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The most popular blog posts about math & algorithms on Hacker News. 204 posts.
On my Introduction to A* page I cover the basics of the A* graph search algorithm for finding shortest paths. Here’s an example from the town of Denerim in Dragon Age Origins. Try moving the start and goal to see A* in action:
A complete guide to quantization: how LLMs store parameters as floats, why shrinking them to 4 or 8 bits barely hurts accuracy, and how to measure the tradeoff.
An interactive visualization to understand how neural networks work
The Millennium Prize Problems were unveiled by the Clay Mathematics Institute (CMI) at a meeting in Paris in 2000 to celebrate “The Universality of Mathematical Thought”. These problems encapsulate some of the most difficult challenges that mathematicians were grappling with at the turn of the millennium. CMI’s…
The notorious Jacobian conjecture can be formulated concretely over the complex numbers as follows. Conjecture 1 (Jacobian Conjecture) Let $latex {F:{\bf C}^n \rightarrow {\bf C}^n}&fg=000000$ …
When life gives you switches...
The graph, the viewer, and the verification tooling all live in the WeakC4 repository on GitHub .
Just a brief announcement that I have been working with Quanta Books to publish a short book in popular mathematics entitled “Six Math Essentials”, which will cover six of the fundament…
Some connections between things, which I have not seen elsewhere. Maybe they mean something?
New : You can now watch a recording of my talk on my YouTube channel ! Or you can just click "play" below, I suppose.
There is no need to update symmetric key sizes as part of the post-quantum transition, due to the details of how Grover's algorithm scales. Most authorities agree.
I have been told that when proposing to formalise mathematics these days, you have to explain why you are not using Lean. And that reminds me why I left the dependent-typed world 40 years ago: its cultism, insularity and conformity. Lean is a great language with good tools, a large library and a huge, enthusiastic…
Each mini-demo below covers one concept used later. Skip the ones you already know.
[This is a guest post by Po-Shen Loh, crossposted from his blog, where an illustrated version appears. This blog post was initially written in a different file format and converted using AI. —…
An exotic data structure and a whole lot of JOINs.
[This post has been cross-posted to Terence Tao’s blog.] When I was around 11 I heard for the first time about Fermat’s Last Theorem. I was immediately captivated by the problem stateme…
An unreleased Claude model improved the lower bound for the fraction of zeroes of the Riemann zeta function that satisfy the hypothesis, raising it from 41.6% to 67.2%.
Notes on Chapter 1 of Principia Mathematica
Deep learning has been built around backprop, the only credit assignment algorithm capable of training modern neural nets, including transformer-based language models. Backprop requires differentiability and produces first-order gradients, and deep learning’s architectures, optimizers, and hardware have co-evolved…
Making English more enjoyable to write.
A positive vision for the future of mathematics: how our institutions can deepen human understanding as AI transforms mathematical research.
You can just prove things, apparently.
A range of fast modulus techniques that beat compiler output
The following presents a fast algorithm for volume computation of a simple, closed, triangulated 3D mesh. This assumption is a consequence of the divergence theorem. Further extensions may generalise to other meshes as well, although that is presently out of scope.
For those of you who haven’t seen, there were actually two “bombshell” QC announcements this week. One, from Caltech, including friend-of-the-blog John Preskill, showed how to do quantum faul…
An international team including Oxford physicists has observed a long-predicted effect of gravity on a falling quantum object for the first time. The study provides an experimental connection between quantum physics and Einstein's theory of gravity.
For the sake of anyone who might read this blog post in the distant future (a month from now, say), let me mention that I am writing it a few days after OpenAI announced that it had solved ten majo…
An accidentally fast variable-length integer encoding
every regex engine that promises linear time breaks that promise the moment you ask for all matches. the problem has been there since the 70s, hiding in the iteration loop.
