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An Intuitive Explanation of Bayes' Theorem
Bayes’ Theorem for the curious and bewildered; an excruciatingly gentle introduction.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,394 posts.
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Sinusoidal Sunlight
The graph of daylight over the course of a year looks like a sine wave, but is it?
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Formally Modeling Dreidel, the Sequel
2 model 2 dreidel
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Two-part Rubik's algorithms
When Rubik’s Cube first appeared decades ago, I jumped on it. I bought one, and spent an entire summer fiddling with it. Over that summer, I developed a solving technique that has stuck with me. My technique is not the fastest; that was never the goal. My algorithms make sense to me because they are constructed, and…
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Jacobian Conjecture for Baby
An illustrated guide that starts from the basics, explains the Jacobian Conjecture, and follows what happened to it in July 2026.
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Calculating the intersection area of 3 or more circles
While attempting to learn Javascript and D3.js a couple months ago, I wrote a little library for displaying area proportional venn diagrams .
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Side-stepping the Secretary Problem, unwittingly
Having played both parts in the kabuki play that is employee-employer matchmaking, I feel the way we play it is a zero-sum game. I wish it were not so. When this post started life in 2024, as a wall of text chat message, it was brutal out there, on both sides of the software industry interview table. The ZIRP had…
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Analytic Fog Rendering with Volumetric Primitives (2025)
In this post I’m going to cover a neat technique for rendering regions of fog with varying density. I’ll start by covering some of the basic principles behind fog rendering and a few co…
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Implementing Levenshtein Automata
Thanks to Ken Hironaka for kindly taking a lot of time to read and fix countless errors in this blog post!
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Flattening Quadratic Béziers
Blog of Raph Levien.
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Papers I like (part 2)
Continued from part 1. Once I was about a thousand words into describing background for GEMM, it became pretty clear that it made more sense to group the numerical math papers into one post, so her…
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Mathematically correct but psychologically wrong
The snowball strategy says to pay off your smallest debt first, then the next smallest, and so on until you're out of debt. When I first heard of this I thought it was silly. Clearly the optimal strategy is to pay off the debt with the highest interest rate first. That assessment is mathematically correct,
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Divisibility by 7
How can you tell whether a number is divisible by 7? Almost everyone knows how to easily tell whether a number is divisible by 2, 3, 5, or 9. A few less know tricks for testing divisibility by 4, 6, 8, or 11. But not many people have ever seen a trick for testing divisibility
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P vs. NP for Dummies
A reader named Darren commented on my last post: I have this feeling that this whole P and NP thing is not only a profound problem that needs solving, but something that can be infinitely curious t…
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Jim Hefferon's Linear Algebra: A free textbook with fascinating applications
Random code snippets, projects and musings about software from Eric Kidd, a developer and occasional entrepreneur.
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The New Science of Causation
It seems like each new day brings another one of those headlines: regular sleep “linked to” life expectancy, playing video games “associated with” surgical prowess, bullies “at risk” of becoming criminals, and “does breastfeeding reduce a baby’s blood pressure?” (the old rhetorical question gambit). Sometimes the…
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Update on Deolalikar’s Proof that P≠NP
An update on the P not equal to NP proof Timothy Gowers, Gil Kalai, Ken Regan, Terence Tao, and Suresh Venkatasubramanian are some of the top people who are trying to unravel what is up with the cl…
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Proving P!=NP: "...Ryan has taken the first real baby step in decades."
On October 8th, when in my graduate complexity course as we discussed the 1987 Razborov-Smolensky result that one can't compute the Mod p b...
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Yacc is dead: An update
The draft of " Yacc is Dead " that David Darais and I posted on arXiv received some attention, so we'd like to share updates and feedback.
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SciPy - the embarrassing way to code
I’ve programmed in many languages before, indeed I’ve spent at least a year working in Basic, C, C++, C#, java, assembler, modula-2, powerhouse and prolog. One thing I’ve never done before is Matlab, well except a few basic exercises for some course I did way back. A couple of years ago I started using python and more…
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S. Cook: “This appears to be a relatively serious claim to have solved P vs NP.”
An email I was recently forwarded (a couple of steps removed) from Vinay Deolalikar from HP Labs:
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52 Factorial
They seem harmless enough, 52 thin slices of laminated cardboard with colorful designs printed on their sides. Yet, as another illustration of the mantra that complexity begins from the most simple systems, the number of variations that these 52 cards can produce is virtually endless. The richness of most playing card…
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You Don't Need Math Skills To Be A Good Developer - What About A Great One
Why everyday CRUD work needs little math, but search, machine learning, cryptography and other interesting fields need plenty.
2310
The 17x17 challenge. "Worth $289.00. This is not a joke."
The 17x17 challenge: worth $289.00. I am not kidding. Definition: The n x m grid is c-colorable if there is a way to c-color the vertic...