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Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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World's shortest explanation of Gödel's theorem
From the highly eclectic blog of Mark Dominus
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Unparalleled Misalignments
This is a list of Unparalleled Misalignments, pairs of non-synonymous phrases where the words in one phrase are each synonyms of the words in the other. I've maintained this list since 2018; attributions (when known) can be seen on hover.
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Experiment with Penrose Tilings and other patterns
Create And Share Mathematical Tiling Patterns
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Faster convergence for diffusion models
Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think
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2D Terrain generation using midpoint displacement
Today I will present how to implement in Python a simple yet effective algorithm for proceduraly generating 2D landscapes. It is called Midpoint Displacement (or Diamond-square algorithm,…
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Why Data Structures Matter: left, right folds, btrees
Our experience on Day 0 of JPR11 yielded a nice example of the need to choose an appropriate implementation of an abstract concept. As I mentioned in the previous post, we experimented with Michael…
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Learning to Play the Chaos Game
I, Thomasina Coverly, have found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone…
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PageRank explained
Picture this, the year is 1996. You find yourself frustrated with the incumbent search engines like AltaVista, which primarily does a content-based search (it'll give you an article on "Hotels for Chickens" if you search "Hotels" because the word matches). There's gotta be a better way, right? Well, in hindsight, of…
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The ABC conjecture has still not been proved
Five years ago, Cathy O’Neil laid out a perfectly cogent case for why the (at that point recent) claims by Shinichi Mochizuki should not (yet) be regarded as constituting a proof of the ABC conjecture. I have nothing further to add on the sociological aspects of mathematics discussed in that post, but I just wanted to…
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The Myers diff algorithm: part 1
If you enjoy this article, I have published a book explaining the internals of Git through implementation: Building Git .
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Abstract algebra for developers and people who hate math
Hi. I think math is really cool, but, most people (sadly) don't think so. This includes many programmers who in fact enjoy many of the sam...
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Visualizing Bayes Theorem (2009)
I recently came up with what I think is an intuitive way to explain Bayes’ Theorem. I searched in google for a while and could not find any article that explains it in this particular way.
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Review: The Book of Why
The Book of Why: The New Science of Cause and Effect is a collaborative effort aimed at a general audience by Judea Pearl , a professor of computer science at UCLA, and Dana Mackenzie , a science writer. As a medical student with a laughably poor formal education in statistics, I believe I qualify as a card-carrying…
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Building a Regex Engine in Fewer Than 40 Lines of Code
A blog about programming and modern web development, particularly Node.js and React
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Hash Functions all the way down
Update! I tested more hash functions in a follow-up post. See More Hash Function Tests .
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Why EdDSA held up better than ECDSA against Minerva
"Minerva attack can recover private keys from smart cards, cryptographic libraries" , says the ZDNet headline. "The Czech team found a problem in the ECDSA and EdDSA algorithms used by the Atmel Toolbox crypto library to sign cryptographic operations on Athena IDProtect cards."
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Zero Zero
I've been thinking about something that we always did junior year when I was on my high school soccer team. When we'd score a goal, we reali...
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Faster Than Dijkstra?
Does a new algorithm that improves on Dijkstra'a classic one actually deliver a practical benefit for networking?
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When Double Precision Is Not Enough
Using greater than double precision to calculate the eigenvalues of the lesp matrix.
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Gradients Are the New Intervals
At the New England Symposium on Graphics , James Tompkin compared graphics researchers to magpies: they're easily distracted by shiny objects and pretty renderings.
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Demystifying Floating Point Precision
Floating point numbers have limited precision. If you are a game programmer, you have likely encountered bugs where things start breaking after too much time has elapsed, or after something has mov…
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Einsum Is All You Need – Einstein Summation in Deep Learning (2018)
Tim Rocktäschel — Co-Founder and Chief Scientist of Recursive; Professor of AI at UCL. Artificial General Intelligence, Open-Endedness, and Recursive Self-Improvement.
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Predict the future with Machine Learning
Learn Machine Learning (ML) and be ahead of the pack in the Software industry. Machine Learning is a sub-field of Artificial Intelligence (A.I), which is heavily used in modern software systems. Machine Learning algorithms can improve software (a robot) and it's ability to solve problems through gaining experience and…
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Does having prime neighbors make you more composite?
Babylonian accountants and land surveyors did their arithmetic in base 60, presumably because sexagesimal numbers help with wrangling fractions. When you organize things in groups of 60, you can divide them into halves, thirds, fourths, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thirtieths, and…