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Programming in Z3 by learning to think like a compiler
Programming in logic can help you produce better optimized, more secure, bug-free code … if only you knew how to do it.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
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A Random Distribution of Wealth (2017)
W hat happens, if 100 persons in a room are given $100 each and give away a Dollar to one randomly chosen person in this room each tick of the clock? How is wealth distributed over time by pure chance?
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The Unknotting Number Is Not Additive
On June 30, 2025, Mark Brittenham and Susan Hermiller uploaded a preprint to the arXiv called “Unknotting number is not additive under connected sum” (and an updated version on Septembe…
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How does a computer/calculator compute logarithms?
Summer of Math Exposition 3 - How does a computer/calculator compute logarithms?
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My Notes on Apple Math Notes
Apple's effort to improve the UX of math.
1238
Towards λ-calculus
lambdaway is built on a wiki engine, lambdatank, and a small Lisp dialect, lambdatalk.
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Fitting Cubic Bézier Curves
Blog of Raph Levien.
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The 280-Year-Old Algorithm Inside Google Trips
Posted by Bogdan Arsintescu, Software Engineer & Sreenivas Gollapudi, Kostas Kollias, Tamas Sarlos and Andrew Tomkins, Research ScientistsAlgor...
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Fourier Transforms
Fourier Transform
1242
The Federalist Papers: Author Identification Through K-Means Clustering
Using K-means clustering on writing style to classify disputed Federalist Papers authorship.
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210 IQ Is Not Enough
You will never have enough IQ, nor money, nor time, nor energy.
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Hindley-Milner Type Inference (2012)
Robin Milner's type system with parametric polymorphism was a significant advance over the systems of Russell and Church. Arguably it is the ability to use type-variables that makes higher order logic a practical vehicle for proving non-trivial theorems. The Hindley-Milner algorithm is used to automatically infer…
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The secret life of NaN
The floating point standard defines a special value called Not-a-Number (NaN) which is used to represent, well, values that aren’t numbers. Double precision ...
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How random are TOTP codes?
I'm pretty sure that the 2FA codes generated by my bank's TOTP app have a bias towards the number 8 - because eight is an auspicious number. But is that just my stupid meaty brain noticing patterns where none exist? The TOTP algorithm uses HMAC, which in turn uses SHA-1. My aforementioned brain is not clever enough to…
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Linear algebra for game developers – Part 1 (2009)
When I posted about decals last week, a number of readers commented that they would be interested in posts about linear algebra as it…
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Reflected Diffusion Models
Diffusion models are trained to reverse a stochastic process through score matching. However, a lot of diffusion models rely on a small but critical implementation detail called thresholding. Thresholding projects the sampling process to the data support after each discretized diffusion step, stabilizing generation at…
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Swift Numerics
I’m excited to announce a new open-source project for the Swift ecosystem, Swift Numerics! Swift Numerics will provide the building blocks of numerical computing in Swift, as a set of fine-grained modules bundled together into a single Swift package. My hope is that we can quickly fill some important gaps in the…
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Patent 5,893,120 reduced to mathematical formulae
I have previously argued that the Bilski ruling renders all software unpatentable in the US because any method of manipulating information ...
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An Illustrated Guide to Elliptic Curve Cryptography Validation
Cutting-edge cyber security research from NCC Group. Find public reports, technical advisories, analyses, & other novel insights from our global experts.
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Algorithms tutorial series for beginners
As a developer, you have the power to change the world! You can write programs that enable new technologies. For instance, develop software to find an earlier diagnosis of diseases. But that’s not the only way. You might do it indirectly by creating projects that make people more productive and help them free up time…
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We're Knot Friends
It’s April Cools again. For a few summers in high school and undergrad, I was a day camp counselor. I’ve written before about how it helped me develop storytelling skills, but recently I thought of it again because, while I was cleaning out a closet full of old junk, I happened upon a bag of embroidery thread. While…
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The most famous transcendental numbers
The mathematical constant pi represents the ratio of the circumference of a circle to its diameter. It is the most famous ratio in mathematics both on Earth and probably for any advanced civilization in the universe. The number pi, like other fundamental constants of mathematics such as e = 2.718..., is a…
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“I don't know the numbers”: a math puzzle
I saw a math puzzle the other day on Hacker News. It reads as follows: Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told the sum of the numbers, while Peter is told the product of the numbers. Then, this dialog occurs between Sandy and Peter: Peter: I don’t know the numbers…