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The most popular blog posts about math & algorithms on Hacker News. 238 posts.
We published our video on zero-knowledge proofs! Surprisingly, making this video took a lot of work. Zero-knowledge proofs for coloring are one of those algorithms that, in hindsight, seem beautifu…
[Updated on 2020-09-03: Updated the algorithm of SARSA and Q-learning so that the difference is more pronounced. [Updated on 2021-09-19: Thanks to 爱吃猫的鱼, we have this post in Chinese].
Collaboratively editing strings of text is a common desire in peer-to-peer applications. For example, a note-taking app might represent each document as a single collaboratively-edited string of text.
Bézier curves are a core building block of text and 2D shapes rendering. There are several approaches to rendering them, but one especially challenging problem, both mathematically and technically, is computing the distance to a Bézier curve. For quadratic curves (one control point), this is fairly accessible, but for…
An explainer for people who don't know computer science and are mildly curious
Posts and writings by Julian Schrittwieser
This is the introduction to a series on Abstract Algebra. In particular, our focus will be on Galois Fields (also known as Finite Fields) and their applications in Computer Science. This is a project I've been excited about for many years now, but have been too busy to dedicate the adequate effort to meet my…
I can't remember where I first saw them, but ever since, I have been unable to forget them: abelian sandpiles. I'm far from the only one . They're remarkably simple, yet produce lovely symmetric patterns. I loved them so much that I adorned the title banner of this blog with an animation of an abelian sandpile. But…
These days, the most common question I get goes something like this: A decade ago, you told people that scalable quantum computing wasn’t imminent. Now, though, you claim it plausibly is immi…
My journey from building cricket bots to building “wind tunnels” with my collaborators — and finding the answer hidden in geometry.
Intel released the powerful Pentium processor in 1993, establishing a long-running brand of high-performance processors. 1 The Pentium incl...
The tools of linear algebra are extremely useful when working in Euclidean space (e.g. \mathbb{R}^3 ). Wouldn’t it be great if we could apply these tools to additional mathematical constructs, such as functions and sequences? Hilbert space allows us to do exactly this - apply linear algebra to functions.
Building on my previous post on sorting algorithms, I implemented the same algorithms using CUDA to explore performance improvements through parallel computing. The goal is to see how we can leverage the power of parallel computing to speed up our sorting algorithms. I went for a NVIDIA recruiting event some days ago…
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.
At the New England Symposium on Graphics , James Tompkin compared graphics researchers to magpies: they're easily distracted by shiny objects and pretty renderings.
Explore Bill Benter’s iconic horse betting strategy, enhanced with modern code and contrasted against three decades of evolving data.
An informal introduction to formality in Lean 4
Crackpots ranging from billionaire Peter Thiel to random YouTube influencers claim that science has been stagnating for the past 50 years. They admit that computing is an exception: they don’t pretend that my personal 32GB laptop is not an advance over the 16MB mainframe that served the whole Caltech community when I…
A new algebraic method for hardware-accelerated bilinear interpolation on convex quadrilaterals is presented, using the Barycentric coordinate feature of modern GPUs.
We’ve learned how to define and apply Monte Carlo integration—fundamentally, it’s the only tool we need. In the remaining chapters, we’ll explore ways to reduce variance and successfully sample difficult distributions.
I have a side project to find the longest line of sight on the planet 1 using a novel Total Viewshed algorithm . At a resolution of 3 arc-seconds (~92m x 92m), the planet contains around 4.5 billion elevation samples 2 . Now obviously we don’t need to calculate the visibility between literally every single one of…
At least a familiarity with the lambda calculus, including how it is evaluated. Some base knowledge of programming languages is also assumed.
Generative Adversarial Networks refer to a family of generative models that seek to discover the underlying distribution behind a certain data generating process. This distribution is discovered through an adversarial competition between a generator and a discriminator. As we saw in an earlier introductory post on…
How a bit of algorithm engineering and low-level details can alter what seems like a straightforward trade-off on a blackboard.
Optimizing a math expression parser for speed and memory.
Exploring the math behind hash collisions.
What's the meaning of "numbers" and "arithmetic operations"? We consult Georg Cantor's turtles and look at Giuseppe Peano's code.
I’ve just uploaded to the arXiv the paper “Decomposing a factorial into large factors”. This paper studies the quantity $latex {t(N)}&fg=000000$, defined as the largest quanti…
The informal definition of an elliptic curve is simple. The formal definition is more involved.
Article explaining simulation algorithms that produce complex organic behaviours, starting with the classic physarum algorithm from Jeff Jones.
