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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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220,000 cores and counting: largest ever public cloud job
An MIT researcher recently broke the record for the largest ever Compute Engine cluster, with 220,000 cores on Preemptible VMs , the largest known high-performance computing cluster to ever run in the public cloud.
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"The worst algorithm in the world?"
You know the Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … Each number is the sum of the previous two. Let’s say the zeroth Fibonacci number is zero, so: $latex \begin{array}{r@{\…
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Entropy of a Large Language Model output
Large language models like ChatGPT & Claude have become ubiquitous in today’s world. I visited a friend for the New years eve and was impressed by how ChatGPT was being extensively used within the family. The friend’s little kid is going to grow up in a world, where turning to large language models (LLM) for quick…
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Simulating and Visualising the Central Limit Theorem
Update: this post was discussed on Hacker News I completed a Computer Science degree at uni, and bundled a lot of maths subjects in as electives: partial differential equations, vector calculus, discrete maths, linear algebra.
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Modular Manifolds
A geometric framework for co-designing neural net optimizers with manifold constraints.
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Where do those undergraduate divisibility problems come from?
Chris Grossack's math blog and professional website.
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Gradient Descent Models Are Kernel Machines
This paper shows that models which result from gradient descent training (e.g., deep neural nets) can be expressed as a weighted sum of simi...
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Comparing City Street Orientations
This post is adapted from this research paper that you can read/cite for more info. It analyzes and visualizes 100 cities around the world.
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Better Geometry Through Graph Theory (2018)
A few months ago, I decided to implement set operations on curved regions. I had the the canonical textbook on computational geometry , which described approaches for polygons comprised of straight lines, and it seemed like other projects had extended these techniques to parametric curves . I figured it would take a…
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Erdős Problem #1026
Problem 1026 on the Erdős problem web site recently got solved through an interesting combination of existing literature, online collaboration, and AI tools. The purpose of this blog post is to try…
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The Fibonacci Matrix
When you think about the Fibonacci sequence, you probably imagine a swirling vortex of oscillating points stretching outwards to infinity: Okay, no, obviously you don’t. Yet.
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Learning the Integral of a Diffusion Model
A deep dive on flow maps.
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Paxos derived
Lamport's fault-intolerant state machine replication algorithm In 1978, Lamport published his classic "Time, Clocks, and the Ordering of E...
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A primer on Bezier curves
A detailed explanation of Bézier curves, and how to do the many things that we commonly want to do with them.
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A homework question in someone’s 11th grade statistics class
My son is in 11th grade. Below you’ll find a HW question which was given in my son’s statistics class. How would you answer?
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The most common errors in undergraduate mathematics
This page describes the errors that I have seen most frequently in undergraduate mathematics, the likely causes of those errors, and their remedies.
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Diving into the world of hash tables
Diving into the world of Hash Tables and understanding the underlying mechanics is extremely interesting, and very rewarding. So let's get into it and get started from the beginning. They are used commonly in algorithm design.
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A gentle introduction to automated reasoning
Meet Amazon Science’s newest research area.
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Planes in 3D Space
Visual and interactive introduction to 2D planes in 3D space.
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My favourite small hash table
I'm the kind of person who thinks about the design and implementation of hash tables. One design which I find particularly cute, and I think deserves a bit more publicity, is Robin Hood open-addressing with linear probing and power-of-two table size. If you're not familiar with hash table terminology, that might look…
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AI for math resources, and erdosproblems.com
This post contains two unrelated announcements. Firstly, I would like to promote a useful list of resources for AI in Mathematics, that was initiated by Talia Ringer (with the crowdsourced assistan…
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Evaluating a class of infinite sums in closed form
A family of infinite sums that evaluate to rational numbers, sometimes integers, and and effective algorithm for finding the sum.
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