog. Some Lisp, some optimisation, mathematical or computer.
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Incremental Regular Expressions
This article was originally published in the Russian functional programming journal http://fprog.ru/ and this translation was intended to be published in Peter Seibel’s http://codequarterly.com/ journal, but as Peter eventually decided not to proceed with the journal, I am publishing it on my personal space.
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What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?
I’m eager to summarize the (largely excellent) discussion of last week’s nightmares and to talk about what it all means. I’ll surely get to that in the next few days. But meanwhil…
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Factorization diagrams in Haskell
Meta Title: Math, Sports Data & IPTV: A Portugal Guide Meta Description: Explore how math-minded sports fans use IPTV in Portugal to watch live football, Champi
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Myths about Hash Tables
A hash table is data structure that is used to search for exact matches to a search key. For searching, they work like this: Take a search key (example: the word “cat”) Hash the search …
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The Opposite of a Bloom Filter
A Bloom filter is a data structure that may report it contains an item that it does not (a false positive), but is guaranteed to report correctly if it contains the item (“no false negatives”). The opposite of a Bloom filter is a data structure that may report a false negative, but can never report a false positive…
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Kolmogorov Complexity - A Primer
The Complexity of Things Previously on this blog (quite a while ago), we’ve investigated some simple ideas of using randomness in artistic design (psychedelic art, and earlier randomized css …
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Finding Unity in the Math Wars
I usually avoid current events, but recent skirmishes in the math world prompted me to chime in. To recap, there've been heated discussions about math…
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A group of Finnish math teachers write an open textbook in a weekend hackathon
A group of Finnish mathematics researchers, teachers and students write an upper secondary mathematics textbook in a booksprint. The event s...
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The birthday paradox in action: calculating the probability of a hash collision
You may feel like you've seen this before. If you have, skip to the end where I talk about a formula, and discuss the relevance to parameters in computer hashing algorithms. In particular, I'm going to talk about how large hash spaces should be to avoid collisions with a given level of probability. If there are just…
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An Intuitive Explanation of Bayes' Theorem
Bayes’ Theorem for the curious and bewildered; an excruciatingly gentle introduction.
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