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The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
Web site content explains the modern view of entropy change and the dispersal of energy in a process (at a specific temperature). It has been selected for instructors in general and physical chemistry by Dr. Frank L. Lambert, Professor Emeritus (Chemistry) of Occidental College, Los Angeles.
Can I make math operations run 100x faster on really, really big numbers?
In 2005, id Software released the source code for their 1999 game Quake III Arena under the GPL-2 license. In the file code/game/q_math.c , there is a function for calculating the reciprocal square root of a number which at first glance seems to use a very peculiar algorithm:
A self-contained introduction to Gröbner bases and solving polynomial systems
Yesterday John Graham-Cumming posted about “Steve Ballmer’s incorrect binary search interview question,” and in the Hacker News discussion, among the predictable “interview culture is flawed!!” complaints, there was some discussion of whether binary search was even the right way to solve Ballmer’s puzzle. Here’s a…
You’ve probably played with model trains, for instance with something like the Brio set shown below.1 And if you’ve built a layout with a model train set, yo...
An informal introduction to formality in Lean 4
A few posts back I was concerned with optimising the WiFi reception in my flat, and I chose a simple method for calculating the distribution of electromagnetic intensity. I casually mentioned that I really should be doing things more rigorously by solving the Helmholtz equation, but then didn't. Well, spurred on by a…
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Earlier this year, I asked a question on Stack Overflow about a data structure for loaded dice . Specifically, I was interested in answering this question:
How does the geometry of a road unfold?
Detecting (and correcting) errors in digital signals.
Important new study from Apple
Benchmarks & Tips for Big Data, Hadoop, AWS, Google Cloud, PostgreSQL, Spark, Python & More...
Scientific American writes about rescuing the enormous theorem (classification of finite simple groups) before the proof vanishes. How can...
When Mathematica seems to not to know how to simplify an expression, it may be doing the right thing, being more sophisticated than you expect.
Tauformer is a topological transformer (see paper ) that replaces dot‑product attention with a Laplacian-derived scalar (taumode) per token/head, then attends using distances in that scalar space. Below is a post-style overview of the idea and the first training signals from a 30M-parameter run.
I have suspected for years that the classic buffet line system is a deeply flawed method, so I decide to simulate different methods to find out better ways
I recently learned an interesting fact about Fibonacci numbers while watching a random number theory video on YouTube. Fibonacci numbers can be used to approximately convert from miles to kilometers and back. Here is how. Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No...
Combinatorics is a branch of mathematics that deal with counting of discrete structures. Two concepts that often come up in the study of c...
On April 8, 2020, John Horton Conway developed symptoms of COVID-19. On April 11, 2020, he succumbed to the disease. 1 2 3 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…
Deep neural networks have long been considered too complex to understand from first principles — but new research does just that, presenting a theoretical framework for DNNs.
A blog about signals, programming, music, and other stuff.
If you'd rather read python than english you can go straight to the code on github: https://github.com/jminardi/volume-from-shadow
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Over the past few years, deep learning has been taking by storm many industries. From voice recognition to image analysis and synthesis, neural networks have turned out to be very efficient at solv…
